Shear instability of the ocean's diurnal warm layer

Under low wind conditions solar radiation is able to heat a thin layer near the ocean surface to create what is known as a diurnal warm layer (DWL).  This layer exhibits relatively strong stratification that decouples it from the rest of the ocean mixed layer below, and leads to increased near-surface velocities within the DWL, called the diurnal jet.  A number of recent studies have observed that the diurnal jet is highly turbulent, and that the entrainment and shear production that results is an important factor in the evolution of the jet momentum and kinetic energy budgets.  Here we investigate shear instability of the stratified diurnal jet as a potential source of turbulence, highlighting a number of important considerations when considering the stability of such a flow.  Based on measurements using turbulence microstructure equipped underwater gliders in the South Atlantic during the SONETT2 expedition, we perform a set of stability analyses of expected flow configurations.  In particular, we find that despite the presence of an upper boundary there is no alteration of the stability criteria from the classic Miles-Howard result, namely the gradient Richardson number must be less than 1/4.  This is in contrast to profiles with a sharp stratified region that is thin compared to the shear thickness, where the flow can be stabilized by the presence of a sufficiently close upper boundary (the sea surface).  We examine the reasons for this difference in the stability criteria for different configurations of the shear and stratification and relate these potential changes in the stability to the observed behaviour of the diurnal jet.  In addition, we discuss some important considerations that the analysis reveals on the propagation of internal waves in the presence of both an upper boundary and strong shears.