The Spatio-Temporal Structure of Internal Waves in Stably Stratified Channel Flow

Abstract:

Stably stratified flows are ubiquitous in natural and industrial fluid dynamics. These flows have a significant impact on mixing in the atmospheric boundary layer, rivers, continental shelf seas, and industrial heat transfer equipment. Internal waves, arising from the restoring effect of buoyancy, have a substantial influence on mixing processes in stably stratified flows, and have been the focus of much research over the last few decades.

Here we investigate the internal waves in Boussinesq, stably stratified, turbulent channel flow. Previous studies have reported internal waves in the core region of stably stratified channel flow, and determined several flow regimes based on the Reynolds and Richardson numbers. However, the spatio-temporal structure of these waves remains poorly quantified. This study addresses this using numerical techniques; Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) are performed using the spectral element code Nek5000 to investigate the structure of internal waves in stably stratified turbulent channel flow at various Reynolds and Richardson numbers. Dynamic Mode Decomposition (DMD), spatial, and temporal spectral analysis are adopted to isolate internal waves from other wave-like structures, determine their dispersion relation, and investigate their structure. Through this analysis we find that wave-like motion in the channel core is comprised of a wide range of spatial and temporal frequencies.