# Invariant manifolds in stratified turbulence

## TL;DR

This paper introduces a reduced 7-ODE system to model stratified turbulence, identifies invariant manifolds, and compares the model with DNS data, revealing insights into turbulence stability and intermittency behavior.

## Contribution

The paper develops a novel reduced-order model with invariant manifolds for stratified turbulence, linking theoretical analysis with numerical simulations.

## Key findings

- Invariant manifolds reduce system complexity.
- Model captures turbulence near instability thresholds.
- Results align with observed intermittency patterns.

## Abstract

We present a reduced system of 7 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 anifolds 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 non-monotonic dependence of intermittency with stratification.