Thin layers of plankton: Formation by shear and death by diffusion

We show that a steady vertically-sheared current can produce a thin layer of plankton by differentially advecting an initial patch whose vertical and horizontal dimensions are H0 and L0, respectively. Our model treats the plankton as an inert passive tracer with vertical diffusivity kv and subject to a vertically-sheared horizontal current with shear a. After a transient of duration L0=aH0 the vertical thickness H of the patch decreases with HðtÞ L0=at. This shear-driven thinning is halted by diffusion at a time of order a 2=3k 1=3 v L 2=3 0 , and at this time the layer achieves a minimum layer thickness of order a 1=3k v L 1=3 0 . For typical oceanic parameters, such as kv 10 5 m s , a 10 2 s , and L