Open AccessOn Adding Thermodynamic Damping Mechanisms to Refine Two Classical Models of Katabatic Winds
Author(s) -
Ruping Mo
Publication year - 2013
Publication title -
journal of the atmospheric sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.853
H-Index - 173
eISSN - 1520-0469
pISSN - 0022-4928
DOI - 10.1175/jas-d-12-0256.1
Subject(s) - katabatic wind , adiabatic process , mechanics , prandtl number , physics , turbulent prandtl number , boundary layer , radiative cooling , buoyancy , classical mechanics , turbulence , thermodynamics , nusselt number , heat transfer , meteorology , reynolds number
The Prandtl and layer-averaged models of katabatic winds contain some nonphysical singularities in the analytical solutions, which give unbounded steady flow anomalies at zero slope angles or adiabatic lapse rates. This study presents some simple refinements of these two classical models, in which the aforementioned singularities are removed when Newtonian cooling and Rayleigh friction are included in the system. It is pointed out that, in the limit of zero slope angles or adiabatic lapse rates, the along-slope buoyancy force and the adiabatic heating caused by air descending approach zero. Under such circumstances, a bounded steady solution for the katabatic winds is impossible unless some damping mechanisms are included to retard the anomalies induced by the radiative cooling effect in the boundary layer. Newtonian cooling and Rayleigh friction are the two simplest thermodynamic damping mechanisms that can be included to balance the effects of eddy viscosity and eddy thermal conductivity in the katabatic-flow model. Physically speaking, the Newtonian cooling term represents a small partition of the radiative effect and the Rayleigh friction term represents an approximation of the bottom drag effect in a turbulent boundary layer.