Stokes drift of plankton in linear internal waves: Cross‐shore transport of neutrally buoyant and depth‐keeping organisms

Abstract

The meroplanktonic larvae of many invertebrate and vertebrate species rely on physical transport to move them across the shelf to their adult habitats. One potential mechanism for cross‐shore larval transport is Stokes drift in internal waves. Here, we develop theory to quantify the Stokes velocities of neutrally buoyant and depth‐keeping organisms in linear internal waves in shallow water. We apply the analyses to theoretical and measured internal wave fields, and compare results with a numerical model. Near the surface and bottom boundaries, both neutrally buoyant and depth‐keeping organisms were transported in the direction of the wave's phase propagation. However, neutrally buoyant organisms were transported in the opposite direction of the wave's phase at mid depths, while depth‐keeping organisms had zero net transport there. Weakly depth‐keeping organisms had Stokes drifts between the perfectly depth‐keeping and neutrally buoyant organisms. For reasonable wave amplitudes and phase speeds, organisms would experience horizontal Stokes speeds of several centimeters per second—or a few kilometers per day in a constant wave field. With onshore‐polarized internal waves, Stokes drift in internal waves presents a predictable mechanism for onshore transport of meroplanktonic larvae and other organisms near the surface, and offshore transport at mid depths.

Life in Internal Waves

“…Linear internal waves, however, induce alternating positive and negative wave velocities of equal magnitudes at all depths (e.g., Figure 2a). The Eulerian transport is therefore zero; net transport for drifting organisms is due only to Stokes drift (Thorpe, 1968;Dewar, 1980;Franks et al, 2020). Although Stokes drift is non-zero in both linear and nonlinear internal waves, it is stronger in nonlinear internal waves (Figures 2 and 3b,e).…”

“…For internal waves in the absence of a mean flow, Stokes drift is in the direction of wave propagation for both passive and depth-keeping organisms near the top and bottom of the water column (Henderson, 2016;Franks et al, 2020; Figures 2a and 3b,e). Mid-water, passive organisms are transported in the opposite direction, while there is no net transport for depth-keeping organisms (Franks et al, 2020; Figures 2a and 3b,e).…”

“…For internal waves in the absence of a mean flow, Stokes drift is in the direction of wave propagation for both passive and depth-keeping organisms near the top and bottom of the water column (Henderson, 2016;Franks et al, 2020; Figures 2a and 3b,e). Mid-water, passive organisms are transported in the opposite direction, while there is no net transport for depth-keeping organisms (Franks et al, 2020; Figures 2a and 3b,e). In all cases, wave-induced horizontal transport will occur along the same axis as internal wave propagation (Lamb, 1997), and while this may be in the crossshore direction for many coastal internal waves (e.g., Lee, 1961;Shroyer et al, 2011;Richards et al, 2013;Colosi et al, 2018;Sinnett et al, 2018), some coastlines favor along-shore displacements (Liévana MacTavish et al, 2016).…”

“…Similar to sessile organisms, depthkeeping plankton encounter a range of along-isopycnal properties throughout internal waves. However, unlike ses-sile organisms, depth-keeping plankton drift with internal waves (Shanks, 1983;Shanks and Wright, 1987;Pineda, 1999;Franks et al, 2020); thus, average environmental conditions differ for sessile organisms and depth-keeping plankton, even at the same depth (Figure 7).…”

“…Prior studies have quantified waveinduced total horizontal transport for water parcels and both neutrally buoyant and vertically swimming plankton (e.g., Inall et al, 2001;Shroyer et al, 2010;Zhang et al, 2015;Franks et al, 2020;Garwood et al, 2020). However, to our knowledge, no studies have investigated how horizontal drift in an internal wave can change the overall exposure of plankton to various environmental properties.…”