Buoyancy-dependent induced flow by vertically migrating swimmers

Abstract

Collective vertical migrations of negatively buoyant swimmers can drive large-scale fluid transport. In the ocean, zooplankton migrate over vertical distances several orders of magnitude larger than their body length. These swimmers experience changes in their buoyancy relative to the stably stratified ocean water column. The impact of net swimmer buoyancy on the scale of aggregate-scale induced flows remains unresolved. We hypothesize that as the net buoyancy of swimmers becomes increasingly negative the speed of induced flow in the opposite direction of swimming will increase due to changes in the required force to swim upward and thus the momentum imparted on the surrounding fluid. Simultaneous three-dimensional swimmer tracking and two-dimensional two-component flow measurements are used to measure the flow induced by collective vertical migration of Artemia salina. Experiments were designed to modulate the buoyant force on the swimmers by changing environmental salinity. Experimental results supported the hypothesis and were used to develop a theoretical model, which was then used to contextualize results to ocean relevant conditions with non-dimensional analysis.

Figures (18)

• Figure 1: Formation and evolution of induced jet during brine shrimp vertical migration at varying salinities visualized with PIV. Images are arranged in columns corresponding to each salinity condition and rows showing snapshots at times t=0, 40, 80 s. Due to differences in the number of swimmers, the 15 and 22 ppt cases are compared independently from the 17 and 19 ppt cases. Swimmer body length (BL) is 1 cm.
• Figure 2: Measured A) salinity and B) density values for the four experimental conditions vs tank depth measured in swimmer body length (BL) which is 1 cm. Salinity was adjusted to four target values (15, 17, 19, and 22 ppt) and then salinity and fluid density were verified using a CastAway CTD profiler (SonTek, USA), with five measurements taken from different locations in the tank immediately before loading the animals. Salinity and density values are shown as the average $\pm$ (accuracy $+$ standard deviation) across these five tank locations for each salinity condition.
• Figure 3: Comparing unshifted and time-shifted data for the four trials completed at 17 ppt salinity. A) Original swimmer speed over time; B) time-shifted swimmer speed aligned such that peak speed occurs simultaneously; C) original peak flow speed within the aggregation over time; D) time-shift defined by (B) applied to peak flow speed.
• Figure 4: Swimmer counts for each salinity condition during induced vertical migration. A) Average swimmer number throughout the migration, plotted as mean values (solid lines) across four trials with standard deviation (shaded region). B) Box plots showing the distribution of swimmer number at the final recorded time step for each salinity condition (15, 17, 19, and 22 ppt). Due to differences in the number of swimmers the 15 and 22 ppt cases are compared and the 17 and 19 ppt cases are compared independently. Boxes represent the inter-quartile range, with the central line indicating the median, and whiskers extending to the minimum and maximum data points. Statistical significance was evaluated using pair-wise ANOVA with n=4 trials per condition. Significant differences between groups are denoted by asterisks (* for $p<0.05$, ** for $p<0.01$, *** for $p<0.001$).
• Figure 5: A) Mean flow velocity, averaged spatially and across four trials per salinity condition. Solid lines indicate the mean, with shaded regions representing the standard deviation. B) Box plots illustrating the distribution of measured flow velocities at swimmer locations at the final recorded timestep for each salinity condition (15, 17, 19, and 22 ppt). Due to differences in the number of swimmers the 15 and 22 ppt cases are compared and the 17 and 19 ppt cases are compared independently. Boxes indicate the inter-quartile range, horizontal lines denote median values, and whiskers extend to minimum and maximum data points excluding outliers. Significant differences between conditions were determined using one-way ANOVA, with pairwise post-hoc comparisons. All pairwise differences shown are statistically significant, indicated by asterisks (* for $p<0.05$, ** for $p<0.01$, *** for $p<0.001$).