# Layer formation in horizontally forced stratified turbulence: connecting exact coherent structures to linear instabilities

## TL;DR

This paper investigates how stratified turbulence in a horizontally forced flow leads to layer formation, linking linear instability predictions to the nonlinear layered states observed in simulations.

## Contribution

It establishes a novel connection between linear stability analysis and the nonlinear layered structures in stratified turbulence under horizontal shear.

## Key findings

- Layered structures form as stratification increases.
- Linear instability theory predicts the formation of layers.
- Vertical length scales relate to primary linear instabilities.

## Abstract

We consider turbulence in a stratified 'Kolmogorov' flow, driven by horizontal shear in the form of sinusoidal body forcing in the presence of an imposed background linear stable stratification in the third direction. This flow configuration allows the controlled investigation of the formation of coherent structures, which here organise the flow into horizontal layers by inclining the background shear as the strength of the stratifica- tion is increased. By numerically converging exact steady states from direct numerical simulations of chaotic flow, we show, for the first time, a robust connection between linear theory predicting instabilities from infinitesimal perturbations to the robust finite amplitude nonlinear layered state observed in the turbulence. We investigate how the observed vertical length scales are related to the primary linear instabilities and compare to previously considered examples of shear instability leading to layer formation in other horizontally sheared flows.