Semianalytical version of approximation of system of equations in the ‘b-ε’ turbulence model

Kochergin, V. P.; Sklyar, S. N.

doi:10.1515/rnam.1992.7.5.405

Cited by 3 publications

(2 citation statements)

References 1 publication

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“…The Tke evolution (figure 9) of the present experiment compares much better with the observations, Stull (1988) and the comparison seen in this experiment is as good as it is in the earlier experiment. As noted by Kochergin and Sklyar (1992), the smaller the differences C4 -C3, the smaller the Tke values. Thus in the last two experiments we note that the Tke evolution agrees with observations (Stull 1988), if the constants chosen are those we have arrived at, namely Ca = 3/2 and C 3 = 4/3 as well as with those proposed by Marchuk et al (1977).…”

Section: Methodsmentioning

confidence: 85%

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The mean and turbulence structure simulation of the monsoon trough boundary layer using a one-dimensional model withe-l ande-ε closures

Rao

Lykossov

Prabhu

et al. 1996

Proc. Indian Acad. Sci. (Earth Planet Sci.)

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An attempt has I~een made here to study the sensitivity of the mean and the turbulence structure of the monsoon trough boundary layer to the choice of the constants in the dissipation equation for two stations Delhi and Calcutta, using one-dimensional atmospheric boundary layer model with e-e turbulence closure. An analytical discussion of the problems associated with the constants of the dissipation equation is presented. It is shown here that the choice of the constants in the dissipation equation is quite crucial and the turbulence structure is very sensitive to these constants. The modification of the dissipation equation adopted by earlier studies, that is, approximating the Tke generation (due to shear and buoyancy production) in the e-equation by max (shear production, shear + buoyancy production), can be avoided by a suitable choice of the constants suggested here. The observed turbulence structure is better simulated with these constants. The turbulence structure simulation with the constants recommended by Aupoix et al (1989) (which are interactive in time) for the monsoon region is shown to be qualitatively similar to the simulation obtained with the constants suggested here, thus implying that no universal constants exist to regulate dissipation rate.Simulations of the mean structure show little sensitivity to the type of the closure parameterization between e-l and e-e closures. However the turbulence structure simulation with e-e closure is far better compared to the e-l model simulations. The model simulations of temperature profiles compare quite well with the observations whenever the boundary layer is well mixed (neutral) or unstable. However the models are not able to simulate the nocturnal boundary layer (stable) temperature profiles. Moisture profiles are simulated reasonably better. With one-dimensional models, capturing observed wind variations is not up to the mark.

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Section: Methodsmentioning

confidence: 85%

“…However the solution of problems ( 34) and ( 35) can tend to zero or to infinity depending on parameters C 3, C 4 and F (Kochergin and Sklyar 1992). Particularly, they have shown that in case F > 0, the solution tends to zero when C 4 < C a and tends to infinity when C 4 > C 3.…”

Section: Analytical Discussionmentioning

confidence: 99%

The mean and turbulence structure simulation of the monsoon trough boundary layer using a one-dimensional model withe-l ande-ε closures

Rao

Lykossov

Prabhu

et al. 1996

Proc. Indian Acad. Sci. (Earth Planet Sci.)

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Modeling of turbulent dissipation and its validation in periodically stratified region in the Liverpool Bay and in the North Sea

2015

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On the performance of a mixed‐layer model based on the κ‐ε turbulence closure

Burchard¹,

Baumert²

1995

J. Geophys. Res.

138

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This paper investigates the interaction between stratification and turbulence by means of turbulence models. The standard and the advanced turbulent kinetic energy -dissipation (k-e) model are derived theoretically, including algebraic stress relations. It is shown that a certain empirical constant in the standard model turns out to be a complicated imphcit function in the advanced model, namely, a function of the turbulent shear number, the turbulent buoyancy number, and a wall correction. For a better understanding and physical interpretation of the k-e models, an analysis is carried out for a simplified case where diffusive fluxes are neglected. For this ideahzation it is shown that (1) the flux Richardson number R] has a certain lower bound R• due to the estabhshment of convection, (2) a steady state flux Richardson number R} t (which is defined here for this purpose) labels the borderline between the tendency of turbulence to decrease or collapse (R] > R} t) or to increase (R] < R}t), and (3) the wen-known upper limit for turbulent shear flow, R• • 0.25, fits our theory. Using the standard model, the advanced model, a modified version of the level-2 model of Mellor and Yamada and a modified version of Kochergin's model, the evolution of thermal stratification in the northern North Sea during the Fladen Ground Experiment (FLEX'76) is simulated numerically and compared with the measurements. In this specific application, the two k-e models performed best. 1. Introduction Ocean-atmosphere interactions are strongly determined by the dynamics of the upper mixed layer and the evolution and erosion of thermoclines. In the water column we find a complex interplay of several processes forced by different fluxes through the boundaries: momentum flux at the surface due to wind and at the bottom due to friction, and buoyancy flux through the surface due to heat flux, evaporation, precipitation or sea ice dynamics and through the bottom due to erosion and deposition of sediment and suspended particulate matter (for recent observations of highly complex phenomena in the upper mixed layer see Mourn and Caldwell [1994]). There are strong motivations to deal with the upper mixed layer of the ocean, including fishery, primary production and eutrophication, and the occurrence of toxic algae (red tide). Finally, our climate dynamics is closely coupled to the storage of heat and CO2 in the upper mixed layer of the world ocean. In shelf seas and estuaries, we often find a lower mixed layer at the bottom, where important geomorphological and transport processes take place. This layer can be separated from the upper mixed layer by a region of stable stratification. If such a stratified region is absent, both mixed layers condense into only one. Physical and numerical models are an important tool for understanding and predicting the complicated processes in these regions of the ocean. Since the first comprehensive review of upper mixed-layer modelling by Kraus [1977], a large number of turbulence closure models were presented. They ...

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Semianalytical version of approximation of system of equations in the ‘b-ε’ turbulence model

Abstract: A model is developed, and a difference scheme is constructed for obtaining the vertical turbulence coefficient. The scheme is based on a mathematical analysis of the 'b-δ' turbulence model and a suitable choice of input parameters.

Cited by 3 publications

References 1 publication

The mean and turbulence structure simulation of the monsoon trough boundary layer using a one-dimensional model withe-l ande-ε closures

The mean and turbulence structure simulation of the monsoon trough boundary layer using a one-dimensional model withe-l ande-ε closures

Modeling of turbulent dissipation and its validation in periodically stratified region in the Liverpool Bay and in the North Sea

On the performance of a mixed‐layer model based on the κ‐ε turbulence closure

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