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  1. 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. 
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    Free, publicly-accessible full text available July 10, 2024
  2. Abstract

    Observations in the Pacific Equatorial Undercurrents (EUC) show that the nighttime deep-cycle turbulence (DCT) in the marginal-instability (MI) layer of the EUC exhibits seasonal variability that can modulate heat transport and sea surface temperature. Large-eddy simulations (LES), spanning a wide range of control parameters, are performed to identify the key processes that influence the turbulent heat flux at multiple time scales ranging from turbulent (minutes to hours) to daily to seasonal. The control parameters include wind stress, convective surface heat flux, shear magnitude, and thickness of the MI layer. In the LES, DCT occurs in discrete bursts during the night, exhibits high temporal variability within a burst, and modulates the mixed layer depth. At the daily time scale, turbulent heat flux generally increases with increasing wind stress, MI-layer shear, or nighttime convection. Convection is found to be important to mixing under weak wind, weak shear conditions. A parameterization for the daily averaged turbulent heat flux is developed from the LES suite to infer the variability of heat flux at the seasonal time scale. The LES-based parameterized heat flux, which takes into account the effects of all control parameters, exhibits a seasonal variability that is similar to the observed heat flux from theχ-pods.

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  3. 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. 
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  4. Abstract

    Several years of moored turbulence measurements fromχpods at three sites in the equatorial cold tongues of Atlantic and Pacific Oceans yield new insights into proxy estimates of turbulence that specifically target the cold tongues. They also reveal previously unknown wind dependencies of diurnally varying turbulence in the near-critical stratified shear layers beneath the mixed layer and above the core of the Equatorial Undercurrent that we have come to understand as deep cycle (DC) turbulence. Isolated by the mixed layer above, the DC layer is only indirectly linked to surface forcing. Yet, it varies diurnally in concert with daily changes in heating/cooling. Diurnal composites computed from 10-min averaged data at fixedχpod depths show that transitions from daytime to nighttime mixing regimes are increasingly delayed with weakening wind stressτ. These transitions are also delayed with respect to depth such that they follow a descent rate of roughly 6 m h−1, independent ofτ. We hypothesize that this wind-dependent delay is a direct result of wind-dependent diurnal warm layer deepening, which acts as the trigger to DC layer instability by bringing shear from the surface downward but at rates much slower than 6 m h−1. This delay in initiation of DC layer instability contributes to a reduction in daily averaged values of turbulence dissipation. Both the absence of descending turbulence in the sheared DC layer prior to arrival of the diurnal warm layer shear and the magnitude of the subsequent descent rate after arrival are roughly predicted by laboratory experiments on entrainment in stratified shear flows.

    Significance Statement

    Only recently have long time series measurements of ocean turbulence been available anywhere. Important sites for these measurements are the equatorial cold tongues where the nature of upper-ocean turbulence differs from that in most of the world’s oceans and where heat uptake from the atmosphere is concentrated. Critical to heat transported downward from the mixed layer is the diurnally varying deep cycle of turbulence below the mixed layer and above the core of the Equatorial Undercurrent. Even though this layer does not directly contact the surface, here we show the influence of the surface winds on both the magnitude of the deep cycle turbulence and the timing of its descent into the depths below.

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  5. Abstract In low winds (≲2 m s −1 ), diurnal warm layers form but shear in the near-surface jet is too weak to generate shear instability and mixing. In high winds (≳8ms −1 ), surface heat is rapidly mixed downward and diurnal warm layers do not form. Under moderate winds of 3–5 m s −1 , the jet persists for several hours in a state that is susceptible to shear instability. We observe low Richardson numbers of Ri ≈ 0.1 in the top 2 m between 10:00 and 16:00 local time (from 4 h after sunrise to 2 h before sunset). Despite Ri being well below the Ri = 1/4 threshold, instabilities do not grow quickly, nor do they overturn. The stabilizing influence of the sea surface limits growth, a result demonstrated by both linear stability analysis and two-dimensional simulations initialized from observed profiles. In some cases, growth rates are sufficiently small (≪1 h −1 ) that mixing is not expected even though Ri < 1/4. This changes around 16:00–17:00. Thereafter, convective cooling causes the region of unstable flow to move downward, away from the surface. This allows shear instabilities to grow an order of magnitude faster and mix effectively. We corroborate the overall observed diurnal cycle of instability with a freely evolving, two-dimensional simulation that is initialized from rest before sunrise. 
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  6. null (Ed.)
    Abstract The origins of an observed weakly sheared nonturbulent (laminar) layer (WSL), and a strongly sheared turbulent layer above the Equatorial Undercurrent core (UCL) in the eastern equatorial Pacific are studied, based mainly on the data from the Tropical Atmosphere and Ocean mooring array. Multiple-time-scale (from 3 to 25 days) equatorial waves were manifested primarily as zonal velocity oscillations with the maximum amplitudes (from 10 to 30 cm s −1 ) occurring at different depths (from the surface to 85-m depths) above the seasonal thermocline. The subsurface-intensified waves led to vertically out-of-phase shear variations in the upper thermocline via destructive interference with the seasonal zonal flow, opposing the tendency for shear instability. These waves were also associated with depth-dependent, multiple-vertical-scale stratification variations, with phase lags of π /2 or π , further altering stability of the zonal current system to vertical shear. The WSL and UCL were consequently formed by coupling of multiple equatorial waves with differing phases, particularly of the previously identified equatorial mode and subsurface mode tropical instability waves (with central period of 17 and 20 days, respectively, in this study), and subsurface-intensified waves with central periods of 6, 5, and 12 days and velocity maxima at 45-, 87-, and 40-m depths, respectively. In addition, a wave-like feature with periods of 50–90 days enhanced the shear throughout the entire UCL. WSLs and UCLs seem to emerge without a preference for particular tropical instability wave phases. The generation mechanisms of the equatorial waves and their joint impacts on thermocline mixing remain to be elucidated. 
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  7. The mixing efficiency of stratified turbulence in geophysical fluids has been the subject of considerable controversy. A simple parameterization, devised decades ago when empirical knowledge was scarce, has held up remarkably well. The parameterization rests on the assumption that the flux coefficient Γ has the uniform value 0.2. This note provides a physical explanation for Γ = 0.2 in terms of the “marginal instability” property of forced stratified shear flows, and also sketches a path toward improving on that simple picture by examining cases where it fails. 
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  8. Abstract

    Multiyear turbulence measurements from oceanographic moorings in equatorial Atlantic and Pacific cold tongues reveal similarities in deep cycle turbulence (DCT) beneath the mixed layer (ML) and above the Equatorial Undercurrent (EUC) core. Diurnal composites of turbulence kinetic energy dissipation rate,ϵ, clearly show the diurnal cycles of turbulence beneath the ML in both cold tongues. Despite differences in surface forcing, EUC strength and core depth DCT occurs, and is consistent in amplitude and timing, at all three sites. Time‐mean values ofϵat 30 m depth are nearly identical at all three sites. Variations of averaged values ofϵin the deep cycle layer below 30 m range to a factor of 10 between sites. A proposed scaling in depth that isolates the deep cycle layers and ofϵby the product of wind stress and current shear collapses vertical profiles at all sites to within a factor of 2.

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