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ABSTRACT The hydrodynamic disturbance generated by the adult copepod _Euchaeta antarctica_ during cruise swimming is quantified. Kinematic results are compared to previous results reported

for different _Euchaeta_ species. The results reveal a linear relationship between cruise speed and prosome length across _Euchaeta_ species, indicating a size-proportional trend that is

indicative of a complicated interaction of species size and environmental factors such as fluid temperature and viscosity. The detailed fluid flow measurements using the tomographic Particle

Image Velocimetry (tomo-PIV) technique provide insight into copepod cruise propulsion during turning events in comparison to straight motions. During straight swimming, _E. antarctica_

demonstrates streamlined flow patterns and reduced vorticity in the near-body fluid shear layer, which is beneficial for sustained motion and energy conservation. In contrast, turning

maneuvers are characterized by maximum flow velocities reaching 1.5 times greater values than during straight cruising with increased flow field complexity and enhanced vorticity. The

viscous dissipation rate generated in the flow disturbance is also greater during turning events, with the total dissipation rate reaching \(\bf3.5-3.8\times 10^{-8}\) W compared to

\(\bf2.6-2.8\times 10^{-8}\) W during straight cruising. The flow disturbance also generates a hydrodynamic cue that prey may sense in order to avoid the predator _E. antarctica_. For the

adult _E. antarctica_, the hydrodynamic cue extends to a volume that is 11–13 times larger than the copepod exoskeleton volume during the straight swimming motion and 22–25 times larger

during the turn events. SIMILAR CONTENT BEING VIEWED BY OTHERS HYDRODYNAMICS OF THE FAST-START CARIDOID ESCAPE RESPONSE IN ANTARCTIC KRILL, _EUPHAUSIA SUPERBA_ Article Open access 02 April

2023 THE FISH ABILITY TO ACCELERATE AND SUDDENLY TURN IN FAST MANEUVERS Article Open access 23 March 2022 AN INERTIAL MECHANISM BEHIND DYNAMIC STATION HOLDING BY FISH SWINGING IN A VORTEX

STREET Article Open access 25 July 2022 INTRODUCTION _Euchaeta antarctica_ is a calanoid copepod that plays a key role in the ecology of the Southern Ocean, where its collective biomass is

dominant among copepod species1,2. This species acts as a voracious carnivorous predator on other copepod species and serves as food for higher planktivores, therefore serving a critical

role in the food web of the Southern Ocean3. Given the ecological importance, there is significant motivation to improve our understanding of this species, including the biomechanics of its

propulsion and hydrodynamic sensory interactions. Fluid motion in the volume surrounding copepods is key to gaining insight into their biomechanics. Copepods propel themselves through the

water via two distinct behavior modes4,5,6. The first mode is a relatively slow swimming behavior that is often described as “cruising”7. This mode encompasses a range of propulsion

velocities, including a nearly stationary (hovering-like) motion in which copepod appendage stroking induces a laminar feeding current to facilitate suspension feeding, which is effective

for a herbivorous dietary habit8. Increasing the propulsion speed through the water is accomplished by high-frequency stroking of the feeding appendages and the four or five-leg appendage

pairs located along the metasome9. The sequential stroking of the appendages located on the ventral side of the copepod generates propulsive thrust as well as a propulsion jet in the

copepod’s wake. At moderate speeds, this swimming mode is generally related to predatory feeding and a carnivorous dietary habit, as observed in _E. antarctica_3. Variations in this mode may

include cruise-and-sink and hop-and-sink behaviors in which copepods temporally alternate between active upward motion and passive downward sinking4. The second propulsion behavior mode

consists of a high-speed “escape” or “jump”7. Typically, the escape mode is evoked due to an external stimulus, such as the presence of a predator, and is directed away from the stimulus10

or toward prey11,12. This fast mode always involves the rapid stroke of the antennules to induce a quick acceleration, which leads to body and wake vortices13,14. For each swimming mode, the

interaction of the appendages with the surrounding fluid leads to a unique flow pattern15,16,17. Quantifying the fluid motion around copepods is also important for sensory ecology

considerations18,19. Detection of prey and avoidance of predators for many copepods is primarily done via hydrodynamic sensing of fluid disturbances. For instance, hydrodynamic sensing leads

to a size selectivity feeding behavior in the adult female stage of _E. antarctica_3. There is evidence that spatial gradients of fluid velocity, specifically the fluid strain rate, signal

copepods to evoke an escape response to evade predators20,21. Alternatively, for a predator perceiving prey, Kiørboe & Visser20 argue that the fluid velocity magnitude provides the

relevant signal. In either scenario, a pathway to understanding the sensory ability and response is to quantify the fluid flow with high spatial and temporal resolution in order to resolve

the rapidly evolving fluid velocity and spatial gradients of fluid velocity surrounding the copepod. It is presumed that copepods have an advantage of being cryptic to prey to facilitate an

effective attack, as well as an advantage of being cryptic to predators to avoid being detected. With an appreciation for the need to understand and quantify the fluid motion induced by

copepods, the genus _Euchaeta_ presents a fascinating case study. The genus _Euchaeta_ ranges throughout the Earth’s oceans. For instance, _Euchaeta rimana_ inhabits relatively warm tropical

waters22. This species is anatomically similar to other species, such as _Euchaeta norvegica_23 and _E. antarctica_1, that inhabit cooler waters at higher latitudes. While anatomically

similar, there are significant differences among these species that are important considerations for the fluid dynamics of propulsion and hydrodynamic sensing. _Euchaeta rimana_ is a

tropical species with a prosome length of roughly 2.5 mm found in \(23 \,^{\circ }\)C waters22; _Euchaeta elongata_ is a temperate species with a prosome length of roughly 4 mm found at \(8

