Second-order turbulence closure models for geophysical boundary layers. A review of recent work

Umlauf, Lars; Burchard, Hans

doi:10.1016/j.csr.2004.08.004

Cited by 379 publications

(333 citation statements)

References 76 publications

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“…Next, as follows from the budget equations for the vertical turbulent fluxes, the velocity scale characterising vertical turbulent transports is determined as the root mean square (r.m.s.) vertical velocity T Weng and Taylor (2003), and Umlauf and Burchard (2005).…”

Section: T Lmentioning

confidence: 99%

Energy- and flux-budget (EFB) turbulence closure model for stably stratified flows. Part I: steady-state, homogeneous regimes

Zilitinkevich

Elperin

Kleeorin

et al. 2007

Boundary-Layer Meteorol

173

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We propose a new turbulence closure model based on the budget equations for the key second moments: turbulent kinetic and potential energies: TKE and TPE (comprising the turbulent total energy: TTE = TKE + TPE) and vertical turbulent fluxes of momentum and buoyancy (proportional to potential temperature). Besides the concept of TTE, we take into account the non-gradient correction to the traditional buoyancy flux formulation. The proposed model grants the existence of turbulence at any gradient Richardson number, Ri. Instead of its critical value separating -as usually assumed -the turbulent and the laminar regimes, it reveals a transition interval, 0.1< Ri <1, which separates two regimes of essentially different nature but both turbulent: strong turbulence at Ri<<1; and weak turbulence, capable of transporting momentum but much less efficient in transporting heat, at Ri>1. Predictions from this model are consistent with available data from atmospheric and lab experiments, direct numerical simulation (DNS) and large-eddy simulation (LES).

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Section: T Lmentioning

confidence: 99%

Energy- and flux-budget (EFB) turbulence closure model for stably stratified flows. Part I: steady-state, homogeneous regimes

Zilitinkevich

Elperin

Kleeorin

et al. 2007

Boundary-Layer Meteorol

173

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show abstract

“…Unfortunately, the resulting second order closure seems to be inconsistent with the variety of boundary-layer data, and many authors took the liberty to introduce additional fitting parameters and sometimes fitting functions to achieve a better agreement with the data (see reviews of Umlauf and Burchard (2005) (Cheng et al, 2002;Canuto, 2002). …”

Section: Dept Of Chemical Physics the Weizmann Institute Of Sciencementioning

confidence: 99%

“…In this paper we consider the description of stably stratified turbulent boundary layers (TBL), taking as an example the case of stable thermal stratification. Since the 50's of twentieth century, traditional models of stratified TBL generalize models of unstratified TBL, based on the budget equations for the kinetic energy and mechanical momentum; see reviews of Umlauf and Burchard (2005), Weng and Taylor (2003). The main difficulty is that the budget equations are not closed; they involve turbulent fluxes of mechanical moments τ ij (known as the "Reynolds stress" tensor) and a thermal flux F (for the case of thermal stratification):…”

Section: Dept Of Chemical Physics the Weizmann Institute Of Sciencementioning

confidence: 99%

Energy conservation and second-order statistics in stably stratified turbulent boundary layers

2008

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We address the dynamical and statistical description of stably stratified turbulent boundary layers with the important example of the atmospheric boundary layer with a stable temperature stratification in mind. Traditional approaches to this problem, based on the profiles of mean quantities, velocity second-order correlations, and dimensional estimates of the turbulent thermal flux run into a well known difficulty, predicting the suppression of turbulence at a small critical value of the Richardson number, in contradiction with observations. Phenomenological attempts to overcome this problem suffer from various theoretical inconsistencies. Here we present an approach taking into full account all the second-order statistics, which allows us to respect the conservation of total mechanical energy. The analysis culminates in an analytic solution of the profiles of all mean quantities and all second-order correlations removing the unphysical predictions of previous theories. We propose that the approach taken here is sufficient to describe the lower parts of the atmospheric boundary layer, as long as the Richardson number does not exceed an order of unity. For much higher Richardson numbers the physics may change qualitatively, requiring careful consideration of the potential Kelvin-Helmoholtz waves and their interaction with the vortical turbulence. * Electronic address: oleksii@wisemail.weizmann.ac.il

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“…Unfortunately, the resulting second-order closure seems to be inconsistent with the variety of boundary-layer data, and many authors took the liberty to introduce additional fitting parameters and sometimes fitting functions to achieve better agreement with the data (see reviews of Umlauf and Burchard (2005), Weng and Taylor (2003), Zeman (1981), Mellor and Yamada (1974)) and references cited therein). Moreover, in the second-order closures the problem of critical Richardson number seems to persist (Canuto 2002, Cheng et al 2002.…”

Section: Introductionmentioning

confidence: 99%

“…Here, we consider the description of stably stratified turbulent boundary layers (TBL), taking as an example the case of stable thermal stratification. Since the 1950s of the twentieth century, traditional models of stratified TBL generalize models of unstratified TBL, based on the budget equations for the kinetic energy and mechanical momentum; see reviews of Umlauf and Burchard (2005) and Weng and Taylor (2003). The main difficulty is that the budget equations are not closed; they involve turbulent fluxes of mechanical moments τ i j (known as the 'Reynolds stress' tensor) and a thermal flux F (for the case of thermal stratification):…”

Section: Introductionmentioning

confidence: 99%

Turbulent fluxes in stably stratified boundary layers

L’vov¹,

Procaccia²,

Rudenko³

2008

Phys. Scr.

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We present here an extended version of an invited talk we gave at the international conference 'Turbulent Mixing and Beyond'. The dynamical and statistical description of stably stratified turbulent boundary layers with the important example of the stable atmospheric boundary layer in mind is addressed. Traditional approaches to this problem, based on the profiles of mean quantities, velocity second-order correlations and dimensional estimates of the turbulent thermal flux, run into a well-known difficulty, predicting the suppression of turbulence at a small critical value of the Richardson number, in contradiction to observations. Phenomenological attempts to overcome this problem suffer from various theoretical inconsistencies. Here, we present an approach taking into full account all the second-order statistics, which allows us to respect the conservation of total mechanical energy. The analysis culminates in an analytic solution of the profiles of all mean quantities and all second-order correlations, removing the unphysical predictions of previous theories. We propose that the approach taken here is sufficient to describe the lower parts of the atmospheric boundary layer, as long as the Richardson number does not exceed an order of unity. For much higher Richardson numbers, the physics may change qualitatively, requiring careful consideration of the potential Kelvin-Helmoholtz waves and their interaction with the vortical turbulence.

show abstract

Second-order turbulence closure models for geophysical boundary layers. A review of recent work

Cited by 379 publications

References 76 publications

Energy- and flux-budget (EFB) turbulence closure model for stably stratified flows. Part I: steady-state, homogeneous regimes

Energy- and flux-budget (EFB) turbulence closure model for stably stratified flows. Part I: steady-state, homogeneous regimes

Energy conservation and second-order statistics in stably stratified turbulent boundary layers

Turbulent fluxes in stably stratified boundary layers

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