Double Diffusion in Oceanography

Schmitt, Raymond W.

doi:10.1146/annurev.fl.26.010194.001351

Cited by 482 publications

(299 citation statements)

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“…Persistent staircases have been well documented in the Tyrrhenian Sea, below the Mediterranean outflow, and in the western tropical North Atlantic (Schmitt 1994). Spontaneous layer formation from the uniform gradients was also observed in laboratory experiments (Krishnamurti 2003).…”

Section: Introductionmentioning

confidence: 67%

What determines the thickness of layers in a thermohaline staircase?

Radko¹

2005

J. Fluid Mech.

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A simple theory is developed for the equilibrium height of steps in a thermohaline staircase. The model is based on a linear stability analysis for a series of salt-finger interfaces, which reveals a tendency for the staircase to evolve in time until the characteristic thickness of layers reaches a critical value (H 0 ). Relatively thin layers successively merge as a result of the parametric variation of the heat/salt flux ratio (γ ), but these mergers cease when the thickness of layers exceeds H 0 . The equilibration of thick steps in our model is caused by the slight inhomogeneity of the convecting layers which has a stabilizing effect on the staircase. The instability theory is successfully tested against fully nonlinear numerical simulations and is qualitatively consistent with oceanic observations.

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Section: Introductionmentioning

confidence: 67%

What determines the thickness of layers in a thermohaline staircase?

Radko¹

2005

J. Fluid Mech.

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“…Therefore, the eddy diffusivity of density (K ρ ) is negative, which should have a destabilizing effect on smoothly stratified regions of the ocean (e.g. Schmitt 1994). The physical reasons are illustrated in figure 2(a).…”

Section: ) Wherementioning

confidence: 99%

“…Schmitt 1994;Ruddick 1997;Kelley et al 2003) to adopt the one-component Phillips-Posmentier conceptualization to double-diffusive layering. The Phillips-Posmentier model captures only one aspect of the problem -the ρ z effect (figure 2a).…”

Section: ) Wherementioning

confidence: 99%

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Applicability and failure of the flux-gradient laws in double-diffusive convection

Radko

2014

J. Fluid Mech.

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Double-diffusive flux-gradient laws are commonly used to describe the development of large-scale structures driven by salt fingers -thermohaline staircases, collective instability waves and intrusions. The flux-gradient model assumes that the vertical transport is uniquely determined by the local background temperature and salinity gradients. While flux-gradient laws adequately capture mixing characteristics on scales that greatly exceed those of primary double-diffusive instabilities, their accuracy rapidly deteriorates when the scale separation between primary and secondary instabilities is reduced. This study examines conditions for the breakdown of the flux-gradient laws using a combination of analytical arguments and direct numerical simulations. The applicability (failure) of the flux-gradient laws at large (small) scales is illustrated through the example of layering instability, which results in the spontaneous formation of thermohaline staircases from uniform temperature and salinity gradients. Our inquiry is focused on the properties of the 'point-of-failure' scale (H pof ) at which the vertical transport becomes significantly affected by the non-uniformity of the background stratification. It is hypothesized that H pof can control some key characteristics of secondary double-diffusive phenomena, such as the thickness of high-gradient interfaces in thermohaline staircases. A more general parametrization of the vertical transport -the flux-gradient-aberrancy lawis proposed, which includes the selective damping of relatively short wavelengths that are inadequately represented by the flux-gradient models. The new formulation is free from the unphysical behaviour of the flux-gradient laws at small scales (e.g. the ultraviolet catastrophe) and can be readily implemented in theoretical and large-scale numerical models of double-diffusive convection.

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“…It is well known that double diffusion transports heat and salt unequally, as a result of the much larger molecular diffusivity for heat (• 10 -3 cm•'s -•) than for salt (• 10 -5 cm2s-1), coupled with the small velocities and length scales involved [Schmitt, 1994]. By contrast, the possibility that weak turbulence in regions stable to double diffusion also may transport heat and salt unequally has received relatively little attention.…”

Section: Introductionmentioning

confidence: 99%