\, ^{\circ }\)C24,25; _E. norvegica_ is a high latitude species with a prosome length of roughly 6 mm found at \(6 \, ^{\circ }\)C23; and _E. antarctica_ is a polar species with a prosome

length of roughly 9 mm found at \(0 \, ^{\circ }\)C3. Hence, quantitative information about the induced hydrodynamic disturbance provides insights into the effects of body size and fluid

viscosity (which decreases with temperature and increases with latitude) on propulsion and sensory capabilities. Previous studies have quantified the fluid motion surrounding _E. rimana_ and

_E. elongata_26 and the CV stage of _E. antarctica_27. These studies were limited to a single plane that bisected the specimen using the Particle Image Velocimetry (PIV) measurement

technique. Despite being limited to a bisecting plane, the flow measurements provide insight into the cruise and escape swimming modes. For the cruise mode, the quantitative information

provided includes the fluid velocity disturbance, strain rate generated in the surrounding fluid flow, and the total viscous dissipation rate. The results reveal a complex interplay between

body size, fluid viscosity, and spatial extent of the hydrodynamic signal to prey for _E. rimana_ and _E. elongata_. The insights gained are limited by the relatively narrow range of

congener sizes studied, as well as the limitations of the planar measurements around a three-dimensional organism. The objectives of this study are to quantify the hydrodynamic disturbance

surrounding a freely moving adult _E. antarctica_ during cruise swimming mode consisting of forward motion at moderate speed. The tomographic PIV measurement approach quantifies the full

three-dimensional flow field in order to provide unprecedented details about the fluid motion surrounding an adult _E. antarctica_. The results provide insight into the propulsion ability of

_E. antarctica_ through analysis of the generated flow. Of particular interest are the characteristics of the flow disturbance during a turning event. The measurements also facilitate a

comparison of the flow disturbance, vorticity, and strain rate field compared to the smaller _Euchaeta_ congeners. Such a comparison is particularly of interest since Svetlichny et al.7 note

that the scaling of swimming speed and power for propulsion (as a function of the prosome length) deviates for _Euchaeta_ species compared to other copepods, perhaps due to the effects of

varying fluid temperature and viscosity. MATERIALS AND METHODS _Euchaeta antarctica_ individuals were collected from Palmer Deep (\(64^{\circ }57^\prime\)S, \(64^{\circ }24^\prime\)W) in the

Southern Ocean on-board RV Laurence M. Gould. After collection, animals were held in large buckets of seawater with a salinity of 34.6 parts per thousand (ppt), stored at \(0^\circ\)C, and

transported to the cold room in Palmer Station (Anvers Island, Antarctica; \(64^{\circ }46^\prime\)S, \(64^{\circ }03^\prime\)W). Measurements were performed within the two weeks since

capture, although the copepods can live for over 3 months in the laboratory. Seawater was obtained from the coastal ocean waters near Palmer Station, filtered, and placed in a glass test

tank (10\(\times\)10\(\times\)12 cm, W\(\times\)D\(\times\)H). The test tank was filled to a height of 10 cm. Within this controlled environment maintained at \(0^\circ\)C, _E. antarctica_

specimens were permitted to swim freely, ensuring natural behavior and accurate representation of their swimming dynamics. High-speed tomographic Particle Image Velocimetry (tomo-PIV) was

used to measure the volumetric velocity field14,28. For illumination, two 7 W continuous-wave infrared lasers (CrystaLaser, Inc.) operating at a wavelength of 808 nm were utilized, which is

important to avoid copepod photo-response that happens for illumination in the optical wavelengths27. The lasers are strategically placed on either side of the tank to prevent “shadowing” by

the _E. antarctica_ specimen (shown in Fig. 1a). The lasers created overlapping illumination volumes, thereby ensuring comprehensive coverage surrounding the specimen. The measurement

region, illuminated with the lasers, had a length (_x_-axis), height (_y_-axis) and thickness (_z_-axis) of 32, 19 and 13 mm, respectively. Four high-speed cameras (Vision Research Inc.

Phantom v210; 1280\(\times\)800 pixels) were mounted on three-axis geared heads (Manfrotto 400) and synchronized to record at 200 fps. The cameras were angled at approximately \(30^{\circ

}\) to the _z_-axis and aimed at the measurement volume (Fig. 1a). Each camera was fitted with a Scheimpflug mount to correct for off-axis optical distortion and a 105 mm lens (Nikon

Micro-NIKKOR). The test tank was seeded with 20 \(\upmu\)m polyamide tracer particles (Orgasol 2002 D NAT 1; Arkema Group) to scatter the infrared illumination without affecting the

copepods. The particles are nearly neutrally-buoyant (1.03 g \(\hbox {cm}^{-3}\)) and accurately move with the surrounding fluid. Processing of the tomo-PIV images was performed using the

