Loading...
2 results
Search Results
Now showing 1 - 2 of 2
- Resonant gravity-wave drag enhancement in linear stratified flow over mountainsPublication . Teixeira, M. A. C.; Miranda, P. M. A.; Argaín, José Luís Almaguer; Valente, M. A.High-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.
- The dependence of mountain wave reflection on the abruptness of atmospheric profile variationsPublication . Teixeira, M. A. C.; Luis Argain, JoseIt is known from geometric optics that a change in refractive index is potentially reflective if it occurs over scales much smaller than the wavelength of the incident waves. The limitations of this assumption for hydrostatic orographic gravity waves are tested here using linear theory and a method recently developed by the authors to evaluate the reflection coefficient, based on the wave drag. Two atmospheric profiles optimally suited to this method are adopted, the first with piecewise constant static stability (representative of a tropopause), and the second with constant wind speed near the surface, and a linearly decreasing wind aloft below a critical level (relevant to downslope windstorms). Both profiles consist of two atmospheric layers separated by a transition layer with controllable thickness, where the parameters vary continuously. The variation of the reflection coefficient between its maximum (for a zero-thickness transition layer) and zero, as the ratio of the thickness of the transition layer to the vertical wavelength increases, is studied systematically. The reflection coefficient attains half of its maximum for a value of this ratio of about 0.3, but its exact variation depends on the jump in static stability between the two layers in the first profile, and the Richardson number at the critical level in the second. For a stronger contrast between the two layers, the reflection coefficient is larger, but also decays to zero faster for thinner transition layers. According to these results, most atmospheric profile features perceived as discontinuities are likely to have close-to-maximum reflection coefficients, and the variation of atmospheric parameters over a sizeable fraction of the troposphere can still lead to significant wave reflection. These results seem to hold quantitatively to a good degree of approximation in moderately nonlinear flow for the first atmospheric profile, but only qualitatively for the second one.