A Boundary-Layer Scaling for Turbulent Katabatic Flow

Shapiro, Alan; Fedorovich, Evgeni

doi:10.1007/s10546-014-9933-3

Cited by 26 publications

(14 citation statements)

References 68 publications

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“…Continued interest in katabatic and anabatic winds stems from the important effects of this type of orographic flows on visibility and fog formation, air pollutant dispersion, agriculture and energy use, fire-fighting operations, sea-ice formation, etc. (e.g., Shapiro and Fedorovich, 2014, and references therein). Katabatic winds develop in stably stratified planetary boundary layers (PBLs), adding an additional level of complexity to the problem of understanding and modeling this specific type of PBLs (e.g., Mahrt, 1998;Holtslag et al, 2013;Sandu et al, 2013;Mahrt, 2014;Sun et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

Energetics of Slope Flows: Linear and Weakly Nonlinear Solutions of the Extended Prandtl Model

et al. 2016

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The Prandtl model succinctly combines the 1D stationary boundary-layer dynamics and thermodynamics of simple anabatic and katabatic flows over uniformly inclined surfaces. It assumes a balance between the along-the-slope buoyancy component and adiabatic warming/cooling, and the turbulent mixing of momentum and heat. In this study, energetics of the Prandtl model is addressed in terms of the total energy (TE) concept. Furthermore, since the authors recently developed a weakly nonlinear version of the Prandtl model, the TE approach is also exercised on this extended model version, which includes an additional nonlinear term in the thermodynamic equation. Hence, interplay among diffusion, dissipation, and temperature-wind interaction of the mean slope flow is further explored. The TE of the nonlinear Prandtl model is assessed in an ensemble of solutions where the Prandtl number, the slope angle and the nonlinearity parameter are perturbed. It is shown that nonlinear effects have the lowest impact on variability in the ensemble of solutions of the weakly nonlinear Prandtl model when compared to the other two governing parameters. The general behavior of the nonlinear solution is similar to the linear solution, except that the maximum of the along-the-slope wind speed in the nonlinear solution reduces for larger slopes. Also, the dominance of PE near the sloped surface, and the elevated maximum of KE in the linear and nonlinear energetics of the extended Prandtl model are found in the PASTEX-94 measurements. The corresponding level where KE>PE most likely marks the bottom of the sublayer subject to shear-driven instabilities. Finally, possible limitations of the weakly nonlinear solutions of the extended Prandtl model are raised. In linear solutions, the local storage of TE term is zero, reflecting the stationarity of solutions by definition. However, in nonlinear solutions, the diffusion, dissipation and interaction terms (where the height of the maximum interaction is proportional to the height of the low-level jet by the factor ≈4/9) do not balance and the local storage of TE attains nonzero values. In order to examine the issue of non-stationarity, the inclusion of velocity-pressure covariance in the momentum equation is suggested for future development of the extended Prandtl model.

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Section: Introductionmentioning

confidence: 99%

Energetics of Slope Flows: Linear and Weakly Nonlinear Solutions of the Extended Prandtl Model

et al. 2016

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“…term to the Monin-Obukhov stability parameter (3) can be also found in Horst and Doran (1988, p. 615). Note that the sign of the α sin factor in the buoyancy term in (1)-(3) depends on the direction of the along-slope axis (e.g., Shapiro and Fedorovich 2014, their…”

Section: The Tke Equation In a Slope-following Coordinate Systemmentioning

confidence: 99%

Structure of Turbulence in Katabatic Flows Below and Above the Wind-Speed Maximum

Grachev

Leo

Sabatino

et al. 2015

Boundary-Layer Meteorol

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Measurements of small-scale turbulence made in the atmospheric boundary layer over complex terrain during the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) Program are used to describe the structure of turbulence in katabatic flows. Turbulent and mean meteorological data were continuously measured on four towers deployed along the east lower slope (2-4 • ) of Granite Mountain near Salt Lake City in Utah, USA. The multi-level (up to seven) observations made during a 30-day long MATER-HORN field campaign in September-October 2012 allowed the study of temporal and spatial structure of katabatic flows in detail, and herein we report turbulence statistics (e.g., fluxes, variances, spectra, and cospectra) and their variations in katabatic flow. Observed vertical profiles show steep gradients near the surface, but in the layer above the slope jet the vertical variability is smaller. It is found that the vertical (normal to the slope) momentum flux and horizontal (along-slope) heat flux in a slope-following coordinate system change their sign below and above the wind maximum of a katabatic flow. The momentum flux is directed downward (upward) whereas the along-slope heat flux is downslope (upslope) below (above) the wind maximum. This suggests that the position of the jet-speed maximum can be obtained by linear interpolation between positive and negative values of the momentum flux (or the along-slope heat flux) to derive the height where the flux becomes zero. It is shown that the standard deviations of all wind-speed components (and therefore of the turbulent kinetic energy) and the dissipation rate of turbulent kinetic energy have a local minimum, whereas the standard deviation of air temperature has an absolute maximum at the height of wind- A. A. Grachev et al. speed maximum. We report several cases when the destructive effect of vertical heat flux is completely cancelled by the generation of turbulence due to the along-slope heat flux. Turbulence above the wind-speed maximum is decoupled from the surface, and follows the classical local z-less predictions for the stably stratified boundary layer.

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“…Interest to the study of gradient flows is maintained due to their prevalence in the environment. Under normal conditions, the perturbations are concentrated in thin layers at the impermeable surfaces and reach storm values forming large temperature gradients in the atmosphere at steep range slopes [3] and nearby glaciers [4]. In recent years, special attention is paid to the study of the influence of induced diffusion flows on the dynamics and structure of processes in the reservoirs, lakes, seas [5] and oceans, taking into account the influence of the global rotation [6].…”

Section: Introductionmentioning

confidence: 99%

Diffusion-Induced Effects in a Stratified Fluid Around a Motionless Wedge

Димитриева¹,

Chashechkin²

2018

Topical Problems of Fluid Mechanics 2018

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The paper is devoted to study continuously stratified fluid flows in field of external mass forces accounting for dissipative factors, viscosity and diffusion. The mathematical model and the numerical implementation method permitting to study simultaneously all the elements of the internally multi-scale stratified currents without additional hypotheses and links are developed on the basis of the fundamental system of equations. Criteria for the reconstruction and optimization of the grids are formulated based on the scale analysis of systems of equations. Influence edge effects upon the current structure is shown. In a stably stratified environment, the integral force inducing self-motion of a free wedge along the neutral buoyancy horizon towards the top is formed by pressure deficit in the adjacent jet streams. In accordance with the results of the experiments, the body in a stably stratified medium moves toward its top. Thin fluid jet streams, formed along each side of the wedge, generate the internal waves in the areas of convergence with the corner points. These waves form thin layers. The transformation of the disturbance field of the medium at the onset of the forced slow motion of the wedge on the neutral buoyancy horizon, the formation of the upstream perturbation, the field of internal waves, the vortices and the wake is traced. The complex structure of the fields of various physical quantities and their gradients is visualized, and the intrinsic time and spatial scales of the structural flow components are determined..

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A Boundary-Layer Scaling for Turbulent Katabatic Flow

Cited by 26 publications

References 68 publications

Energetics of Slope Flows: Linear and Weakly Nonlinear Solutions of the Extended Prandtl Model

Energetics of Slope Flows: Linear and Weakly Nonlinear Solutions of the Extended Prandtl Model

Structure of Turbulence in Katabatic Flows Below and Above the Wind-Speed Maximum

Diffusion-Induced Effects in a Stratified Fluid Around a Motionless Wedge

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