THE ROLE OF BIOCONVECTION IN PLANKTON POPULATION WITH THERMAL STRATIFICATION

Abstract

This paper investigates hydrodynamic processes of suspended planktonic population within a thermal stratification to represent a thermocline, in using a model of coupled equations: Navier–Stokes' equation for the fluid dynamic motion, Fisher's equation for the planktonic population with logistic growth, energy conservation equation for thermal effects and the Boussinesq approximation for the dependence on mass density of plankton. The planktonic population is assumed to be slightly denser than the fluid and to follow logistic growth. A numerical investigation is conducted to study patterns of plankton distribution under thermal stratification, and we adopt the finite volume method for solving the system of governing equations in simulations. It is found that thermal stratification constrains the feedback between hydrodynamic and plankton dynamics. More precisely, when temperature is lower in the upper than in the lower layer, the temperature gradient is destabilizing and both convection mechanisms — plankton motility (i.e. taxis behavior that can induce bioconvection) and temperature gradient — are additive. In the case of higher temperature in the upper than the lower layer, which applies to most natural systems, thermal stratification can dampen bioconvection and induce oscillatory dynamics if plankton diffuses faster than temperature. In all cases, if hydrodynamic and demographic time scales overlap, plankton growth rate has a strong effect on hydrodynamic processes involving both thermal convection and convection created by gravitaxis mechanism. Our study thus reveals the potential feedback between hydrodynamic and local demographic processes in plankton populations.