Joint Seminar: Oscillatory flow regimes and self-similarity in numerically simulated slope winds

Slope flows (winds) play an important role in the weather of vast areas of the Earth. In terms of basic fluid dynamics, such flows are buoyantly driven motions of a stratified fluid along heated or cooled sloping surfaces. They conflate three charismatic aspects of geophysical fluid dynamics: buoyant forcing, stratification, and turbulence. It is common to distinguish between anabatic winds, which are driven by surface heating, and katabatic winds, which result from surface cooling. Many questions remain regarding the physics and properties of these flows. Of particular interest for practical applications (e.g., for modeling purposes) are parameters of slope flows as functions of the surface thermal forcing, ambient stratification, and slope angle.

Phenomenology of the slope flows will be briefly reviewed in the talk. Results of direct numerical simulations of idealized turbulent katabatic and anabatic flows will be presented and discussed with an emphasis on two specific features of the slope winds: (i) their inherently oscillatory character and (ii) their boundary-layer organization which may be particularly representative of katabatic flows along shallow slopes. In basic terms, the investigated flows are the turbulent analogs of one-dimensional laminar slope flow that was first analytically described by Ludwig Prandtl in 1942.

Long-period oscillations of velocity and buoyancy fields in natural and modeled/simulated slope flows (both anabatic and katabatic) have been extensively reported in the literature. Their frequency was found to be approximately equal to the product of the environmental Brunt-Väisälä frequency and the sine of the slope angle. However, evolution of the oscillation amplitude in time and, especially, the terminal state of oscillations remain among topics of scientific discussion. In observational studies, shortness of measurement records precludes definitive conclusions regarding the evolution of oscillations, while spurious computational effects often obscure their dynamics in numerical model/simulation exercises. In this study, the evolution of the oscillations was tracked over considerable time intervals (up to several hundreds of oscillation periods). Simulated oscillations were analyzed in terms of velocity and buoyancy integrals as functions of time in conjunction with the time evolution of the surface stress. As theoretical considerations show, this stress is the principal oscillation-damping factor. Analysis of the numerical data indicates that the slope flow system behaves as an imperfect (“dirty”) underdamped oscillator: after an initial gradual decay of the oscillation amplitude, the flow evolves into a regime characterized by intermittent, although persistent, oscillatory eruptions whose magnitude remains relatively small but essentially non-zero.

Application of the scaling analysis to the governing differential equations (and boundary conditions) of the turbulent slope flows shows that the scaled flow is fully characterized by three non-dimensional parameters: the slope angle, Prandtl number, and a dimensionless combination of viscosity, buoyancy frequency, and a surface buoyancy or buoyancy flux (this combination may be interpreted as a Reynolds number). The structure of the governing slope-flow equations in the boundary-layer form, which is hypothetically a valid approximation for a katabatic flow along a shallow slope, has been examined. For this approximate flow case, the scaling laws have been deduced that involve only two non-dimensional parameters: the Prandtl number and a modified Reynolds number. The slope angle in the scaled boundary-layer equations appears only as a factor in the modified Reynolds number and in the scales for the flow variables. The validity of the proposed scaling hypothesis is assessed using data from direct numerical simulations.




13:30 Uhr


Bundesstr. 53, room 022/023
Seminar Room 022/023, Ground Floor, Bundesstrasse 53, 20146 Hamburg, Hamburg


Evgeni Fedorovich, University of Oklahoma


Juan Pedro Mellado

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