Scorer parameter

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Scorer parameter

The quantity l(z) arising from the wave equation for atmospheric gravity waves describing flow over a mountain barrier:
ams2001glos-Se10
where N = N(z) is the Brunt–Väisälä frequency and U = U(z) is the vertical profile of the horizontal wind, both quantities determined from an atmospheric sounding upstream of the barrier.

The first term on the right-hand side usually dominates, but occasionally the second term, the velocity-profile curvature term, can be of similar magnitude. When l2 is nearly constant with height, conditions are favorable for vertically propagating mountain waves. This parameter is most often used, however, as an indicator of when trapped lee waves (
see mountain wave) can be expected; they occur when l2(z) decreases strongly with height. This is especially true if this decrease occurs suddenly in mid troposphere, dividing the troposphere into two regions, a lower layer of large l2(z) (high stability) and an upper layer of small l2(z) (low stability). l, the square root of the parameter, has units of wavenumber (inverse length), and the wavenumber of the resonant lee wave lies between l of the upper layer and l of the lower layer—the equivalent wavelength generally lying between 5 and 25 km in the atmosphere. Mountain ranges wide enough to force wavelengths long relative to lupper (the l in the upper layer) produce vertically propagating waves with wavenumbers less than lupper. Small objects (that force wavenumbers greater than llower) produce waves that are evanescent, or vanishing with height.

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