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.

We investigate numerically transient linear growth of three-dimensional perturbations in a stratified shear layer to determine which perturbations optimize the growth of the total kinetic and potential energy over a range of finite target time intervals. The stratified shear layer has an initial parallel hyperbolic tangent velocity distribution with Reynolds number Re = U 0 h/ν = 1000 and Prandtl number ν/κ = 1, where ν is the kinematic viscosity of the fluid and κ is the diffusivity of the density. The initial stable buoyancy distribution has constant buoyancy frequency N 0 , and we consider a range of flows with different bulk Richardson number Ri b = N 2 0 h 2 /U 2 0 , which also corresponds to the minimum gradient Richardson number Ri g (z) = N 2 0 /(dU/dz) 2 at the midpoint of the shear layer. For short target times, the optimal perturbations are inherently three-dimensional, while for sufficiently long target times and small Ri b the optimal perturbations are closely related to the normal-mode 'Kelvin-Helmholtz' (KH) instability, consistent with analogous calculations in an unstratified mixing layer recently reported by Arratia et al. (J. Fluid Mech., vol. 717, 2013, pp. 90-133). However, we demonstrate that non-trivial transient growth occurs even when the Richardson number is sufficiently high to stabilize all normal-mode instabilities, with the optimal perturbation exciting internal waves at some distance from the midpoint of the shear layer.

Acrucial region of the ocean surface boundary layer (OSBL) is the strongly-sheared and -stratified transition layer (TL) separating the mixed layer from the upper pycnocline, where a diverse range of waves and instabilities are possible. Previous work suggests that these different waves and instabilities will lead to different OSBL behaviours. Therefore, understanding which physical processes occur is key for modelling the TL. Here we present observations of the TL from a Lagrangian float deployed for 73 days near Ocean Weather Station Papa (50°N, 145°W) during Fall 2018. The float followed the vertical motion of the TL, continuously measuring profiles across it using an ADCP, temperature chain and salinity sensors. The temperature chain made depth/time images of TL structures with a resolution of 6cm and 3 seconds. These showed the frequent occurrence of very sharp interfaces, dominated by temperature jumps of O(1)°C over 6cm or less. Temperature inversions were typically small (≲ 10cm), frequent, and strongly-stratified; very few large overturns were observed. The corresponding velocity profiles varied over larger length scales than the temperature profiles. These structures are consistent with scouring behaviour rather than Kelvin-Helmholtz-type overturning. Their net effect, estimated via a Thorpe-scale analysis, suggests that these frequent small temperature inversions can account for the observed mixed layer deepening and entrainment flux. Corresponding estimates of dissipation, diffusivity, and heat fluxes also agree with previous TL studies, suggesting that the TL dynamics is dominated by these nearly continuous 10cm-scale mixing structures, rather than by less frequent larger overturns.

The Miles–Howard theorem states that a necessary condition for normal-mode instability in parallel, inviscid, steady stratified shear flows is that the minimum gradient Richardson number, $Ri_{g,min}$, is less than $1/4$ somewhere in the flow. However, the non-normality of the Navier–Stokes and buoyancy equations may allow for substantial perturbation energy growth at finite times. We calculate numerically the linear optimal perturbations which maximize the perturbation energy gain for a stably stratified shear layer consisting of a hyperbolic tangent velocity distribution with characteristic velocity $U_{0}^{\ast }$ and a uniform stratification with constant buoyancy frequency $N_{0}^{\ast }$. We vary the bulk Richardson number $Ri_{b}=N_{0}^{\ast 2}h^{\ast 2}/U_{0}^{\ast 2}$ (corresponding to $Ri_{g,min}$) between 0.20 and 0.50 and the Reynolds numbers $\mathit{Re}=U_{0}^{\ast }h^{\ast }/\unicode[STIX]{x1D708}^{\ast }$ between 1000 and 8000, with the Prandtl number held fixed at $\mathit{Pr}=1$. We find the transient growth of non-normal perturbations may be sufficient to trigger strongly nonlinear effects and breakdown into small-scale structures, thereby leading to enhanced dissipation and non-trivial modification of the background flow even in flows where $Ri_{g,min}>1/4$. We show that the effects of nonlinearity are more significant for flows with higher $\mathit{Re}$, lower $Ri_{b}$ and higher initial perturbation amplitude $E_{0}$. Enhanced kinetic energy dissipation is observed for higher-$Re$ and lower-$Ri_{b}$ flows, and the mixing efficiency, quantified here by $\unicode[STIX]{x1D700}_{p}/(\unicode[STIX]{x1D700}_{p}+\unicode[STIX]{x1D700}_{k})$ where $\unicode[STIX]{x1D700}_{p}$ is the dissipation rate of density variance and $\unicode[STIX]{x1D700}_{k}$ is the dissipation rate of kinetic energy, is found to be approximately 0.35 for the most strongly nonlinear cases.