Teixeira, M. A. C., Argaín J. L.
It 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.