DaVis 8.4 software package (LaVision GmbH). A calibration plate was traversed to six positions along the _z_-axis and provided calibration images for a preliminary mapping function. A

self-calibration procedure corrected the mapping function for all cameras, thereby reducing calibration errors29. The visual hull method was employed as a mask to eliminate the appearance of

the _E. antarctica_ specimen within the reconstructed volume28,30. Automating the image processing sequence to detect the silhouette of the _E. antarctica_ specimen in the individual images

streamlined the labor-intensive manual tracing used in prior studies28. A series of image filtering operations shown in Fig. 1b, including median and standard deviation filters, were

applied to enhance the edge contrast, followed by applying the Canny edge detection method. Morphological operations, including dilation and erosion, were then used to refine the silhouette,

effectively masking out noisy reconstructions near the organism’s body. This processing sequence was applied to the four simultaneous images, and a MLOS algorithm in DaVis 8.4 was employed

to obtain a three-dimensional visual hull, which is shown in Fig. 1c. Following the visual hull masking operation, particle intensity volumes were reconstructed using the MLOS-CSMART

algorithm in DaVis 8.4, resulting in a measurement volume of -16 mm \(<x<\) 16 mm, -7 mm \(< y<\) 12 mm, and 0.5 mm \(< z<\) 13.5 mm. The volume of velocity vectors was

calculated by cross-correlating reconstructed volume pairs separated by \(\Delta t = 5\) ms. The interrogation volume was 32 \(\times\) 32 \(\times\) 32 voxels, with a 75% overlap resulting

in volumetric fields with a vector grid spacing of 0.21 mm. The velocity measurement uncertainty was estimated to be 0.7 mm \(\hbox {s}^{-1}\). _Euchaeta antarctica_ kinematics were computed

using the average of the three-dimensional locations of the points along the forepart of the head of the specimen (i.e., the rostrum) calculated from the visual hull analysis. From the

tomo-PIV velocity measurements, the vorticity (\(\omega\)) was calculated using $$\begin{aligned} \begin{bmatrix} \omega _x=\frac{1}{2}(\frac{du_z}{dy}-\frac{du_y}{dz}) \\ \omega

_y=\frac{1}{2}(\frac{du_x}{dz}-\frac{du_z}{dx}) \\ \omega _z=\frac{1}{2}(\frac{du_y}{dx}-\frac{du_x}{dy}) \end{bmatrix} \end{aligned}$$ (1) where \(u_x\), \(u_y\), and \(u_z\) are the

velocity components in the _x_, _y_, and _z_ directions, respectively, and derivatives were calculated via central finite difference. Previous research indicates that predators/prey

interactions are mediated by velocity difference within the surrounding flow field10,20,31. Fluid strain rate, which can be separated into normal and shear components, quantifies the rate of

deformation of material elements in the fluid motion. Notably, a copepod or other prey may not be aligned with the coordinate system when they detect fluid disturbances created by the

predator (_E. antarctica_ in this case), which presents a challenge in accurately quantifying the potential sensory cue created by the predator. To overcome this, the maximum strain rate

(\(E_{max}\)) is utilized, which provides a coordinate-independent measure of hydrodynamic disturbances. This metric is calculated by extracting the eigenvalues from the strain rate tensor,

with \(E_{max}\) defined as the largest absolute value along the tensor’s principal axes26. This approach effectively decouples the orientation of the prey from the orientation of the _E.

antartica_ and the corresponding flow disturbance. The strain rate tensor (\({\mathop {e}\limits ^\rightrightarrows }\)) components were directly calculated using the measured volumetric

velocity fields (in the coordinate system of the measurement volume): $$\begin{aligned} \begin{bmatrix} e_{xx}=\frac{du_x}{dx} & e_{xy}=\frac{1}{2}(\frac{du_x}{dy}+\frac{du_y}{dx}) &

e_{xz}=\frac{1}{2}(\frac{du_z}{dx}+\frac{du_x}{dz}) \\ e_{yx}=e_{xy} & e_{yy}=\frac{du_y}{dy} & e_{yz}=\frac{1}{2}(\frac{du_z}{dy}+\frac{du_y}{dz}) \\ e_{zx}=e_{xz} &

e_{zy}=e_{yz} & e_{zz}=\frac{du_z}{dz} \end{bmatrix} \end{aligned}$$ (2) and the eigenvalues, \(\lambda\), were determined by $$\begin{aligned} det({\mathop {e}\limits ^\rightrightarrows

}-\lambda {\mathop {I}\limits ^\rightrightarrows })=0, \end{aligned}$$ (3) where \({\mathop {I}\limits ^\rightrightarrows }\) is the identity matrix and _det_ indicates the determinant

operation for the tensor. This calculation yields three root values for \(\lambda\) that correspond to the eigenvalues (i.e., \(\lambda _1,\lambda _2,\lambda _3\)) of the strain rate tensor.

The maximum strain rate, then, is the maximum absolute value of the eigenvalues (i.e., the magnitude of the strain rate along the principal axes) of the strain rate tensor:

$$\begin{aligned} E_{max}=max(|\lambda _1|,|\lambda _2|,|\lambda _3|). \end{aligned}$$ (4) The purpose and advantage of presenting the strain rate measurements in this framework is to

eliminate the arbitrary orientation of the coordinate system, which is aligned with neither the copepod nor the potential prey or predator. The dissipation rate of kinetic energy due to

viscosity, \(\Psi\), is also of interest because it provides a measure of the mechanical cost of propulsion through the viscous fluid. Further, a larger dissipation rate indicates that fluid

velocity gradients are smoothed more rapidly, hence reducing the period that the flow disturbance may persist and be sensed in a predator/prey context. The viscous dissipation rate is

another quantity calculated from the spatial gradients of the fluid velocity field: $$\begin{aligned} \Psi =\mu \Biggl [2\Bigl [(\frac{\partial u_x}{\partial x})^2+(\frac{\partial

u_y}{\partial y})^2+(\frac{\partial u_z}{\partial z})^2\Bigr ]+(\frac{\partial u_x}{\partial y}+\frac{\partial u_y}{\partial x})^2+(\frac{\partial u_x}{\partial z}+\frac{\partial

u_z}{\partial x})^2+(\frac{\partial u_y}{\partial z}+\frac{\partial u_z}{\partial y})^2\Biggr ], \end{aligned}$$ (5) where \(\mu\) is the fluid dynamic viscosity. An additional advantage of

the current tomo-PIV measurements is that each of these gradients may be calculated directly from the volumetric velocity field (again performed via central finite difference). RESULTS

