Characteristics of a double-diffusive interface at high density stability ratios

Newell, T.A.

doi:10.1017/s0022112084002718

Cited by 38 publications

(86 citation statements)

References 13 publications

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“…These boundary conditions mean that no heat or salt is able to escape the domain, and the T and S differences across the diffusive interface gradually decrease in time. This 'run-down' scenario is similar to a number of previous laboratory experiments that have been carried out in containers that are either insulated against the escape of heat (Newell 1984), or that have been conducted with a scalar other than heat, for example a salt-sugar system (Turner, Shirtcliffe & Brewer 1970;Shirtcliffe 1973;Stamp et al 1998). …”

Section: Simulations Of a Double-diffusive Interfacementioning

confidence: 53%

“…In keeping with the analogy with run-down laboratory experiments of previous investigations that have used heat, salt, and other soluble components with various diffusivities (e.g. Turner et al 1970;Shirtcliffe 1973;Newell 1984;Stamp et al 1998), we have chosen four simulations in which τ is varied (simulations I-IV). The range of τ chosen is from the heat-salt value of 0.01 to the salt-sugar value of 0.33.…”

Section: Comparison With Geophysical Observations and Laboratory Expementioning

confidence: 99%

“…Linden & Shirtcliffe 1978;Newell 1984;Fernando 1989;Kelley 1990;Worster 2004). Convection begins at t ≈ 2 h when the gravitationally unstable boundary layers break away from the stable interface core.…”

Section: Time Evolutionmentioning

confidence: 99%

“…This is seen to be the case in each of the simulations (I-IV) in figure 4, as well as the h 0 = 2.5 and 5 cm simulations (VIII, IX) of figure 5. The run-down evolution of the diffusive interface once this state is reached may be understood by referring to the basic assumptions behind the model of Newell (1984), which can also be recovered from the more general formulation of Worster (2004). Initially formulated for the large-R ρ region, with R ρ > τ −1/2 , Newell (1984) was able to predict reasonable estimates of interface thicknesses and fluxes based largely on the assumption that the S-interface growth is controlled by molecular diffusion.…”

Section: Dependence On Initial Conditionsmentioning

confidence: 99%

“…This is seen to be nearly the case for three of the four simulations. Details of the Newell (1984) model and its implications for the heat fluxes will be discussed further in § 5.…”

Section: Dependence On Initial Conditionsmentioning

confidence: 99%

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Simulations of a double-diffusive interface in the diffusive convection regime

2012

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Three-dimensional direct numerical simulations are performed that give us an in-depth account of the evolution and structure of the double-diffusive interface. We examine the diffusive convection regime, which, in the oceanographically relevant case, consists of relatively cold fresh water above warm salty water. A 'double-boundary-layer' structure is found in all of the simulations, in which the temperature (T) interface has a greater thickness than the salinity (S) interface. Therefore, thin gravitationally unstable boundary layers are maintained at the edges of the diffusive interface. The TS-interface thickness ratio is found to scale with the diffusivity ratio in a consistent manner once the shear across the boundary layers is accounted for. The turbulence present in the mixed layers is not able to penetrate the stable stratification of the interface core, and the TS-fluxes through the core are given by their molecular diffusion values. Interface growth in time is found to be determined by molecular diffusion of the S-interface, in agreement with a previous theory. The stability of the boundary layers is also considered, where we find boundary layer Rayleigh numbers that are an order of magnitude lower than previously assumed.

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Section: Simulations Of a Double-diffusive Interfacementioning

confidence: 53%

Section: Comparison With Geophysical Observations and Laboratory Expementioning

confidence: 99%

Section: Time Evolutionmentioning

confidence: 99%

Section: Dependence On Initial Conditionsmentioning

confidence: 99%

“…This is seen to be nearly the case for three of the four simulations. Details of the Newell (1984) model and its implications for the heat fluxes will be discussed further in § 5.…”

Section: Dependence On Initial Conditionsmentioning

confidence: 99%

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Simulations of a double-diffusive interface in the diffusive convection regime

2012

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Interface structure and flux laws in a natural double-diffusive layering

Sommer

Carpenter

Schmid

et al. 2013

J. Geophys. Res. Oceans

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The diffusive regime of double‐diffusive convection generates staircases consisting of thin high‐gradient interfaces sandwiched between convectively mixed layers. Simultaneous microstructure measurements of both temperature and conductivity from the staircases in Lake Kivu are used to test flux laws and theoretical models for double diffusion. Density ratios in Lake Kivu are between one and ten and mixed layer thicknesses on average 0.7 m. The larger interface thickness of temperature (average 9 cm) compared to dissolved substances (6 cm) confirms the boundary‐layer structure of the interface. Our observations suggest that the boundary‐layer break‐off cannot be characterized by a single critical boundary‐layer Rayleigh number, but occurs within a range of O(102) to O(104). Heat flux parameterizations which assume that the Nusselt number follows a power law increase with the Rayleigh number Ra are tested for their exponent η. In contrast to the standard estimate η = 1/3, we found η = 0.20 ± 0.03 for density ratios between two and six. Therefore, we suggest a correction of heat flux estimates which are based on η = 1/3. The magnitude of the correction depends on Ra in the system of interest. For Lake Kivu (average heat flux 0.10 W m−2) with Ra = O(108), corrections are marginal. In the Arctic Ocean with Ra = O(108) to O(1012), however, heat fluxes can be overestimated by a factor of four.

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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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Characteristics of a double-diffusive interface at high density stability ratios

Cited by 38 publications

References 13 publications

Simulations of a double-diffusive interface in the diffusive convection regime

Simulations of a double-diffusive interface in the diffusive convection regime

Interface structure and flux laws in a natural double-diffusive layering

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

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