What determines the thickness of layers in a thermohaline staircase?

Radko, Timour

doi:10.1017/s0022112004002290

Cited by 50 publications

(69 citation statements)

References 31 publications

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“…Our layering model is analogous to the multiscale models of collective instability (Holyer 1981(Holyer , 1985 and thermohaline interleaving (Radko 2011). It also bears resemblance to the multiscale analyses of mixing in one-component flows (Balmforth & Young 2002, 2005 and to models illustrating spontaneous generation of planetary-scale flows by mesoscale variability (Manfroi & Young 1999. The starting point for such analyses is the choice of the periodic small-scale pattern, which is frequently represented by the Kolmogorov solution -the steady sinusoidal background flow.…”

Section: Layering Instability As a Multiscale Problemmentioning

confidence: 99%

“…Formulation and calibration An obvious candidate for selective damping of high wavenumbers is biharmonic diffusion. As suggested by Radko (2005) the flux-gradient model (2.3) can be modified as follows:…”

Section: Validation Of the Point-of-failure Theorymentioning

confidence: 99%

“…The biharmonic model has been used in the past to surmount numerical difficulties associated with the singularity of the double-diffusive flux-gradient laws as m → ∞ (Radko 2005;Radko et al 2014). However, until now, there has been no guidance with regard to the choice of the aberrancy coefficient µ.…”

Section: T Radkomentioning

confidence: 99%

“…by (6.1) for regions susceptible to fingering (∂ρ/∂z < 0), whereas for convective conditions (∂ρ/∂z > 0) we assume uniform and equal diffusivities of heat and salt (K T = K S = 5000). The resulting system was integrated numerically in time using the pseudospectral method described and used by Radko (2005). Figure 11(a) presents an experiment initiated by a small-amplitude fundamental harmonic with wavelength H = 300.…”

Section: T Radkomentioning

confidence: 99%

“…As a result of this failure, the parametric model cannot predict the fundamental characteristics of thermohaline staircases, such as the initial layer heights or the thicknesses of high-gradient interfaces (e.g. Radko 2005). These deficiencies underscore the need to quantify the applicability range of the flux-gradient laws and to suggest alternative parametrizations for moderately small scales.…”

Section: Introductionmentioning

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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Section: Layering Instability As a Multiscale Problemmentioning

confidence: 99%

Section: Validation Of the Point-of-failure Theorymentioning

confidence: 99%

Section: T Radkomentioning

confidence: 99%

Section: T Radkomentioning

confidence: 99%

Section: Introductionmentioning

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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Minimal model for double diffusion and its application to Kivu, Nyos, and Powell Lake

2015

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Double diffusion originates from the markedly different molecular diffusion rates of heat and salt in water, producing staircase structures under favorable conditions. The phenomenon essentially consists of two processes: molecular diffusion across sharp interfaces and convective transport in the gravitationally unstable layers. In this paper, we propose a model that is based on the one‐dimensional description of these two processes only, and—by self‐organization—is able to reproduce both the large‐scale dynamics and the structure of individual layers, while accounting for different boundary conditions. Two parameters characterize the model, describing the time scale for the formation of unstable water parcels and the optimal spatial resolution. Theoretical relationships allow for the identification of the influence of these parameters on the layer structure and on the mass and heat fluxes. The performances of the model are tested for three different lakes (Powell, Kivu, and Nyos), showing a remarkable agreement with actual microstructure measurements.

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Seismic Oceanography in the Tyrrhenian Sea: Thermohaline Staircases, Eddies, and Internal Waves

et al. 2017

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We use seismic oceanography to document and analyze oceanic thermohaline fine structure across the Tyrrhenian Sea. Multichannel seismic (MCS) reflection data were acquired during the MEDiterranean OCcidental survey in April–May 2010. We deployed along‐track expendable bathythermograph probes simultaneous with MCS acquisition. At nearby locations we gathered conductivity‐temperature‐depth data. An autonomous glider survey added in situ measurements of oceanic properties. The seismic reflectivity clearly delineates thermohaline fine structure in the upper 2,000 m of the water column, indicating the interfaces between Atlantic Water/Winter Intermediate Water, Levantine Intermediate Water, and Tyrrhenian Deep Water. We observe the Northern Tyrrhenian Anticyclone, a near‐surface mesoscale eddy, plus laterally and vertically extensive thermohaline staircases. Using MCS, we are able to fully image the anticyclone to a depth of 800 m and to confirm the horizontal continuity of the thermohaline staircases of more than 200 km. The staircases show the clearest step‐like gradients in the center of the basin while they become more diffuse toward the periphery and bottom, where impedance gradients become too small to be detected by MCS. We quantify the internal wave field and find it to be weak in the region of the eddy and in the center of the staircases, while it is stronger near the coastlines. Our results indicate this is because of the influence of the boundary currents, which disrupt the formation of staircases by preventing diffusive convection. In the interior of the basin, the staircases are clearer and the internal wave field weaker, suggesting that other mixing processes such as double diffusion prevail.

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What determines the thickness of layers in a thermohaline staircase?

Cited by 50 publications

References 31 publications

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

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

Minimal model for double diffusion and its application to Kivu, Nyos, and Powell Lake

Seismic Oceanography in the Tyrrhenian Sea: Thermohaline Staircases, Eddies, and Internal Waves

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