COPEPOD KINEMATICS A three-dimensional trajectory of an adult _E. antarctica_ during cruise swimming is depicted in Fig. 2a,b, with colors representing the swimming speed. This trajectory

was selected as a typical example of the recorded swimming behavior of _E. antarctica_ and additionally corresponded to a recording with excellent optical access around the specimen for

subsequent tomo-PIV analysis of the surrounding fluid motion. The trajectory points specifically correspond to the forepart of the head (the rostrum). The trajectory covers a distance of

roughly 25 mm and has a duration of roughly one second. This visualization captures the intricate movement patterns, emphasizing the organism’s ability to maneuver with a high degree of

control in an aquatic environment. The trajectory includes two turns that are each followed by straight cruise swimming motions. Turning angle is defined as the angular change measured

between the direction of two consecutive segments of the swimming trajectory. The time record of the turning angle (Fig. 2c) reveals two sharp peaks that correspond to rapid changes in the

trajectory heading. The time record of the speed of the organism (Fig. 2d) varies in a manner that appears to be correlated with the turning angle. The copepod demonstrates elevated speed at

roughly the same time points as the turning events, suggesting that the organism increases its propulsion thrust as it changes direction. The stroke frequency of the cephalic appendages

that generate propulsive thrust varies in a manner that is consistent with these behaviors, as well. During the straight trajectory motion, the stroke frequency is 20 Hz, whereas during the

higher-speed turning events, the stroke frequency is 34 Hz. Figure 3 compares the swimming speed measured for nine adult _E. antarctica_ specimens (during straight swimming) in this study to

previous measurements of speed during cruise swimming for the genus _Euchaeta_. The plot shows a clear correlation between prosome length and swimming speed, indicating that larger

specimens of the genus _Euchaeta_ cruise faster than their smaller counterparts. The error bars associated with each data point correspond to the standard error in order to report the

variation in length and speed of the specimens measured. The specimen for the presented flow field analysis in this study has a prosome length of 8.3 mm. FLOW FIELDS Figure 4 presents the

magnitude of the fluid velocity (\(|V|=\sqrt{u_x^2+u_y^2+u_z^2}\)) on the mid-plane (relative to the animal body position in the _z_-direction) of the swimming _E. antarctica_ captured at

four distinct time points: initial acceleration/turn, straight motion, second acceleration/turn, and second straight motion. The images reveal dynamic changes in the flow field as the

organism maneuvers through the water. During the first turn and acceleration event (Fig. 4a), a high-velocity region is observed on each side of the organism in the \(x-y\) plane, indicative

of the powerful thrust generation required to accelerate and turn. During the straight cruising period (Fig. 4b), the fluid velocity around the organism is relatively smaller in magnitude

and more spatially uniform, suggesting a balance between thrust and drag forces allowing for efficient sustained movement. This time point (\(t = 0.4\) s) demonstrates the ability of _E.

antarctica_ to maintain a streamlined body position to minimize resistance and optimize forward propulsion. The next time point (\(t = 0.68\) s) captures a second turn/acceleration event

(Fig. 4c), in which the regions of large fluid velocity near the tail of the organism result from the significant tail and appendage movements involved in rapid directional changes. Finally,

the second straight motion (Fig. 4d) is characterized by a significant decrease in the fluid velocity around and especially behind the organism, signifying a return to balanced thrust and

drag forces after the turn. Figure 5 reports transverse profiles of fluid velocity on the mid-plane (relative to the animal’s body position in the \(z\)-direction) at the same time points as

Figure 4. The coordinate system (\(x'-y'\)) is rotated to align with the copepod’s central axis, allowing for examination of the flow patterns relative to the organism’s body

orientation, as labeled in Fig. 5b. Two velocity profiles, \(u_{x'}\) and \(u_{y'}\), which report the fluid motion perpendicular and parallel to the copepod’s body axis,

respectively, are shown. It should be noted that \(u_{z'}\) is consistently near zero due to the alignment of the axes with the organism. Each profile in Fig. 5 corresponds to the

\(y'\) location at the base of the prosome. The velocity profiles in Fig. 5a, c correspond to time points during the turn/acceleration motions and display elevated fluid velocity due to

the organism’s active maneuvering. During each counter-clockwise turning motion (in the \(x-y\) plane) at \(t=0.1\) s (Fig. 5a) and \(t=0.68\) s (Fig. 5c), \(u_{x'}\) is negative close

to the organism, indicating a strong flow toward the left in the inset field plots, due to the turning motion. This indicates leftward movement of the tail, consistent with the organism’s

counter-clockwise turn. In contrast, during the straight copepod trajectory segments at \(t=0.4\) s (Fig. 5b) and \(t=1\) s (Fig. 5d), the \(u_{x'}\) profiles are fairly flat and near

zero, reflecting a more streamlined flow pattern during straight swimming motion. Additionally, the peak magnitude in the fluid velocity parallel to the copepod body axis, \(u_{y'}\),

is roughly 1.5 times larger during turning events compared to the straight motion periods (i.e., the peak velocity magnitude is near 30 mm \(\hbox {s}^{-1}\) in Fig. 5a, c compared to near

