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| Titel |
An analytic solution for periodic thermally-driven flows over an infinite slope |
| VerfasserIn |
Dino Zardi, Stefano Serafin |
| Konferenz |
EGU General Assembly 2013
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 15 (2013) |
| Datensatznummer |
250083905
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| Zusammenfassung |
| The flow generated along an infinite slope in an unperturbed stably stratified atmosphere at
rest by a time periodic surface temperature forcing is examined.
Following Defant (1949), a set of equations is derived which extends Prandtl’s (1942)
theory to allow for nonstationary conditions. Uniform boundary conditions 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. Solutions include
both a transient part and a subsequent periodic regime. The former can only be expressed in
an integral form, whereas the latter is a combination of exponential and sine or cosine
functions of time and height normal to the slope.
Key parameters are the quantity Nα = N sinα (where α is the slope angle, and N is the
Brunt-Väisälä frequency of the unperturbed atmosphere) and the angular frequency of the
driving surface temperature cycle, Ï. Three different flow regimes may occur, namely
subcritical (Nα < Ï), critical (Nα = Ï) and supercritical (Nα > Ï). The properties of the
solutions in each regime are examined and discussed. The relationship between the present
solutions and the earlier time-dependent slope flow model by Defant (1949) is also
discussed.
References
Defant, F., 1949: Zur Theorie der Hangwinde, nebst Bemerkungen zur Theorie der Berg-
und Talwinde. [A theory of slope winds, along with remarks on the theory of mountain winds
and valley winds]. Arch. Meteor. Geophys. Bioclimatol., Ser. A, 1, 421-450 (Theoretical and
Applied Climatology). [English translation: Whiteman, C.D., and E. Dreiseitl, 1984: Alpine
meteorology: Translations of classic contributions by A. Wagner, E. Ekhart and F. Defant.
PNL-5141 / ASCOT-84-3. Pacific Northwest Laboratory, Richland, Washington, 121
pp].
Prandtl, L., 1942: Strömungslehre [Flow Studies]. Vieweg und Sohn, Braunschweig, 382
pp. |
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