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We explore numerical methods for the stability analysis of stratified, parallel shear flows considering the effects of small-scale turbulence represented by eddy viscosity and diffusivity. The result is an extension of the classical Taylor–Goldstein problem applicable to oceanic and atmospheric flows. Solutions with imaginary frequency describe shear and convective instabilities, whereas those with real frequency represent internal gravity waves. Application to large observational datasets can involve considerable computation and therefore requires a compromise between speed and accuracy. We compare several numerical methods to identify optimal approaches to various problems.

The life cycles of three Madden–Julian oscillation (MJO) events were observed over the Indian Ocean as part of the Dynamics of the MJO (DYNAMO) experiment. During November 2011 near 0°, 80°E, the site of the research vesselRoger Revelle, the authors observed intense multiscale interactions within an MJO convective envelope, including exchanges between synoptic, meso, convective, and turbulence scales in both atmosphere and ocean and complicated by a developing tropical cyclone. Embedded within the MJO event, two bursts of sustained westerly wind (>10 m s−1; 0–8-km height) and enhanced precipitation passed over the ship, each propagating eastward as convectively coupled Kelvin waves at an average speed of 8.6 m s−1. The ocean response was rapid, energetic, and complex. The Yoshida–Wyrtki jet at the equator accelerated from less than 0.5 m s−1to more than 1.5 m s−1in 2 days. This doubled the eastward transport along the ocean's equatorial waveguide. Oceanic (subsurface) turbulent heat fluxes were comparable to atmospheric surface fluxes, thus playing a comparable role in cooling the sea surface. The sustained eastward surface jet continued to energize shear-driven entrainment at its base (near 100-m depth) after the MJO wind bursts subsided, thereby further modifying sea surface temperature for a period of several weeks after the storms had passed.

Dynamical understanding of the Madden–Julian Oscillation (MJO) has been elusive, and predictive capabilities therefore limited. New measurements of the ocean’s response to the intense surface winds and cooling by two successive MJO pulses, separated by several weeks, show persistent ocean currents and subsurface mixing after pulse passage, thereby reducing ocean heat energy available for later pulses by an amount significantly greater than via atmospheric surface cooling alone. This suggests that thermal mixing in the upper ocean from a particular pulse might affect the amplitude of the following pulse. Here we test this hypothesis by comparing 18 pulse pairs, each separated by <55 days, measured over a 33-year period. We find a significant tendency for weak (strong) pulses, associated with low (high) cooling rates, to be followed by stronger (weaker) pulses. We therefore propose that the ocean introduces a memory effect into the MJO, whereby each event is governed in part by the previous event. The Madden-Julian Oscillation (MJO) describes an eastward propagating pulse of tropical convection. Here, using short-term field measurements, Moum et al . illustrate an MJO memory effect: strong pulses drive enhanced ocean heat loss, weakening subsequent pulses, with implications for MJO prediction.

Turbulent bottom Ekman layers are among the most important energy conversion sites in the ocean. Their energetics are notoriously complex, in particular near sloping topography, where the feedback between cross-slope Ekman transports, buoyancy forcing, and mixing affects the energy budget in ways that are not well understood. Here, the authors attempt to clarify the energy pathways and different routes to mixing, using a combined theoretical and modeling approach. The analysis is based on a newly developed energy flux diagram for turbulent Ekman layers near sloping topography that allows for an exact definition of the different energy reservoirs and energy pathways. Using a second-moment turbulence model, it is shown that mixing efficiencies increase for increasing slope angle and interior stratification, but do not exceed the threshold of 5% except for very steep slopes, where the canonical value of 20% may be reached. Available potential energy generated by cross-slope advection may equal up to 70% of the energy lost to dissipation for upwelling-favorable flow, and up to 40% for downwelling-favorable flow.

In a stably stratified shear layer, multiple competing instabilities produce sensitivity to small changes in initial conditions, popularly called the butterfly effect (as a flapping wing may alter the weather). Three ensembles of 15 simulated mixing events, identical but for small perturbations to the initial state, are used to explore differences in the route to turbulence, the maximum turbulence level and the total amount and efficiency of mixing accomplished by each event. Comparisons show that a small change in the initial state alters the strength and timing of the primary Kelvin–Helmholtz instability, the subharmonic pairing instability and the various three-dimensional secondary instabilities that lead to turbulence. The effect is greatest in, but not limited to, the parameter regime where pairing and the three-dimensional secondary instabilities are in strong competition. Pairing may be accelerated or prevented; maximum turbulence kinetic energy may vary by up to a factor of 4.6, flux Richardson number by 12 %–15 % and net mixing by a factor of 2.

Studies of Kelvin–Helmholtz (KH) instability have typically modelled the initial flow as an isolated shear layer. In geophysical cases, however, the instability often occurs near boundaries and may therefore be influenced by boundary proximity effects. Ensembles of direct numerical simulations are conducted to understand the effect of boundary proximity on the evolution of the instability and the resulting turbulence. Ensemble averages are used to reduce sensitivity to small variations in initial conditions. Both the transition to turbulence and the resulting turbulent mixing are modified when the shear layer is near a boundary: the time scales for the onset of instability and turbulence are longer, and the height of the KH billow is reduced. Subharmonic instability is suppressed by the boundary because phase lock is prevented due to the diverging phase speeds of the KH and subharmonic modes. In addition, the disruptive influence of three-dimensional secondary instabilities on pairing is more profound as the two events coincide more closely. When the shear layer is far from the boundary, the shear-aligned convective instability is dominant; however, secondary central-core instability takes over when the shear layer is close to the boundary, providing an alternate route for the transition to turbulence. Both the efficiency of the resulting mixing and the turbulent diffusivity are dramatically reduced by boundary proximity effects.