20 mm \(\hbox {s}^{-1}\) in Fig. 5b, d. This highlights the increased induced flow, which is connected to enhanced thrust force generation during the turn and acceleration events. The fluid

vorticity (_z_-component) around swimming _E. antarctica_ is depicted and analyzed in Figs. 6, 7, and 8. Given that the animal exhibits two counter-clockwise turns in the \(x\)-\(y\) plane,

the \(z\)-component of vorticity (\(\omega _z\)) is particularly relevant to examine the shear layers along the side of the copepod. Figure 6 presents iso-surfaces of positive (red) and

negative (blue) regions of the _z_-component of vorticity, highlighting the generation and evolution of vorticity as the copepod maneuvers through the water. At the time point of the first

turn/acceleration event (Fig. 6a), the iso-surfaces reveal volumes of elevated vorticity that are convoluted and disordered in spatial arrangement. The volumes of elevated vorticity are more

coherent and organized during the second turn/acceleration event (Fig. 6c), but the volumes of elevated vorticity are large (consistent with Fig. 6a) due to the strong shear layers along

the side of copepod. During the straight trajectory periods (Fig. 6b, d), coherent volumes of positive and negative vorticity appear along the sides of the copepod due to the flow shear on

the left and right sides of the organism. Figure 7 shows the _z_-component of vorticity overlaid with velocity vectors on the midplane (relative to the animal body position in the

_z_-direction). During the turn/acceleration events, the distribution of vorticity in the midplane is marked by intense regions of both positive and negative vorticity, reflecting the

dynamic changes in the fluid flow as the copepod redirects its path (Fig. 7a, c). In contrast, the straight swimming phases exhibit weaker regions of vorticity on either side of the copepod

(Fig. 7b, d). In these cases, the velocity vector field reveals a streamlined flow pattern along the sides of the organism, which are highlighted by the relatively modest vorticity regions

in the shear layers. The peak values of vorticity during the turn/acceleration events are around 30 \(\hbox {s}^{-1}\) and -25 \(\hbox {s}^{-1}\), which is approximately 1.67 to 2 times

larger than the peak values during the straight motions at around ± 15 \(\hbox {s}^{-1}\). Figure 8 provides a temporal record of the magnitude of the total (i.e., volume integrated) values

of positive and negative _z_-component of vorticity. The time records provide an integrated view of the copepod’s influence on its fluid environment at each time point in the trajectory. The

time records for positive and negative vorticity are near mirrors of each other, with peaks and troughs of the absolute value occurring during the same time segments. The total vorticity

exhibits two peaks corresponding to the turns with subsequent troughs during straight swimming, reflecting the alternating dynamics between high-energy maneuvers during turn/acceleration

events and less energetic motions during straight cruise swimming. Figure 9 provides a detailed view of the largest components of the fluid strain rate tensor (\(e_{xy}\) and \(e_{yy}\)) on

the midplane (relative to the animal body position in the _z_-direction) at two time points. Figure 9a, c display the shear strain rate component (\(e_{xy}\)) during the second

turn/acceleration event and a straight swimming motion, respectively. At \(t=0.68\) s (Fig. 9a), elevated regions of shear strain rate adjacent to the organism are observed. These elevated

levels of \(e_{xy}\) correspond with the active turning maneuver and suggest significant fluid deformation due to the copepod’s rapid directional change and increase in swimming speed. In

the subsequent straight swimming phase at \(t=1\) s (Fig. 9c), the shear strain rate appears relatively less intense around the copepod. Figure 9b, d show the normal strain rate component

(\(e_{yy}\)), which can be associated with extension or compression in the flow. During the second turn/acceleration event at \(t=0.68\) s (Fig. 9b), there is a clear asymmetry in intense

regions of \(e_{yy}\) on opposite sides of the copepod body that suggest the flow is being compressed on one side and extended on the other. At \(t=1\) s (Fig. 9d), the normal strain rate is

relatively smaller in magnitude, consistent with a streamlined flow pattern that would be expected when the copepod is swimming in a straight trajectory path. DISCUSSION The present study,

with its unique approach, quantitatively assesses the hydrodynamic disturbances generated by adult _E. antarctica_ during cruise swimming in straight and turning motions. This study offers

fresh and intriguing insights into the locomotion and ecological interactions of _E. antarctica_ in the Southern Ocean. In broad terms, the current volumetric tomo-PIV data confirm an

intricate interaction between the adult _E. antarctica_ and the surrounding fluid motion during cruise swimming, which is consistent with observations of other copepod species18,26,27,32.

