The length scale equation in turbulence models

Kantha, Lakshmi

doi:10.5194/npg-11-83-2004

Cited by 37 publications

(28 citation statements)

References 69 publications

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“…In fact, it is reported that, when the prognostic equation for q 2 L proposed by Mellor and Yamada (1982) is used to describe the variation of the length scale with stability in the surface layer, the characteristics of the surface layer including dimensionless shear, dimensionless temperature gradient, and second-order moments are not reproduced for typical range of the dimensionless height z ¼ z=L M (Niino 1990). Recently, Kantha (2004) formulated a general equation for q m L n , where m and n are integer values. We also plan to utilize our diagnostic equation for L for exploring a suitable variable among q m L n and empirical constants in its prognostic equation.…”

Section: Summary and Discussionmentioning

confidence: 99%

Development of an Improved Turbulence Closure Model for the Atmospheric Boundary Layer

Nakanishi

Niino

2009

Journal of the Meteorological Society of Japan

803

447

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An improved Mellor-Yamada (MY) turbulence closure model (MYNN model: Mellor-YamadaNakanishi-Niino model) that we have developed is summarized and its performance is demonstrated against a large-eddy simulation (LES) of a convective boundary layer. Unlike the original MY model, the MYNN model considers e¤ects of buoyancy on pressure covariances and e¤ects of stability on the turbulent length scale, with model constants determined from a LES database. One-dimensional simulations of Day 33 of the Wangara field experiment, which was conducted in a flat area of southeastern Australia in 1967, are made by the MY and MYNN models and the results are compared with horizontal-average statistics obtained from a threedimensional LES. The MYNN model improves several weak points of the MY model such as an insu‰cient growth of the convective boundary layer, and underestimates of the turbulent kinetic energy and the turbulent length scale; it reproduces fairly well the results of the LES including the vertical distributions of the mean and turbulent quantities. The improved performance of the MYNN model relies mainly on the new formulation of the turbulent length scale that realistically increases with decreasing stability, and partly on the parameterization of the pressure covariances and the expression for stability functions for third-order turbulent fluxes.

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Section: Summary and Discussionmentioning

confidence: 99%

Development of an Improved Turbulence Closure Model for the Atmospheric Boundary Layer

Nakanishi

Niino

2009

Journal of the Meteorological Society of Japan

803

447

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“…The value of this constant has been the subject of considerable controversy from the very beginning (Baumert and Peters 2000), and it is noteworthy that DM experiments provide one means of calibrating this constant! Note that any prevailing length scale model (Kantha 2004), with Cψ2 and Cψ3 chosen such that (m+n−2Cψi)/n (i=2,3) in Eq. 13 is invariant, would yield identical results.…”

Section: Traditional Turbulence Decay Modelmentioning

confidence: 99%

On leakage of energy from turbulence to internal waves in the oceanic mixed layer

Kantha¹,

Clayson²

2007

Ocean Dynamics

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In this paper, we address the question of energy leakage from turbulence to internal waves (IWs) in the oceanic mixed layer (OML). If this leakage is substantial, then not only does this have profound implications as far as the dynamics of the OML is concerned, but it also means that the equation for the turbulence kinetic energy (TKE) used in OML models must include an appropriate sink term, and traditional models must be modified accordingly. Through comparison with the experimental data on gridgenerated turbulence in a stably stratified fluid, we show that a conventional two-equation turbulence model without any IW sink term can explain these observations quite well, provided that the fluctuating motions that persist long after the decay of grid-generated turbulence are interpreted as being due to IW motions generated by the initial passage of the grid through the stably stratified fluid and not during turbulence decay. We conclude that there is no need to postulate an IW sink term in the TKE equation, and conventional models suffice to model mixing in the OML.

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“…The standard equation for the transport of E employed by all closures that are discussed below is (Kantha 2004)…”

Section: Governing Equationsmentioning

confidence: 99%

Modification of Two-Equation Models to Account for Plant Drag

Sogachev

Panferov

2006

Boundary-Layer Meteorol

116

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A modification of the most popular two-equation (E-ϕ) models, taking into account the plant drag, is proposed. Here E is the turbulent kinetic energy (TKE) and ϕ is any of the following variables: El (product of E and the mixing length l), ε (dissipation rate of TKE), and ω (specific dissipation of TKE, ω = ε/E). The proposed modification is due to the fact that the model constants estimated experimentally for 'free-air' flow do not allow for adequate reconstruction of the ratio between the production and dissipation rates of TKE in the vegetation canopy and have to be adjusted. The modification is universal, i.e. of the same type for all E-ϕ models considered. The numerical experiments carried out for both homogeneous and heterogeneous plant canopies with E-ϕ models (and with the E-l model taken as a kind of reference) show that the modification performs well. They also suggest that E-ε and E-ω schemes are more promising than the E-El scheme for canopy flow simulation since they are not limited by the need to use a wall function.In addition, a new parameterization for enhanced dissipation within the plant canopy is derived. It minimizes the model sensitivity to C μ , the key parameter for two-equation schemes, and whose estimates unfortunately vary considerably from experiment to experiment. The comparison of results of new modified E-ε and E -ω models with observations from both field and wind-tunnel experiments shows that the proposed parameterization is quite robust. However, because of uncertainties with the turbulence Prandtl and Schmidt numbers for the E-ε model within the canopy, the E-ω model is recommended for future implementation, with the suggested modifications.

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The length scale equation in turbulence models

Cited by 37 publications

References 69 publications

Development of an Improved Turbulence Closure Model for the Atmospheric Boundary Layer

Development of an Improved Turbulence Closure Model for the Atmospheric Boundary Layer

On leakage of energy from turbulence to internal waves in the oceanic mixed layer

Modification of Two-Equation Models to Account for Plant Drag

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