Studies of Kelvin–Helmholtz (KH) instability have typically modelled the initial mean flow as an isolated stratified shear layer. However, geophysical flows frequently exhibit multiple layers. As a step towards understanding these flows, we examine the case of two adjacent stratified shear layers using both linear stability analysis and direct numerical simulations. With sufficiently large layer separation, the characteristics of instability and mixing converge towards the familiar KH turbulence, and similarly when the separation is near zero and the layers add to make a single layer, albeit with a reduced Richardson number. Here, our focus is on intermediate separations, which produce new and complex phenomena. As the separation distance $D$ increases from zero to a critical value $D_c$, approximately half the thickness of the shear layer, the growth rate and wavenumber both decrease monotonically. The minimum Richardson number is relatively low, potentially inducing pairing, and shear-aligned convective instability (SCI) is the primary mechanism for transition. Consequently, mixing is relatively strong and efficient. When $D\\sim D_c$, billow length is increased but growth is slowed. Despite the modest growth rate, mixing is strong and efficient, engendered primarily by secondary shear instability manifested on the braids, and by SCI occurring on the eyelids. Shear-aligned vortices are driven in part by buoyancy production; however, shear production and vortex stretching are equally important mechanisms. When $D>D_c$, neighbouring billow interactions suppress the growth of both KH instability and SCI. Strength and efficiency of mixing decrease abruptly as $D_c$ is exceeded. As turbulence decays, layers of marginal instability may arise.

The role of turbulent mixing in regulating the ocean’s response to the Madden–Julian oscillation (MJO) is assessed from measurements of surface forcing, acoustic, and microstructure profiles during October–early December 2011 at 0°, 80.5°E in the Indian Ocean. During the active phase of the MJO, the surface mixed layer was cooled from above by air–sea fluxes and from below by turbulent mixing, in roughly equal proportions. During the suppressed and disturbed phases, the mixed layer temperature increased, primarily because of the vertical divergence between net surface warming and turbulent cooling. Despite heavy precipitation during the active phase, subsurface mixing was sufficient to increase the mixed layer salinity by entraining salty Arabian Sea Water from the pycnocline. The turbulent salt flux across the mixed layer base was, on average, 2 times as large as the surface salt flux. Wind stress accelerated the Yoshida–Wyrtki jet, while the turbulent stress was primarily responsible for decelerating the jet through the active phase, during which the mean turbulent stress was roughly 65% of the mean surface wind stress. These turbulent processes may account for systematic errors in numerical models of MJO evolution.

In this paper the authors investigate the action of ambient turbulence on thermohaline interleaving using both theory and numerical calculations in combination with observations from Meddy Sharon and the Faroe Front. The highly simplified models of ambient turbulence used previously are improved upon by allowing turbulent diffusivities of momentum, heat, and salt to depend on background gradients and to evolve as the instability grows. Previous studies have shown that ambient turbulence, at typical ocean levels, can quench the thermohaline interleaving instability on baroclinic fronts. These findings conflict with the observation that interleaving is common in baroclinic frontal zones despite ambient turbulence. Another challenge to the existing theory comes from numerical experiments showing that the Schmidt number for sheared salt fingers is much smaller than previously assumed. Use of the revised value in an interleaving calculation results in interleaving layers that are both weaker and thinner than those observed. This study aims to resolve those paradoxes. The authors show that, when turbulence has a Prandtl number greater than unity, turbulent momentum fluxes can compensate for the reduced Schmidt number of salt fingering. Thus, ambient turbulence determines the vertical scale of interleaving. In typical oceanic interleaving structures, the observed property gradients are insufficient to predict interleaving growth at an observable level, even when improved turbulence models are used. The deficiency is small, though: gradients sharper by a few tens of percent are sufficient to support instability. The authors suggest that this is due to the efficiency of interleaving in erasing those property gradients. A new class of mechanisms for interleaving, driven by flow-dependent fluctuations in turbulent diffusivities, is identified. The underlying mechanism is similar to the well-known Phillips layering instability; however, because of Coriolis effects, it has a well-defined vertical scale and also a tilt angle opposite to that of finger-driven interleaving.

Kelvin-Helmholtz (KH) instability, characterized by the distinctive finite-amplitude billows it generates, is an important mechanism in the development of turbulence in the stratified interior of the ocean. In particular, it is often assumed that the onset of turbulence in internal waves begins in this way. Clear recognition of the importance of KH instability to ocean mixing arises from recent observations of the phenomenon in a broad range of oceanic environments. KH instability is a critical link in the chain of events that leads from internal waves to mixing. After 150 years of research, identifying the prevalence of KH instability in the ocean and defining useful parameterizations that quantify its contribution to ocean mixing in numerical models remain first-order problems.