Phytoplankton growth driven by stratified shear instabilities

Phytoplankton populations grow in the sunlit upper ocean where they often interact with strong gradients in buoyancy and velocity at the bottom of the well-mixed layer. We explore this interaction using direct numerical simulations of phytoplankton forced by two different stratified shear instabilities, the Kelvin-Helmholtz (KH) and Holmboe instabilities, with different mixing behaviors. The phytoplankton was parameterized as a reacting passive scalar using a simple linear model with a depth-dependent growth rate, mimicking the decay of sunlight with depth. We observe that KH instability causes the phytoplankton to become more evenly distributed, while Holmboe instability maintains a sharper gradient at the interface. Additionally, the non-uniform growth rate results in asymmetric phytoplankton distributions on either side of the interface. We further examine the effect of a Damköhler number, defined as the ratio of fluid flow and phytoplankton growth timescales, on the system. We discuss the importance of our results for developing a model of upper ocean phytoplankton growth that accounts for different stratified mixing behaviors.