CRUISE SPEED AND KINEMATICS The linear regression between cruise speed and prosome length (shown in Fig. 3) reveals a seemingly simple relationship. The relationship suggests that cruise

swimming in _Euchaeta_ follows a size-proportionality trend and that cruise velocity in _Euchaeta_ can be reliably estimated from prosome length. Drag forces typically scale on area, i.e.,

projected area for form drag and surface area for shear drag, hence implying an expected non-linear relationship with prosome length. Indeed, Svetlichny et al.7 found that over a wide range

of copepod species, the cruise speed scales with prosome length to the power of 1.4 (for copepods with prosome length less than 4 mm). In the case of _Euchaeta_ presented here, the complex

interaction of size, temperature, and fluid viscosity combined with similar morphology across species size leads to the observed linear relationship. Based on the current recordings, _E.

antarctica_ increases the beat frequency of its cephalic appendages to increase its cruise swimming speed. Appendage beat frequency data are unavailable for the smaller _Euchaeta_ species

for comparison, but the current data agree well with the trend reported by Svetlichny et al.7 over a wide range of copepod species for frequency as a function of prosome length (again noting

that their data are for prosome length less than 4 mm, which is much smaller than _E. antarctica_). Water temperature also varies across prosome length for the _Euchaeta_ genus since the

species size increases with latitude. Fluid viscosity increases as the temperature decreases; hence, the larger _E. antarctica_ specimens are moving through an enhanced viscous environment

(i.e., kinematic viscosity is \(\nu = 1.8\)\(\hbox {mm}^2\)\(\hbox {s}^{-1}\) for high latitude seawater at \(0^\circ\)C, whereas \(\nu = 1.0\)\(\hbox {mm}^2\)\(\hbox {s}^{-1}\) for tropical

latitudes at \(23^\circ\)C). Despite the variation in viscosity, the size-proportional trend during cruise swimming dominates the balance of inertial effects compared to viscous effects, as

quantified by the Reynolds number (_Re_). Since the length and velocity scales appear in the numerator of the _Re_ formulation (i.e., \(Re=UL/\nu\)), _Re_ is larger for the larger species

that are moving faster. The fluid viscosity varies inversely with temperature, but the changes are relatively modest compared to the changes in length and velocity. _Re_ for the adult _E.

antarctica_ reported here is roughly 145. For comparison, the \(Re =17\) value for _E. rimana_, at the smaller end of the size range, is roughly an order of magnitude smaller. Hence,

_Euchaeta_ clearly does not follow dynamic similarity (i.e., maintaining constant _Re_) across congeners. Nevertheless, each species swims in an intermediate _Re_ number range in which

inertial and viscous effects each play an influencing role, leading to a compromise of the effects of body size, fluid viscosity, and swimming speed. The linear relationship of swimming

speed and prosome length also suggests a potential adaptation to the thermal conditions of their environment, where larger organisms within this genus may have enhanced appendage stroking

efficiency or greater muscle power to achieve greater speeds. Further, larger body sizes and faster cruising speeds may confer advantages in colder habitats, such as enhanced metabolic

efficiency or improved predation26. FLOW DISTURBANCE The detailed velocity measurements show a strong flow disturbance surrounding the cruising adult _E. antarctica_. The fluid velocity is

elevated in the region adjacent to the organism, with the elevated fluid velocity region extending 2-4 mm from the copepod body. The observed fluid velocity peaks at approximately 21-23 mm

\(\hbox {s}^{-1}\) during straight cruising - a sharp increase from the 12 mm \(\hbox {s}^{-1}\) recorded for _E. antarctica_ CV27. The peak fluid velocity is also smaller for the smaller

species _E. elongata_ (10 mm \(\hbox {s}^{-1}\)) and _E. rimana_ (7.5 mm \(\hbox {s}^{-1}\)), as reported by Catton et al.26. Clearly, the larger fluid velocity corresponds to the elevated

swimming speed for the larger _E. antarctica_ adult. The velocity decreases rapidly with distance from the copepod, creating an intense shear layer (Fig. 5). The enhanced vorticity regions

observed along the sides of the copepod correspond to the shear layers (as seen in Figs. 6 and 7). A similar pattern of vorticity distribution was quantified in the 2D measurements for _E.

antarctica_ CV in Catton et al.27, with patches of opposite sign vorticity located along the sides of the copepod. The magnitude of the peak value of vorticity is similar, with roughly 20

\(\hbox {s}^{-1}\) for _E. antarctica_ CV27, 15 \(\hbox {s}^{-1}\) for straight swimming, and 25-30 \(\hbox {s}^{-1}\) during turn/acceleration events for the adult. It is also clear that

the spatial extent of the regions of elevated vorticity is much larger for the adult specimen compared to the CV, which, of course, relates to their relative body sizes. As noted above,

cruise speed and fluid velocity are larger for the adult. Hence, the combination of a larger change in fluid velocity across the shear layer occurring over a greater spatial distance (due to

the size-proportional trend) yields similar velocity gradient magnitudes and, hence, similar vorticity values in the shear layers. The detailed fluid velocity measurements reveal a

remarkable contrast between straight cruising motion and turn/acceleration events. The two prominent peaks observed in the time record of turning angle correspond to major directional

changes. These events suggest that _E. antarctica_ can quickly alter its course, potentially as a predator evasion strategy or while pursuing prey. The copepod performed the

turn/acceleration events at elevated swimming speed (Fig. 3). Consistently, the copepod increased the beat frequency of its cephalic appendages to achieve elevated swimming speed. The peak

fluid velocity near the organism correspondingly increases to 31-33 mm \(\hbox {s}^{-1}\) during the turn/acceleration events, which is approximately 1.5 times greater than the fluid

velocity during straight swimming. During periods of straight cruise swimming, the fluid motion follows a streamlined pattern in the dorso-ventral view (most clearly seen in Fig. 7 (_b_) and

