From waves to convection and back again: The phase space of stably stratified turbulence

TL;DR

This paper explores the phase space of stably stratified turbulence, revealing two main invariant manifolds related to waves and convection, and proposes a reduced model to understand energy transfer, intermittency, and flow structures.

Contribution

It introduces a reduced model derived from Boussinesq equations that captures the dynamics between wave and convection manifolds in stratified turbulence.

Findings

Identification of two main invariant manifolds in stratified turbulence

Energy accumulation in wave manifold leads to transition to convection

Increased stratification enlarges wave manifold, affecting flow intermittency

Abstract

We show that the phase space of stratified turbulence mainly consists of two slow invariant manifolds with rich physics, embedded on a larger basin with fast evolution. A local invariant manifold in the vicinity of the fluid at equilibrium corresponds to waves, while a global invariant manifold corresponds to the onset of local convection. Using a reduced model derived from the Boussinesq equations, we propose that waves accumulate energy nonlinearly up to a point such that fluid elements escape from the local manifold and evolve fast to the global manifold, where kinetic energy can be more efficiently dissipated. After this, fluid elements return to the first manifold. As the stratification increases, the volume of the first manifold increases, and the second manifold becomes harder to access. This explains recent observations of enhanced intermittency and marginal instability in these flows. The reduced model also allows us to study structure formation, alignment of field gradients in the flow, and to identify balance relations that hold for each fluid element.