An analytic solution for time‐periodic thermally driven slope flows

Zardi, Dino; Serafin, Stefano

doi:10.1002/qj.2485

Cited by 22 publications

(17 citation statements)

References 31 publications

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“…This type of flow is often observed in regions of complex orography and substantially affects the weather and climate in these regions (e.g., Poulos and Zhong, 2008). The topic of katabatic and anabatic wind is being actively explored and the work on its understanding includes the application of numerical models (direct numerical simulations (DNS): (e.g., Shapiro and Fedorovich, 2008); large eddy simulations (LES): e.g., Skyllingstad, 2003;Smith and Porté-Agel, 2013); mesoscale models: (e.g., Smith and Skyllingstad, 2005;Zammett and Fowler, 2007); and analytical models (e.g., Prandtl, 1942;Defant, 1949;Grisogono and Oerlemans, 2001;Zardi and Serafin, 2014). 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.…”

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%

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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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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%

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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“…A few extensions of this model have been proposed as an attempt to introduce some additional complexity while keeping the problem mathematically tractable [90,91]. For instance, extended Prandtl models include the effects of slope curvature [92], differential heat fluxes along the slope [93], unsteady behaviour due to daily periodicity [94], and turbulent mixing in the form of a gradually varying eddy viscosity [95][96][97]. Generally speaking, none of these extensions successfully removes all of the restrictions under which the Prandtl model is valid.…”

Section: Pointwise Perspective On Upslope Windsmentioning

confidence: 99%

“…The applicability of Prandtl profiles in the case of anabatic winds is instead dramatically reduced under weakly stratified conditions, due to convective mixing [88,94,98]. The Prandtl model has already been used to quantify the mesoscale heat and mass fluxes due to slope winds [85], but further investigations are necessary in order to understand if its applicability in this context is warranted in general.…”

Section: Pointwise Perspective On Upslope Windsmentioning

confidence: 99%

Exchange Processes in the Atmospheric Boundary Layer Over Mountainous Terrain

et al. 2018

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Abstract:The exchange of heat, momentum, and mass in the atmosphere over mountainous terrain is controlled by synoptic-scale dynamics, thermally driven mesoscale circulations, and turbulence. This article reviews the key challenges relevant to the understanding of exchange processes in the mountain boundary layer and outlines possible research priorities for the future. The review describes the limitations of the experimental study of turbulent exchange over complex terrain, the impact of slope and valley breezes on the structure of the convective boundary layer, and the role of intermittent mixing and wave-turbulence interaction in the stable boundary layer. The interplay between exchange processes at different spatial scales is discussed in depth, emphasizing the role of elevated and ground-based stable layers in controlling multi-scale interactions in the atmosphere over and near mountains. Implications of the current understanding of exchange processes over mountains towards the improvement of numerical weather prediction and climate models are discussed, considering in particular the representation of surface boundary conditions, the parameterization of sub-grid-scale exchange, and the development of stochastic perturbation schemes.

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“…Under fair weather in the warm season, the meteorological conditions are dominated by characteristic thermally-driven circulations, such as valley and slope winds [39][40][41][42][43][44][45][46], which also enhance the formation of clouds over the mountain crests, while in the cold months, long-lived thermal inversions based at the valley floor are rather common [47]. Besides cloudiness, these meteorological situations deeply affect the dispersion of particulate matter and other substances [48,49], affecting atmospheric turbidity in the area [3], and hence the local climatology of global, diffuse, and beam radiation (cf.…”

Section: The Experimental Datasetmentioning

confidence: 99%

Estimating Hourly Beam and Diffuse Solar Radiation in an Alpine Valley: A Critical Assessment of Decomposition Models

et al. 2018

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Accurate solar radiation estimates in Alpine areas represent a challenging task, because of the strong variability arising from orographic effects and mountain weather phenomena. These factors, together with the scarcity of observations in elevated areas, often cause large modelling uncertainties. In the present paper, estimates of hourly mean diffuse fraction values from global radiation data, provided by a number (13) of decomposition models (chosen among the most widely tested in the literature), are evaluated and compared with observations collected near the city of Bolzano, in the Adige Valley (Italian Alps). In addition, the physical factors influencing diffuse fraction values in such a complex orographic context are explored. The average accuracy of the models were found to be around 27% and 14% for diffuse and beam radiation respectively, the largest errors being observed under clear sky and partly cloudy conditions, respectively. The best performances were provided by the more complex models, i.e., those including a predictor specifically explaining the radiation components' variability associated with scattered clouds. Yet, these models return non-negligible biases. In contrast, the local calibration of a single-equation logistical model with five predictors allows perfectly unbiased estimates, as accurate as those of the best-performing models (20% and 12% for diffuse and beam radiation, respectively), but at much smaller computational costs.

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An analytic solution for time‐periodic thermally driven slope flows

Cited by 22 publications

References 31 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

Exchange Processes in the Atmospheric Boundary Layer Over Mountainous Terrain

Estimating Hourly Beam and Diffuse Solar Radiation in an Alpine Valley: A Critical Assessment of Decomposition Models

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