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On the use of an analytic solution in estimating eddy viscosity distribution and water vapour flux in a mature hurricane
Author(s) -
Evans H. P.,
Davies D. R.
Publication year - 1979
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49710544505
Subject(s) - mechanics , physics , momentum (technical analysis) , hydrostatic equilibrium , thermodynamics , eddy , turbulence modeling , boundary value problem , convection , turbulence , mathematical analysis , classical mechanics , mathematics , finance , quantum mechanics , economics
An analytic solution, in p coordinates, of the dynamical equations of a mature hurricane system is used to determine the p dependence of eddy viscosity coefficients for an assumed quasi‐stationary and axisymmetric phase. The solution is based on: (i) eddy viscosity coefficients K 1 and K 2 , describing respectively horizontal and vertical transfers of momentum, expressed as general functions of p ; and (ii) the premise that the radial variation of the magnitudes of the tangential and radial components of velocity are of similar form. This leads to an integral equation for the tangential velocity. Explicit expressions for K 1 and K 2 are finally obtained by choosing power law forms, in the p variable, which lead to good agreement of the tangential velocity solution with observed distributions. By using this (inverse) method of calculating K 1 and K 2 , the whole eddy system, ranging from eddies created by the very strong velocity shear close to the sea surface to those connected with violent cloud convection, is described by continuous mathematical functions. The associated temperature and condensation heating distributions are then calculated from the hydrostatic relation and the thermodynamic equation. To complete the model an integral water vapour flux condition relates the sea surface temperature to prescribed humidity conditions at the outer boundary of the model.