Zahlentheorie

Leutbecher, Armin

doi:10.1007/978-3-642-61405-7

Cited by 6 publications

(9 citation statements)

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“…Clark and Peltier 1984), the difference is too large (0.48), but that study used a hyperbolic-tangent wind profile, where the relation between z 1 and z c is harder to define. It is interesting to note that, in a model applicable to an atmosphere with discontinuous N (Leutbecher 2001), the shape of the resonant drag curves is very similar to that displayed in Fig. 1, but the maxima occur instead at exact integer values of the dimensionless height of the interface separating the layers with different N .…”

Section: (A) Linear Flow Over a 2d Ridgesupporting

confidence: 52%

“…the peaks of the curve become narrower than the troughs). This effect was also verified in the study of Leutbecher (2001). One way to estimate the width of the maxima is by determining the heights for which the drag takes the normalized value of 1.…”

Section: (A) Linear Flow Over a 2d Ridgementioning

confidence: 61%

“…In this study, the surface drag is calculated, and found to be given, for flow over a ridge, by a closed analytical formula that depends on two parameters: the height of the level where the first derivative of the wind profile is discontinuous and the Richardson number in the shear layer above. The present approach is similar to that of Leutbecher (2001) where, however, the more familiar problem of an environment with discontinuities in the Brunt-Väisälä frequency was investigated.…”

Section: Introductionmentioning

confidence: 99%

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Resonant gravity‐wave drag enhancement in linear stratified flow over mountains

Teixeira

Miranda

Argaín

et al. 2005

Quart J Royal Meteoro Soc

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SUMMARYHigh-drag states produced in stratified flow over a 2D ridge and an axisymmetric mountain are investigated using a linear, hydrostatic, analytical model. A wind profile is assumed where the background velocity is constant up to a height z 1 and then decreases linearly, and the internal gravity-wave solutions are calculated exactly. In flow over a 2D ridge, the normalized surface drag is given by a closed-form analytical expression, while in flow over an axisymmetric mountain it is given by an expression involving a simple 1D integral. The drag is found to depend on two dimensionless parameters: a dimensionless height formed with z 1 , and the Richardson number, Ri, in the shear layer. The drag oscillates as z 1 increases, with a period of half the hydrostatic vertical wavelength of the gravity waves. The amplitude of this modulation increases as Ri decreases. This behaviour is due to wave reflection at z 1 . Drag maxima correspond to constructive interference of the upward-and downward-propagating waves in the region z < z 1 , while drag minima correspond to destructive interference. The reflection coefficient at the interface z = z 1 increases as Ri decreases. The critical level, z c , plays no role in the drag amplification. A preliminary numerical treatment of nonlinear effects is presented, where z c appears to become more relevant, and flow over a 2D ridge qualitatively changes its character. But these effects, and their connection with linear theory, still need to be better understood.

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Section: (A) Linear Flow Over a 2d Ridgesupporting

confidence: 52%

Section: (A) Linear Flow Over a 2d Ridgementioning

confidence: 61%

Section: Introductionmentioning

confidence: 99%

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Resonant gravity‐wave drag enhancement in linear stratified flow over mountains

Teixeira

Miranda

Argaín

et al. 2005

Quart J Royal Meteoro Soc

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“…The measurability of S has already been observed in [7] and [18]. For the estimate (3.2) we start with the case Λ = Z D , using various constants c which depend only on D.…”

Section: Lemma 2 Let S Inmentioning

confidence: 97%

“…The versions in [6] (p. 128) or [7] (p. 294) can easily be made to yield explicit constants, and in [18] this is efficiently carried out for Λ = Z D . But in these proofs there is the danger of bringing in also the last successive minimum λ D of Λ.…”

Section: Lemma 2 Let S Inmentioning

confidence: 99%