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- 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 importance of friction in mountain wave drag amplification by scorer parameter resonancePublication . Teixeira, M. A. C.; Argaín, José Luís Almaguer; Miranda, P. M. A.A mechanism for amplification of mountain waves, and their associated drag, by parametric resonance is investigated using linear theory and numerical simulations. This mechanism, which is active when the Scorer parameter oscillates with height, was recently classified by previous authors as intrinsically nonlinear. Here it is shown that, if friction is included in the simplest possible form as a Rayleigh damping, and the solution to the TaylorGoldstein equation is expanded in a power series of the amplitude of the Scorer parameter oscillation, linear theory can replicate the resonant amplification produced by numerical simulations with some accuracy. The drag is significantly altered by resonance in the vicinity of n/l0 = 2, where l0 is the unperturbed value of the Scorer parameter and n is the wave number of its oscillation. Depending on the phase of this oscillation, the drag may be substantially amplified or attenuated relative to its non-resonant value, displaying either single maxima or minima, or double extrema near n/l0 = 2. Both non-hydrostatic effects and friction tend to reduce the magnitude of the drag extrema. However, in exactly inviscid conditions, the single drag maximum and minimum are suppressed. As in the atmosphere friction is often small but non-zero outside the boundary layer, modelling of the drag amplification mechanism addressed here should be quite sensitive to the type of turbulence closure employed in numerical models, or to computational dissipation in nominally inviscid simulations. Copyright (c) 2012 Royal Meteorological Society
- Drag produced by trapped lee waves and propagating mountain waves in a two-layer atmospherePublication . Teixeira, M. A. C.; Argaín, José Luís Almaguer; Miranda, P. M. A.The surface drag force produced by trapped lee waves and upward propagating waves in non-hydrostatic stratified flow over a mountain ridge is explicitly calculated using linear theory for a two-layer atmosphere with piecewise-constant static stability and wind speed profiles. The behaviour of the drag normalized by its hydrostatic single-layer reference value is investigated as a function of the ratio of the Scorer parameters in the two layers l2/l1 and of the corresponding dimensionless interface height l1H, for selected values of the dimensionless ridge width l1a and ratio of wind speeds in the two layers. When l2/l1 1, the propagating wave drag approaches 1 in approximately hydrostatic conditions, and the trapped lee wave drag vanishes. As l2/l1 decreases, the propagating wave drag progressively displays an oscillatory behaviour with l1H, with maxima of increasing magnitude due to constructive interference of reflected waves in the lower layer. The trapped lee wave drag shows localized maxima associated with each resonant trapped lee wave mode, occurring for small l2/l1 and slightly higher values of l1H than the propagating wave drag maxima. As l1a decreases, i.e. the flow becomes more non-hydrostatic, the propagating wave drag decreases and the regions of non-zero trapped lee wave drag extend to higher l2/l1. These results are confirmed by numerical simulations for l2/l1 = 0.2. In parameter ranges of meteorological relevance, the trapped lee wave drag may have a magnitude comparable to that of propagating wave drag, and be larger than the reference single-layer drag. This may have implications for drag parametrization in global climate and weather-prediction models. Copyright (c) 2012 Royal Meteorological Society
- 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.