Weakly nonlinear Prandtl model for simple slope flows

Grisogono, Branko; Jurlina, Toni; Večenaj, Željko; Güttler, Ivan

doi:10.1002/qj.2406

Cited by 20 publications

(48 citation statements)

References 74 publications

(130 reference statements)

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“…This study is independent but based on the work of Grisogono et al (2015). There it was shown that with the weakly nonlinear Prandtl model one obtains solutions with stronger near-surface stratification and weaker katabatic wind speed (with both constant and variable eddy heat conductivity).…”

Section: Introductionmentioning

confidence: 98%

“…This paper starts with the classical theoretical model of slope flows developed by Prandtl (1942), somewhat modified and verified by Defant (1949), who deployed it specifically for anabatic flow (see also Zardi and Whiteman, 2013), and an extended Prandtl model that includes weakly nonlinear effects as done in Grisogono et al (2015). It includes the standard concepts of potential, kinetic and total energy, now for katabatic and anabatic flows.…”

Section: Introductionmentioning

confidence: 99%

“…A detailed description of the extended Prandtl model is presented in Grisogono et al (2015; their Section 2). The new term that extends the original Prandtl model is presumably weak and regulated by the nonlinearity parameter ε.…”

Section: Introductionmentioning

confidence: 99%

“…The new term that extends the original Prandtl model is presumably weak and regulated by the nonlinearity parameter ε. Our approach is relatively simple and general, and may be applied to solutions of Prandtl-type models that include 3D effects (e.g., Burkholder et al, 2009;Shapiro et al, 2012), effects of the Coriolis force (e.g., Stiperski et al, 2007), time-dependent types of solutions (e.g., Zardi and Serafin, 2014), effects of vertically varying turbulent mixing coefficients (e.g., Grisogono and Oerlemans, 2001;Grisogono et al, 2015), etc. To sum up, this study combines the work of Mauritsen et al (2007) and Grisogono et al (2015), i.e., the energy concept and weak nonlinearity, respectively, to shed more light on the physics of simple slope flows.…”

Section: Introductionmentioning

confidence: 99%

“…In order to explore the sensitivity of our results to several model assumptions, we present a set of solutions where three governing parameters are perturbed: (1) the turbulent Prandtl number Pr, (2) the slope angle α, and (3) the so-called nonlinearity parameter ε as defined in Grisogono et al (2015). We will present certain characteristics of the solutions of the Prandtl model, the vertical profiles of kinetic KE, potential PE and total energy TE, and the governing terms in the total energy TE equation.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2016

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An analytic solution for time‐periodic thermally driven slope flows

Zardi

Serafin

2014

Quart J Royal Meteoro Soc

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The article examines the flow generated by time-periodic variations in surface temperature along an infinite slope in an initially unperturbed, stably stratified atmosphere at rest. Uniform boundary conditions at the surface are conducive to an along-slope parallel flow, governed by a periodically reversing local imbalance between along-slope advection and slope-normal fluxes of momentum and heat. It is shown that solutions include both a transient part and a periodic regime and that three different flow regimes may occur. The properties of the solutions in each regime are examined and discussed, outlining novelties with respect to previously known results.

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On the turbulence structure of deep katabatic flows on a gentle mesoscale slope

Stiperski

Holtslag

Lehner

et al. 2020

Quart J Royal Meteoro Soc

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A comprehensive analysis of the turbulence structure of relatively deep midlatitude katabatic flows (with jet maxima between 20 and 50 m) developing over a gentle (1 • ) mesoscale slope with a long fetch upstream of the Meteor Crater in Arizona is presented. The turbulence structure of flow below the katabatic jet maximum shows many similarities with the turbulence structure of shallower katabatic flows, with decreasing turbulence fluxes with height and almost constant turbulent Prandtl number. Still stark differences occur above the jet maximum where turbulence is suppressed by strong stability, is anisotropic and there is a large sub-mesoscale contribution to the flux. Detecting the stable boundary-layer top depends on the method used (flux-vs. anisotropy-profiles) but both methods are highly correlated. The top of the stable boundary layer, however, mostly deviates from the jet maximum height or the top of the near-surface inversion. The flat-terrain formulations for the boundary-layer height correlate well with the detected top of the stable boundary layer if the near-surface and not the background stratification is used in their formulations; however, they mostly largely overestimate this boundary-layer height. The difference from flat-terrain boundary layers is also shown through the dependence of size of the dominant eddy with height. In katabatic flows the eddy size is semi-constant with height throughout the stable boundary-layer depth, whereas in flat terrain, eddy size varies significantly with height. Flux-gradient and flux-variance relationships show that turbulence data from different stable boundary-layer scaling regimes collapse on top of each other showing that the dominant dependence is not on the scaling regime but on the local stability. K E Y W O R D S boundary-layer depth, low-level jet, scaling regimes, stable boundary layer This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Weakly nonlinear Prandtl model for simple slope flows

Cited by 20 publications

References 74 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

An analytic solution for time‐periodic thermally driven slope flows

On the turbulence structure of deep katabatic flows on a gentle mesoscale slope

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