(_d_)), which is familiar based on lower-resolution 2D measurements surrounding other copepods15,26,27,33. However, during turns, the flow field undergoes a significant, tail-induced

distortion where the location of maximum fluid velocity shifts from the appendage region to near the tail (most clearly seen in Fig. 4 (_a_) and (_c_)). The shear layer intensity also

increases during the turn/acceleration events, which is most clearly identified in the time records of the volume-integrated vorticity (z-component) where the magnitude in each shear layer

is elevated during the turn/acceleration events (Fig. 8). These time records reveal symmetry between the left and right shear layers during straight motion, but a small imbalance between

positive and negative vorticity was observed during turns. Such rapid turn maneuvers reveal the ability for swift directional changes, which may serve multiple ecological functions,

including re-positioning relative to environmental flow structure, increasing encounter rates with prey, or minimizing exposure to predators. The difference in total z-component of vorticity

between the two periods of straight cruise swimming can be attributed to the residual vorticity generated during the preceding turning maneuvers. The first turn produces stronger vorticity

structures, which persist into the first straight segment, resulting in higher total vorticity. By contrast, the second turning event induces weaker vorticity, and therefore the vorticity

decreases more rapidly during the second straight motion, leading to lower overall vorticity levels. The peak values and asymmetry in vorticity during turns in _E. antarctica_ are similarly

observed in turns of other aquatic organisms. Studies have shown that fish (at much larger _Re_) generate complex wake patterns with enhanced vorticity during turns compared to swimming in a

straight motion, which is attributed to the lateral forces exerted by their bodies and fins to create stronger vortical structures for rapid directional changes34,35,36. Moreover, the

slight imbalance between positive and negative vorticity observed along the shear layers of _E. antarctica_ during turns, compared to the balanced vorticity pattern during straight swimming,

reflects the use of body movement to facilitate swift directional changes (Fig. 8). This concept was also observed by Dabiri et al.37, who reported that jellyfish and zebrafish create

asymmetrical vorticity regions and pressure gradients as a result of their body motion to assist in turning. For the adult _E. antarctica_, the peak value of viscous dissipation rate

observed is 52 W \(\hbox {m}^{-3}\) during the straight swimming period and 76 W \(\hbox {m}^{-3}\) during the turn/acceleration events, which is roughly twice the peak calculated by Catton

et al.27 for the _E. antarctica_ CV (28-30 W \(\hbox {m}^{-3}\), based on estimates from 2D data). The dissipation rate field may be integrated over the fluid volume to determine the total

rate of energy dissipated in the flow disturbance. During straight swimming periods, the current data yield a total dissipation rate of 2.6-2.8\({\times }10^{-8}\) W. Resulting from the

enhanced swimming speed and elevated fluid velocity during the turn/acceleration events, the total dissipation rate increases to 3.5-3.8\({\times }10^{-8}\) W. Despite not having full

volumetric data (which required estimates for both the velocity gradient calculations and the volume integration step), Catton et al.27 reported the total dissipation for the _E. antarctica_

CV as 1.0\({\times }10^{-8}\) W. It is fascinating that the total dissipation rates differ by only a factor of 2.6 to 3.8 between the adult and CV _E. antarctica_ despite the large

differences in swimming speed and size (which potentially influences volumetric quantities as a cubed function). As related to the discussion above for the vorticity field, the compensation

of the velocity gradients is part of the explanation (i.e., a larger velocity difference over a larger distance yields a similar gradient). There is also a substantial difference in the

volume of the integration, which likely contributes to the larger total dissipation rate for the adult specimen. As another comparison point, Yen et al.15 reported a total dissipation rate

for _E. rimana_ of 9.3\({\times }10^{-10}\) W. While this value is more than an order of magnitude smaller than the values reported above, there are significant caveats that the copepod

specimen was described in the study as “stationary”, and their particle tracking data were very low resolution and also necessitated assumptions and estimates to calculate the total

dissipation rate from the 2D field. HYDRODYNAMICAL SIGNALING The fluid strain rate is an important signal for prey to avoid predators, such as _Euchaeta_, as prey will respond with an

escape20,21. As described above, the flow disturbance generated by the adult _E. antarctica_ is considerable in strength and spatial extent. The shear strain rate (\(e_{xy}\)) reveals a

similar spatial pattern in the shear layers as previously discussed for vorticity. Specifically, regions of different-signed elevated shear strain rate appear along the sides of the copepod

in the dorsal-ventral view (Fig. 9 (_a_) and (_c_)). Further, the normal strain rate component during the turn/acceleration event reveals an intense asymmetric spatial pattern with

compression and extension on the opposite sides of the copepod (Fig. 9 (_b_)), which could influence the copepod’s perception of its three-dimensional environment, affecting how it navigates

and responds to external stimuli. For each strain rate component, the strength is greater during the turn/acceleration events (peak of 21 \(\hbox {s}^{-1}\)) compared to the periods of

straight swimming motion (peak of 11 \(\hbox {s}^{-1}\)) in which the copepod appears to minimize the flow disturbance, likely to maintain energy efficiency and perhaps to reduce

hydrodynamic signals that could alert predators or prey. The elevated intensity during the turn/acceleration events is consistent with other flow characteristics discussed above. As a

comparison point, Catton et al.27 reported a peak value for the normal strain rate component of 10 \(\hbox {s}^{-1}\) for _E. antarctica_ CV, which is remarkably consistent in magnitude with

the results for straight cruising reported in the current data. Although not reported explicitly in the paper, the data in Catton et al.26 yield a peak for \(E_{max}\) of 9 \(\hbox

