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  • Author or Editor: William J. Merryfield x
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William J. Merryfield

Abstract

Intrusions like those observed in double-diffusively stable regions of the Arctic Ocean can grow from uniform ambient temperature and salinity gradients if diapycnal mixing of these two components differs. Assuming this to be the driving mechanism, the observed 40–60 m intrusion heights constrain the turbulent diffusivity for heat to be less than about 0.01 cm2 s−1 and the salt-to-heat turbulent diffusivity ratio to be greater than about 0.6 if the diffusivities are constant. Observations indicate that the intrusions slope across isopycnals in a sense that is consistent with such a scenario, although the along-intrusion density ratio is greater than that predicted by linear theory for the fastest-growing intrusions. Numerical solutions for growing intrusions resemble observed temperature and salinity profiles.

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William J. Merryfield

Abstract

Mechanisms and parameter dependence of differential mixing of heat and salt by ocean turbulence are investigated numerically by extending a previous study to examine dependence upon buoyancy frequency N and density gradient ratio Rρ . In these experiments a burst of turbulence mixes temperature T and pseudosalinity S having molecular diffusivity 0.1 times that of T across background vertical gradients of both quantities. In contrast to previous results, which found turbulent diffusivity ratios d = KS /KT < 1 at a fixed N, the present study finds that d > 1 when N = 0 and that d tends to approach this value as N → 0. In all cases considered, d is larger at high Rρ (buoyancy dominated by T) than at low Rρ (buoyancy dominated by S). It is shown that this tendency is consistent with differential mixing being largely due to preferential restratification of the slower-diffusing component S. This conclusion is reinforced by the finding that d scales linearly with a fractional restratification measure over a wide range of conditions.

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William J. Merryfield

Abstract

Hypotheses concerning the origin of thermohaline staircases in salt fingering regions are reviewed and assessed. One such hypothesis, that staircases arise from thermohaline intrusions, is developed into a quantitative theory. It is shown that growing intrusions evolve toward staircases when the background density ratio lies below a threshold value, and nonlinear computations confirm that staircases are viable intrusion equilibria. Staircase properties such as step heights, lateral density ratios, and layer slopes lie closest to observed values when salt fingers are assumed not to contribute to shear stress and when turbulent mixing rates are smaller than usual thermocline values.

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William J. Merryfield
,
Greg Holloway
, and
Ann E. Gargett

Abstract

A global ocean model is described in which parameterizations of diapycnal mixing by double-diffusive fingering and layering are added to a stability-dependent background turbulent diffusivity. Model runs with and without double-diffusive mixing are compared for annual-mean and seasonally varying surface forcing. Sensitivity to different double-diffusive mixing parameterizations is considered. In all cases, the locales and extent of salt fingering (as diagnosed from buoyancy ratio R ρ ) are grossly comparable to climatology, although fingering in the models tends to be less intense than observed. Double-diffusive mixing leads to relatively minor changes in circulation but exerts significant regional influences on temperature and salinity.

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William J. Merryfield
,
Patrick F. Cummins
, and
Greg Holloway

Abstract

Inviscid equilibria of barotropic flows over finite-amplitude topography are determined by means of statistical mechanics, extending previous quasigeostrophic theory. Imposing constraints of energy and enstrophy conservation leads to a linear relation between equilibrium mean potential vorticity and mean transport streamfunction. This relation is tested numerically and is found to hold over a wide range of topographic amplitudes. Implications for improving parameterizations of entropy generation by eddies are discussed.

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Ann E. Gargett
,
William J. Merryfield
, and
Greg Holloway

Abstract

The potential for differential turbulent transport of oceanic temperature (T) and salinity (𝒮) is explored using three-dimensional direct numerical simulations of decaying stratified turbulence. The simulations employ a realistic molecular diffusion coefficient for T, and one for a “salt” scalar S that is 10 times smaller. Initially, a uniformly stratified medium is disturbed by a turbulent burst whose initial energy is assigned a range of values. In each instance, transports of T integrated over the subsequent decay of the burst exceed those of S. The more energetic cases occupy parameter ranges similar to, and exhibit spectral characteristics that are essentially indistinguishable from, those of direct observations of turbulence in the stratified ocean interior. In these cases, the turbulent diffusivity of T exceeds that of S by 6%–22%. These simulations underestimate the degree of differential diffusion between T and salinity 𝒮 (which has a molecular diffusivity 100 times less than T); thus at the Reynolds numbers attained by the simulations these results constitute lower bounds for differential diffusion associated with sporadic turbulence in the ocean. The simulation results are consistent with previous laboratory and two-dimensional numerical experiments and suggest that the assumption of equal turbulent diffusivities for T and 𝒮, commonly used in circulation modeling and in interpreting oceanic mixing measurements, should be reconsidered.

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Ann E. Gargett
,
William J. Merryfield
, and
Greg Holloway

Abstract

The potential for differential turbulent transport of oceanic temperature (T) and salinity ( S ) is explored using three-dimensional direct numerical simulations of decaying stratified turbulence. The simulations employ a realistic molecular diffusion coefficient for T, and one for a “salt” scalar S that is 10 times smaller. Initially, a uniformly stratified medium is disturbed by a turbulent burst whose initial energy is assigned a range of values. In each instance, transports of T integrated over the subsequent decay of the burst exceed those of S. The more energetic cases occupy parameter ranges similar to, and exhibit spectral characteristics that are essentially indistinguishable from, those of direct observations of turbulence in the stratified ocean interior. In these cases, the turbulent diffusivity of T exceeds that of S by 6%–22%. These simulations underestimate the degree of differential diffusion between T and salinity S (which has a molecular diffusivity 100 times less than T); thus at the Reynolds numbers attained by the simulations these results constitute lower bounds for differential diffusion associated with sporadic turbulence in the ocean. The simulation results are consistent with previous laboratory and two-dimensional numerical experiments and suggest that the assumption of equal turbulent diffusivities for T and S , commonly used in circulation modeling and in interpreting oceanic mixing measurements, should be reconsidered.

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Oleg A. Saenko
,
Xiaoming Zhai
,
William J. Merryfield
, and
Warren G. Lee

Abstract

Several recent studies have shown that ocean western boundaries are the primary regions of eddy energy dissipation. Globally, the eddy energy sinks have been estimated to integrate to about 0.2 TW. This is a sizable fraction of the tidal energy dissipation in the deep oceanic interior, estimated at about 1.0 TW and contributing to diapycnal mixing. The authors conduct sensitivity experiments with an ocean general circulation model assuming that the eddy energy is scattered into high-wavenumber vertical modes, resulting in energy dissipation and locally enhanced diapycnal mixing. When only the tidal energy dissipation maintains diapycnal mixing, the overturning circulation, and stratification in the deep ocean are too weak. With the addition of the eddy dissipation, the deep-ocean thermal structure becomes closer to that observed and the overturning circulation and stratification in the abyss become stronger. Furthermore, the mixing associated with the eddy dissipation can, on its own, drive a relatively strong overturning. The stratification and overturning in the deep ocean are sensitive to the vertical structure of diapycnal mixing. When most of this energy dissipates within 300 m above the bottom, the abyssal overturning and stratification are too weak. Allowing for the dissipation to penetrate higher in the water column, such as suggested by recent observations, results in stronger stratification and meridional circulation. Zonal circulation is also affected. In particular, the Drake Passage transport becomes closer to its observational estimates with the increase in the vertical scale for turbulence above topography. Consistent with some theoretical models, the Drake Passage transport increases with the increase in the mean upper-ocean diffusivity.

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