Stratified shear instability in a field of pre-existing turbulence

Abstract

Turbulent mixing of heat and momentum in the stably-stratified ocean interior occurs in discrete events driven by vertical variations of the horizontal velocity. Typically, these events have been modelled assuming an initially laminar stratified shear flow which develops wavelike instabilities, becomes fully turbulent, and then relaminarizes into a stable state. However, in the real ocean there is always some level of turbulence left over from previous events. Using direct numerical simulations, we show that the evolution of a stably-stratified shear layer may be significantly modified by pre-existing turbulence. The classical billow structure associated with Kelvin-Helmholtz instability is suppressed and eventually eliminated as the strength of the initial turbulence is increased. A corresponding energetics analysis shows that potential energy changes and dissipation of kinetic energy depend non-monotonically on initial turbulence strength, with the largest effects when initial turbulence is present but insufficient to prevent billow formation. The mixing efficiency decreases with increasing initial turbulence amplitude as the development of the Kelvin-Helmholtz billow, with its large pre-turbulent mixing efficiency, is arrested.

Evolution of thermally stratified turbulent open channel flow after removal of the heat source

“…This indicates that most of the reversible buoyancy flux is rapidly transferred to via irreversible mixing due to interaction with turbulent eddies from the turbulent region of the channel below. Similar small values of relative to have been observed by Brucker & Sarkar (2007) and Kaminski & Smyth (2019) in studies of shear instabilities in initially turbulent flows.…”

Turbulence in forced stratified shear flows

“…Here, we see that the initial transient broadening period for all three cases lasts approximately 100–200 (non-dimensional) time units. In simulation , during this transient period the flow develops turbulent billows, similar to those seen in the intermediate or strongly turbulent initial condition simulations of Kaminski & Smyth (2019). The resulting growth of the buoyancy interface causes to decrease from its initial value to its steady-state value of .…”

“…2006; Brucker & Sarkar 2007; Mashayek & Peltier 2012 a , b ; Smyth & Moum 2012; Salehipour & Peltier 2015; Salehipour et al. 2016 a ; Kaminski & Smyth 2019).…”

Acoustic Observations of Kelvin‐Helmholtz Billows on an Estuarine Lutocline

“…(d) Echosounder from Connecticut River estuary (Geyer et al, 2010) for comparison. (e) Simulated echosounder signal from a passing KH billow train (modified from Kaminski & Smyth, 2019), showing the classic S‐shape with strong signal in the braids.…”

“…The initial Richardson and Reynolds numbers were Ri 0 = 0.16 and Re 0 = 1,000, and the Prandtl number was unity. Further details of the DNS can be found in Kaminski and Smyth (2019) (The constant 1 in the velocity profile was added after the fact via a Galilean transformation of the DNS data.). The squared vertical density gradient was plotted as a proxy for the flow property registered by the echosounder (e.g., Ross et al, 2004).…”