Search Results

You are looking at 1 - 10 of 12 items for

  • Author or Editor: William D. Smyth x
  • Refine by Access: All Content x
Clear All Modify Search
William D. Smyth and Satoshi Kimura

Abstract

The linear stability of a double-diffusively stratified, inflectional shear flow is investigated. Double-diffusive stratification has little effect on shear instability except when the density ratio Rρ is close to unity. Double-diffusive instabilities have significant growth rates and can represent the fastest-growing mode even in the presence of inflectionally unstable shear with a low Richardson number. In the linear regime, background shear has no effect on double-diffusive modes except to select the orientation of the wave vector. The converse is not true: double-diffusive modes modify the mean shear via momentum fluxes. The momentum flux driven by salt sheets is parameterized in terms of a Schmidt number (ratio of eddy viscosity to saline diffusivity) Scs. In the oceanic parameter regime, Scs is less than unity and can be approximated as Scs = 0.08 ln[Rρ/(Rρ − 1)]. Enhanced molecular dissipation by unstable motions is quantified in terms of the dissipation ratio Γ, and the results are compared with observations. Corresponding results are given for diffusive convection in an inflectional shear flow, though linear theory is expected to give a less accurate description of this mechanism.

Full access
Ryuichiro Inoue and William D. Smyth

Abstract

The dependence of mixing efficiency on time-varying forcing is studied by direct numerical simulation (DNS) of Kelvin–Helmholtz (KH) instability. Time-dependent forcing fields are designed to reproduce a wavelike oscillation by solving the equations of motion in a tilted coordinate frame and allowing the tilt angle to vary in time. Mixing efficiency Γc is defined as the ratio of potential energy gain to dissipation, both averaged over one forcing cycle and first examined via parameters characterizing waves: the minimum Richardson number Rimin and the normalized frequency of the forcing ω/N. The effect of Reynolds number Re0 and the initial random disturbance amplitude b are also examined. In the experiments presented, Γc varies between 0.21 and 0.36 and is controlled by the timing of two events: the emergence of KH billows and the arrival of the deceleration of the mean shear by the wavelike forcing. Here, Γc is higher than a canonical value of 0.2 when the deceleration phase of the forcing suppresses the less efficient turbulence after breakdown of KH billows. However, when Rimin and ω/N are small, KH billows start to develop before Rimin is achieved. Therefore, the forcing accelerates the mean shear and thereby sustains turbulence after the breakdown of KH billows. The canonical value is then reproduced in the DNS. Although larger values of Re0 and b intensify the development of KH billows and modify Γc, this effect is less significant when forcing fields act to sustain turbulence. The time-averaged Thorpe scale and Ozmidov scale are also used to see how mixing is modified by forcing fields and compared with past microstructure measurements. It is found that DNS also corresponds to past observations if the forcing accelerates the mean shear to sustain turbulence.

Full access
William D. Smyth and Barry Ruddick

Abstract

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.

Full access
Qiang Lian, William D. Smyth, and Zhiyu Liu

Abstract

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.

Free access
Martín S. Hoecker-Martínez, William D. Smyth, and Eric D. Skyllingstad

Abstract

The dominant processes governing ocean mixing during an active phase of the Madden–Julian oscillation are identified. Air–sea fluxes and upper-ocean currents and hydrography, measured aboard the R/V Revelle during boreal fall 2011 in the Indian Ocean at 0°, 80.5°E, are integrated by means of a large-eddy simulation (LES) to infer mixing mechanisms and quantify the resulting vertical property fluxes. In the simulation, wind accelerates the mixed layer, and shear mixes the momentum downward, causing the mixed layer base to descend. Turbulent kinetic energy gains due to shear production and Langmuir circulations are opposed by stirring gravity and frictional losses. The strongest stirring of buoyancy follows precipitation events and penetrates to the base of the mixed layer. The focus here is on the initial 24 h of an unusually strong wind burst that began on 24 November 2011. The model shows that Langmuir turbulence influences only the uppermost few meters of the ocean. Below the wave-energized region, shear instability responds to the integrated momentum flux into the mixed layer, lagging the initial onset of the storm. Shear below the mixed layer persists after the storm has weakened and decelerates the surface jet slowly (compared with the acceleration at the peak of the storm). Slow loss of momentum from the mixed layer extends the effect of the surface wind burst by energizing the fluid at the base of the mixed layer, thereby prolonging heat uptake due to the storm. Ocean turbulence and air–sea fluxes contribute to the cooling of the mixed layer approximately in the ratio 1:3, consistent with observations.

Full access
Rachael D. Mueller, William D. Smyth, and Barry Ruddick

Abstract

Thermohaline interleaving is an important mechanism for laterally fluxing salt, heat, and nutrients between water masses. Interleaving is driven by a release of potential energy resulting from the differing diffusivities of heat and salt in seawater. The flows are composed of stacked intrusions that flux more and less buoyant water in opposite directions. In this paper, the role of shear instability caused by this juxtaposed motion is investigated. The model described in Walsh and Ruddick is modified to include both the effects of shear-induced turbulence and an improved convective mixing parameterization. Shear and convective mixing play a similar and significant role in interleaving dynamics. In the absence of either instability, cross-front fluxes are increased by approximately 30%. While in situ observations of horizontal diffusivity resulting from interleaving are not yet precise enough to calibrate the parameterizations independently, parameter values based on independent laboratory and numerical studies lead to diffusivity predictions that are within the error of the observations.

Full access
Kandaga Pujiana, James N. Moum, and William D. Smyth

Abstract

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.

Full access
Lars Umlauf, William D. Smyth, and James N. Moum

Abstract

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.

Full access
Hieu T. Pham, William D. Smyth, Sutanu Sarkar, and James N. Moum

Abstract

The seasonal cycles of the various oceanic and atmospheric factors influencing the deep cycle of turbulence in the eastern Pacific cold tongue are explored. Moored observations at 140°W have shown seasonal variability in the stratification, velocity shear, and turbulence above the Pacific Equatorial Undercurrent (EUC). In boreal spring, the thermocline and EUC shoal and turbulence decreases. Marginal instability (clustering of the local gradient Richardson number around the critical value of 1/4), evident throughout the rest of the year, has not been detected during spring. While the daily averaged turbulent energy dissipation in the EUC is weakest during the spring, it is not clear whether the diurnal fluctuations that define the deep cycle cease. Large-eddy simulations are performed using climatological initial and boundary conditions representative of January, April, July, and October. Deep cycle turbulence is evident in all cases; the mechanism remains the same, and the maximum turbulence levels are similar. In the April simulation, however, the deep cycle is confined to the uppermost ~30 m, explaining why it has not been detected in moored microstructure observations.

Full access
Chuanyu Liu, Xiaowei Wang, Zhiyu Liu, Armin Köhl, William D. Smyth, and Fan Wang

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.

Open access