{s}^{-1}\) for _E. elongata_ and 10 \(\hbox {s}^{-1}\) for _E. rimana_, which is also remarkably consistent with the adult (in straight cruising) and CV _E. antarctica_. Again, the

relatively modest differences in the peak strain rate values, despite the technical limitations of previous data, are explained by the velocity gradients remaining relatively constant due to

the specimens following a size-proportional trend, as discussed above. As noted by Catton et al.27, the volume surrounding a predatory copepod that exceeds a critical strain rate threshold

is much larger than the copepod exoskeleton, hence increasing the predator’s conspicuousness to potential prey (that are sensitive to hydrodynamic cues). Catton et al.27 employed the 0.5

\(\hbox {s}^{-1}\) contour for strain rate to represent a typical threshold to induce an escape. Based on planar PIV measurements, the 0.5 \(\hbox {s}^{-1}\) contour area in the

dorso-ventral view extends to 11 times the exoskeletal form of the _E. antarctica_ CV. The current data facilitate consideration of the total volume of the flow disturbance and potential

sensory cue. Figure 10 presents the iso-surface for the same sensory threshold level of \(E_{max} = 0.5\)\(\hbox {s}^{-1}\). The size of the iso-surface highlights the extensive region

surrounding the copepod that may present a hydrodynamic cue to potential prey. The figure panels report the total volume enclosed by the iso-surface. Note that these estimates may be

slightly under-valued since the iso-surface extends to the measurement domain boundary, hence clipping the volume calculation. The visual hull volume may be used as a surrogate for the

volume of the copepod exoskeleton. Hence, the volume enclosed by the \(E_{max} = 0.5\)\(\hbox {s}^{-1}\) iso-contour is 11-13 times the copepod exoskeleton volume during the straight

swimming motion and 22-25 times during the turn/acceleration events. It is impractical to compare the planar measurements described above quantitatively, but each set of measurements

confirms the large spatial extent of the hydrodynamic cue. CONCLUSION This study comprehensively analyzes the hydrodynamic characteristics surrounding adult _E. antarctica_ during straight

cruise swimming and turn/acceleration motions utilizing the tomo-PIV technique. The comparative analysis between straight swimming and turn/acceleration motions in adult _E. antarctica_

demonstrates an ability to alter its course rapidly. During straight swimming, the fluid velocity field is characterized by a streamlined flow pattern with fluid shear layers on each side of

the copepod for efficiency beneficial for sustained propulsion and energy conservation. In contrast, turn/acceleration maneuvers exhibit a dramatic increase in the complexity of the fluid

velocity and vorticity fields, indicative of the rapid, directional change. The turn/acceleration events also demonstrate a period of heightened viscous dissipation rate, thus revealing an

added cost of propulsion to generate the higher-speed turns. These maneuvers generate significant hydrodynamic disturbances; notably, a sharp increase in strain rate during the

turn/acceleration events suggests increased conspicuousness during rapid turns. This contrast in hydrodynamic cue signatures between straight cruising and turn/acceleration maneuvering

highlights the dual demands of population efficiency and survival agility faced by _E. antarctica_ in the challenging Southern Ocean ecosystem. Such insights reveal the intricate

interactions between morphology, behavior, and the environment. The study also provides a comparative perspective across different species of the _Euchaeta_ genus. Larger species like _E.

antarctica_ exhibit larger cruising speeds compared to their smaller counterparts such as _E. rimana_ and _E. elongata_, reflecting a size-proportional trend in organism swimming speed and

flow velocity. Despite variations in body size and environmental temperature, the fluid velocity gradient quantities, such as vorticity and shear strain rate, remain relatively consistent

across species. This consistency is connected to the linear relationship found between prosome length and swimming speeds among different _Euchaeta_ species during cruising, and the

size-proportional trend ultimately dictates effective propulsion and sensory interactions across different ecological niches. DATA AVAILABILITY The data used and analyzed during the current

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maneuverability. _Fluids. _5, 106. https://doi.org/10.3390/fluids5030106 (2020). Article  ADS  CAS  Google Scholar  Download references ACKNOWLEDGEMENTS We thank the United States Antarctic

Program for their support on RV Laurence M. Gould and at Palmer Station, Antarctica, that made the data acquisition possible. Special thanks to Jeannette Yen for collecting the copepod

specimens and to Deepak Adhikari for collecting the raw images. This work was supported by National Science Foundation grant PLR-1246296 and the Karen and John Huff Chair endowment. AUTHOR

INFORMATION AUTHORS AND AFFILIATIONS * School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0355, USA Mohammad Mohaghar & Donald R. Webster

Authors * Mohammad Mohaghar View author publications You can also search for this author inPubMed Google Scholar * Donald R. Webster View author publications You can also search for this

author inPubMed Google Scholar CONTRIBUTIONS M.M. and D.R.W. conceived and designed the study. M.M. processed and analyzed the data. M.M. and D.R.W. interpreted the data and wrote the

manuscript. All authors reviewed the manuscript. CORRESPONDING AUTHOR Correspondence to Mohammad Mohaghar. ADDITIONAL INFORMATION PUBLISHER’S NOTE Springer Nature remains neutral with regard

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in _Euchaeta antarctica_. _Sci Rep_ 14, 28217 (2024). https://doi.org/10.1038/s41598-024-76439-1 Download citation * Received: 24 July 2024 * Accepted: 14 October 2024 * Published: 15

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hydrodynamics * Tomographic particle image velocimetry