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On the vertical velocity in an isentropic layer
Author(s) -
Verkley W. T. M.
Publication year - 2000
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.49712656213
Subject(s) - isentropic process , hydrostatic equilibrium , material derivative , mechanics , conservation of mass , physics , primitive equations , atmosphere (unit) , hydrostatic pressure , classical mechanics , geology , meteorology , mathematics , mathematical analysis , partial differential equation , quantum mechanics , numerical partial differential equations
We investigate the dynamics of an isentropic layer of air, governed by the hydrostatic primitive equations. In such a layer the horizontal velocity is independent of height if this is assumed to be the case at some initial time. From the mass‐conservation equation in pressure coordinates it follows that ω, the material derivative of the pressure, varies linearly with pressure. From the mass‐conservation equation in height coordinates the vertical velocity ω is obtained. The resulting expression is shown to be in accordance with Richardson's equation for the vertical velocity in a general hydrostatic atmosphere, when particularized to an isentropic layer.