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On the consistency between dynamical and thermodynamic equations with prescribed vertical motion in an analytical tropical cyclone model
Author(s) -
Kieu Chanh Q.,
Zhang DaLin
Publication year - 2010
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.671
Subject(s) - consistency (knowledge bases) , tropical cyclone , momentum (technical analysis) , horizontal and vertical , equations of motion , primitive equations , thermal wind , motion (physics) , nonlinear system , meteorology , mathematics , geology , mechanics , physics , classical mechanics , wind speed , simultaneous equations , wind shear , geodesy , geometry , finance , quantum mechanics , economics
In our earlier paper, we presented an analytical model for intensifying tropical cyclones (TCs), in which the effects of all nonlinear terms in the horizontal momentum equations are retained. This analytical model was obtained by prescribing the time evolution of the vertical motion. In this paper, we demonstrate that, with the prescribed vertical motion, the system of governing equations for geophysical flows can be separated into two subsystems: one consisting of the horizontal momentum and continuity equations, and the other including the vertical momentum and thermodynamical equations. Results show that the analytical solutions for the horizontal winds obtained from the first subsystem are consistent with the mass field in the second subsystem, such as the thermal wind relationship in TCs. Furthermore, we show that use of any functional form for the mean vertical motion will not affect our previous major conclusions about the different growth rates either between the secondary and primary circulations or between the inner and outer regions in TCs. Copyright © 2010 Royal Meteorological Society