Turbulent velocity profiles for dissipation rate of 1e-6 W/kg

Fundamental marine ecosystem dynamics such as mating, predation, and
infection require individual plankton to move relative to one another.
Ambient turbulence is often invoked as a mechanism to facilitate such
interactions. The local intensity of turbulence is quantified as the
dissipation rate of turbulent kinetic energy. While the dissipation rate
is central to understanding large-scale fluxes of heat, salt, and
nutrients in the ocean, we show that it can be a poor descriptor of the
turbulent environment experienced by individual plankton. A dissipation
rate is a single integrated quantity representing all the complex motions
in a turbulent region; the instantaneous turbulent environment of plankton
may bear little resemblance to that predicted by the dissipation rate or
quantities derived from it. Most importantly, the statistics
(probabilities) of the relative motions of plankton in turbulence cannot
be recovered from the dissipation rate or its spectrum: the probabilities
of the plankton experiencing any given turbulent shear are lost in the
calculation. This presents a fundamental barrier to our understanding of
the effects of ambient turbulence on planktonic ecosystem dynamics in the
ocean. Rather than relying on dissipation rates, we show that quantifying
the probability distributions of the microscale turbulent motions can
provide much richer insights into the turbulent environment of individual
plankton. Expanding such statistical analyses, and improving our
understanding of the Lagrangian properties of ocean turbulence as
experienced by plankton in the ocean will lead to significant increases in
our ability to understand and quantify the effects of turbulence on
plankton.