The Height Correction of Similarity Functions in the Stable Boundary Layer

Sorbjan, Zbigniew

doi:10.1007/s10546-011-9653-x

Cited by 25 publications

(31 citation statements)

References 14 publications

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“…5a, b. As pointed out by Sorbjan (2011), this result can be understood as an extension of the Monin-Obukhov similarity formulation above the stable surface layer.…”

Section: The "Basic Set-up" Resultssupporting

confidence: 56%

“…and which were obtained from the SHEBA observations (Sorbjan 2010a,b;Sorbjan and Grachev 2010), and verified based on the CASES-99 data (Sorbjan 2011). …”

Section: Model Equationsmentioning

confidence: 60%

“…The turbulence closure of the model follows the K-theory approach, with empirical stability functions of the Richardson number evaluated by using the SHEBA (Sorbjan 2010a,b;Sorbjan and Grachev 2010) and the CASES-99 data (Sorbjan 2011). A comparison of the SCM and results of two large-eddy simulations shows very good agreement of the considered profiles for wind velocity, temperature turbulent fluxes, and standard deviations of vertical velocity and temperature.…”

Section: Discussionmentioning

confidence: 99%

“…The "basic set" of initial conditions describes a 100-m layer, with a constant potential temperature, Θ o = 265 K; above the 100-m deep layer, the potential temperature increases according to the gradient Γ = 0.01 K m −1 , and a prescribed surface cooling rate of C R = 0.25 K h −1 is applied for 9 h. The x-axis of the coordinate system is aligned with the geostrophic wind vector, with the geostrophic wind G set to 8 m s −1 , the Coriolis parameter f = 1.39 × 10 −4 s −1 , which corresponds to latitude ϕ = 73 • N, and z o = 0.1 m. In the above "basic set-up", the subsidence velocity w s , and the baroclinicity parameters, T x , and T y , are set to zero. For G = 8 m s −1 , f = 1.39 × 10 −4 s −1 , and for c = 2.7 × 10 −4 , suggested by Blackadar (1962), one obtains λ = 15.5 m. Based on Sorbjan (2011), this value was slightly reduced, and assumed to be equal to 12 m. For comparison, Kim and Mahrt (1992) obtained λ = 14.2 m through the use of aircraft data from three different field programs.…”

Section: Initial and Boundary Conditionsmentioning

confidence: 99%

“…Specifically, the standard deviations of the vertical velocity and temperature can be estimated based on the following gradient-based similarity expressions, and valid in the range Ri < 0.7 (Sorbjan 2010a,b;Sorbjan 2011):…”

Section: Diagnostic Equationsmentioning

confidence: 99%

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A Study of the Stable Boundary Layer Based on a Single-Column K-Theory Model

Sorbjan

2011

Boundary-Layer Meteorol

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We document numerical experiments with a single-column, high-resolution model of the stable boundary layer. The model resolves the logarithmic layer, and does not require inverting the Monin-Obukhov similarity functions in order to calculate the surface fluxes. The turbulence closure is based on the K-theory approach, with a new form of stability functions of the Richardson number, evaluated by using the Surface Heat Budget of the Arctic Ocean (SHEBA) and the Cooperative Atmosphere-Surface Exchange Study (CASES-99) data. A comparison with two, high-resolution large-eddy simulation models shows very good agreement. The reported numerical experiments test the effects of shear, surface cooling, the Coriolis parameter, subsidence, and baroclinicity. The time evolution of the drag coefficient, the heat-transfer coefficient, and the cross-isobar angle is also evaluated.

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“…5a, b. As pointed out by Sorbjan (2011), this result can be understood as an extension of the Monin-Obukhov similarity formulation above the stable surface layer.…”

Section: The "Basic Set-up" Resultssupporting

confidence: 56%

“…and which were obtained from the SHEBA observations (Sorbjan 2010a,b;Sorbjan and Grachev 2010), and verified based on the CASES-99 data (Sorbjan 2011). …”

Section: Model Equationsmentioning

confidence: 60%

Section: Discussionmentioning

confidence: 99%

Section: Initial and Boundary Conditionsmentioning

confidence: 99%

Section: Diagnostic Equationsmentioning

confidence: 99%

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A Study of the Stable Boundary Layer Based on a Single-Column K-Theory Model

Sorbjan

2011

Boundary-Layer Meteorol

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Similarity theory based on the Dougherty–Ozmidov length scale

Grachev

Andreas

Fairall

et al. 2014

Quart J Royal Meteoro Soc

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Local similarity theory is suggested based on the Brunt-Vaisala frequency and the dissipation rate of turbulent kinetic energy instead the turbulent fluxes used in the traditional Monin-Obukhov similarity theory. Based on dimensional analysis (Pi theorem), it is shown that any properly scaled statistics of the small-scale turbulence are universal functions of a stability parameter defined as the ratio of a reference height z and the Dougherty-Ozmidov length scale which in the limit of z-less stratification is linearly proportional to the Obukhov length scale. Measurements of atmospheric turbulence made at five levels on a 20-m tower over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are used to examine the behaviour of different similarity functions in the stable boundary layer. It is found that in the framework of this approach the non-dimensional turbulent viscosity is equal to the gradient Richardson number whereas the non-dimensional turbulent thermal diffusivity is equal to the flux Richardson number. These results are a consequence of the approximate local balance between production of turbulence by the mean flow shear and viscous dissipation. The turbulence framework based on the Brunt-Vaisala frequency and the dissipation rate of turbulent kinetic energy may have practical advantages for estimating turbulence when the fluxes are not directly available.Comment: Manuscript submitted to Quarterly Journal of the Royal Meteorological Society (04 April 2014

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Similarity scaling systems for stably stratified turbulent flows

Sorbjan

2015

Quart J Royal Meteoro Soc

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The article discusses the gradient‐based similarity theory in stably stratified turbulent flows. Gradient‐based similarity scales are classified into two categories, referred to as explicit and implicit. The explicit scaling employs the length scale as a specified function of height above the underlying surface. Within the implicit type, the length scale is locally related to various moments of turbulence. The form of the gradient‐based similarity functions, for the three considered implicit scaling systems, is obtained by the renormalization of explicit‐type expressions. Similarity functions for the dissipation‐type scaling are compared with data obtained during the SHEBA experiment in the Arctic surface layer. Since the implicit approach is not directly dependent on height, it can be applied not only in the stable boundary layer, but also in other stably stratified turbulent flows in the upper atmosphere, in lakes, and in oceans.

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The Height Correction of Similarity Functions in the Stable Boundary Layer

Cited by 25 publications

References 14 publications

A Study of the Stable Boundary Layer Based on a Single-Column K-Theory Model

A Study of the Stable Boundary Layer Based on a Single-Column K-Theory Model

Similarity theory based on the Dougherty–Ozmidov length scale

Similarity scaling systems for stably stratified turbulent flows

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