Synthetizing hydrodynamic turbulence from noise: formalism and applications to plankton dynamics

Abstract

We present an analytical scheme, easily implemented numerically, to generate synthetic Gaussian 2D turbulent flows by using linear stochastic partial differential equations, where the noise term acts as a random force of well-prescribed statistics. This methodology leads to a divergence-free, isotropic, stationary and homogeneous velocity field, whose characteristic parameters are well reproduced, in particular the kinematic viscosity and energy spectrum. This practical approach to tailor a turbulent flow is justified by its versatility when analizing different physical processes occurring in advectely mixed systems. Here, we focuss on an application to study the dynamics of Planktonic populations in the ocean