Invariant manifolds in stratified turbulence

Abstract

We present a reduced system of seven ordinary differential equations that captures the time evolution of spatial gradients of the velocity and the temperature in fluid elements of stratified turbulent flows. We show the existence of invariant manifolds (further reducing the system dimensionality), and compare the results with data stemming from direct numerical simulations of the full incompressible Boussinesq equations in the stably stratified case. Numerical results accumulate over the invariant manifolds of the reduced system, indicating the system lives at the brink of an instability. Finally, we study the stability of the reduced system, and show that it is compatible with recent observations in stratified turbulence of nonmonotonic dependence of intermittency with stratification.