Long-time evolution of density layers and interfaces in forced stably-stratified flows

TL;DR

This study uses long-duration direct numerical simulations to investigate the slow evolution and formation of density staircases in forced stably stratified flows, revealing different coarsening dynamics and the role of turbulence-interface interactions.

Contribution

It provides unprecedented long-time simulations of stratified turbulence, demonstrating the coarsening processes and dynamics of staircase formation under sustained forcing.

Findings

Staircase formation occurs through interface decay or merging.

Kinetic energy remains stable during decay but bursts during merging.

Layer-interface interactions drive intermittency and strong turbulent events.

Abstract

Stably stratified fluids subject to sustained forcing are known to develop step-like density "staircases", where nearly homogeneous layers alternate with thin interfaces of strong stratification. However, long-time numerical investigations of this phenomenon have been limited by the intrinsically slow evolution of large-scale modes and the sensitivity of stratified turbulence to physical parameters. We present direct numerical simulations of forced Boussinesq flows for three stratification strengths (Fr = 0.42, 0.22, 0.076) and of unprecedented time extensions - up to O(10000) turnover times - with the purpose of reproducing and studying the very slow coarsening of the layered state. A large-scale friction term is introduced to arrest shear-mode growth and mimic finite-domain constraints. Staircase formation is observed for both medium and strong stratified cases, following two different coarsening dynamics: interfaces decaying or merging. While kinetic energy remains quasi-stationary during interface decay, it exhibits sharp bursts during merging events. The emergence and persistence of density steps can be explained by the non-monotonic relation between buoyancy flux and buoyancy gradient. Intermittency in vertical velocity and density fluctuations is confined to the vicinity of layer-interface boundaries, indicating that strong events arise from the interaction between turbulent mixing and layer formation rather than from regions of large density gradients alone.