Trends in Stroke Kinematics, Reynolds Number, and Swimming Mode in Shrimp-Like Organisms

Abstract

Metachronal propulsion is commonly seen in organisms with the caridoid facies body plan, i.e. shrimp-like organisms, as they beat their pleopods in an adlocomotory sequence. These organisms exist across length scales ranging several orders of Reynolds number magnitude, from 10 to 104, during locomotion. Further, by altering their stroke kinematics, these organisms achieve three distinct swimming modes. To better understand the relationship between Reynolds number, stroke kinematics, and resulting swimming mode, Euphausia pacifica stroke kinematics were quantified using high-speed digital recordings and compared to the results for the larger E. superba. Euphausia pacifica consistently operate with a greater beat frequency and smaller stroke amplitude than E. superba for each swimming mode, suggesting that length scale may affect the kinematics needed to achieve similar swimming modes. To expand on this observation, these euphausiid data are used in combination with previously-published stroke kinematics from mysids and stomatopods to identify broad trends across swimming mode and length scale in metachrony. Principal component analysis (PCA) reveals trends in stroke kinematics and Reynolds number as well as the variation among taxonomic order. Overall, larger beat frequencies, stroke amplitudes, between-cycle phase lags, and Reynolds numbers are more representative of the fast forward swimming mode compared to the slower hovering mode. Additionally, each species has a unique combination of kinematics that result in metachrony, indicating that there are other factors, perhaps morphological, which affect the overall metachronal characteristics of an organism. Finally, uniform phase lag, in which the timing between power strokes of all pleopods is equal, in 5-paddle systems is achieved at different Reynolds numbers for different swimming modes, highlighting the importance of taking into consideration stroke kinematics, length scale, and the resulting swimming mode.

Metachronal coordination enables omnidirectional swimming via spatially distributed propulsion

“…Through a combination of freely swimming animal observations and a reduced-order analytical model, we have shown that metachronal swimming, particularly as used in the ctenophore body plan, represents significant untapped potential for bioinspired swimming robots. Ctenophores' higher number of propulsive rows differentiates them from other metachronal swimmers, which typically have only one or two rows of propulsors [7,[29][30][31][32]. Flexibility in controlling a higher number of appendages, combined with the ability to swim both backward and forward, allows for nearly omnidirectional swimming.…”

Omnidirectional propulsion in a metachronal swimmer

“…Through a combination of freely swimming animal observations and a reduced-order analytical model, we have shown that metachronal swimming, particularly as used in the ctenophore body plan, represents significant untapped potential for bioinspired swimming robots. Ctenophores’ higher number of propulsive rows differentiates them from other metachronal swimmers, which typically have only one or two rows of propulsors [ 7 , 46 – 49 ]. Flexibility in controlling a higher number of appendages, combined with the ability to swim both backward and forward, allows for nearly omnidirectional swimming.…”

Hydrodynamics of the fast-start caridoid escape response in Antarctic krill, Euphausia superba

“…A direct linear transform (DLT) software was applied to triangulate the three-dimensional location of each point using the same calibration plate images employed for the tomo-PIV measurements 42 . Similar approaches for quantifying kinematics have been used for several species of krill, and the procedure results in minimal noise in the velocity estimate due to the high recording resolution, high recording frame rate, excellent animal visibility, and robust internal DLT calibration process 30 , 31 . In this study, the points chosen were one point at the eye (point 1), one point along the each of the five segments of the dorsal region (points 2–6), one point at the base of each pleopod pair (points 10–14), one point at the base of the tail (point 7), and two points at the end of the tail (points 8–9) (Supplementary Fig.…”

“…Krill use their five sets of pleopods, as well as their tail, to achieve a high level of maneuverability 30 . As a result, there is a growing field with the objective of quantifying the pleopod kinematics and locomotion 30 , 31 , schooling behavior 24 , 26 , and propulsion hydrodynamics 32 , 33 of Antarctic krill.…”