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Linear theory of momentum fluxes in 3‐D flows with turning of the mean wind with height
Author(s) -
Broad Adrian S.
Publication year - 1995
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.49712152806
Subject(s) - physics , orography , momentum (technical analysis) , drag , flux (metallurgy) , wind stress , orographic lift , mechanics , meteorology , atmospheric sciences , precipitation , materials science , finance , economics , metallurgy
Current orographically forced gravity‐wave‐drag parametrization schemes in numerical weather‐prediction models are based on two‐dimensional linear momentum‐flux theory. the vertical flux of horizontal‐momentum vector is considered parallel to the surface‐stress vector and independent of height unless the Richardson number falls below a quarter, or a critical level exists where the mean wind becomes zero in the direction of the flux vector. Non‐zero gravity‐wave drag is then taken to be parallel and opposite to the flux vector. Consideration of the full three‐dimensional linear problem reveals a number of fundamental differences: (i) the drag force is perpendicular to the mean wind where there is no wavebreaking, and (ii) the variation of the stress vector with height is dependent on the wave‐number decomposition of the underlying orography. For a general orographic profile having a continuous Fourier spectrum spanning an azimuthal angle of 180°: (a) critical levels exist at every height in the atmosphere for any wind profile, and (b) the momentum‐flux vector decreases in magnitude and turns with height.