Instabilities in a staircase stratified shear flow

TY - JOUR

T1 - Instabilities in a staircase stratified shear flow

AU - Ponetti, Giordano

AU - Balmforth, Neil J.

AU - Eaves, Tom S.

PY - 2018

Y1 - 2018

N2 - We study stratified shear flow instability where the density profile takes the form of a staircase of interfaces separating uniform layers. Internal gravity waves riding on density interfaces can resonantly interact due to a background shear flow, resulting in the Taylor-Caulfield instability. The many steps of the density profile permit a multitude of interactions between different interfaces, and a rich variety of Taylor-Caulfield instabilities. We analyse the linear instability of a staircase with piecewise-constant density profile embedded in a background linear shear flow, locating all the unstable modes and identifying the strongest. The interaction between nearest-neighbour interfaces leads to the most unstable modes. The nonlinear dynamics of the instabilities are explored in the long-wavelength, weakly stratified limit (the defect approximation). Unstable modes on adjacent interfaces saturate by rolling up the intervening layer into a distinctive billow. These nonlinear structures coexist when stacked vertically and are bordered by the sharp density gradients that are the remnants of the steps of the original staircase. Horizontal averages remain layer-like.

AB - We study stratified shear flow instability where the density profile takes the form of a staircase of interfaces separating uniform layers. Internal gravity waves riding on density interfaces can resonantly interact due to a background shear flow, resulting in the Taylor-Caulfield instability. The many steps of the density profile permit a multitude of interactions between different interfaces, and a rich variety of Taylor-Caulfield instabilities. We analyse the linear instability of a staircase with piecewise-constant density profile embedded in a background linear shear flow, locating all the unstable modes and identifying the strongest. The interaction between nearest-neighbour interfaces leads to the most unstable modes. The nonlinear dynamics of the instabilities are explored in the long-wavelength, weakly stratified limit (the defect approximation). Unstable modes on adjacent interfaces saturate by rolling up the intervening layer into a distinctive billow. These nonlinear structures coexist when stacked vertically and are bordered by the sharp density gradients that are the remnants of the steps of the original staircase. Horizontal averages remain layer-like.

KW - Stratified shear flow instability

KW - layers

U2 - 10.1080/03091929.2017.1378877

DO - 10.1080/03091929.2017.1378877

M3 - Article

SN - 0309-1929

VL - 112

SP - 1

EP - 19

JO - Geophysical & Astrophysical Fluid Dynamics

JF - Geophysical & Astrophysical Fluid Dynamics

IS - 1

ER -