Impact of non‐hydrostatic effects and trapped lee waves on mountain‐wave drag in directionally sheared flow

Yu, Chau Lam; Teixeira, Miguel A. C.

doi:10.1002/qj.2459

Cited by 9 publications

(7 citation statements)

References 35 publications

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“…(). Yet, two approaches are typically used to study the effects of wind and static stability vertical variations in the atmosphere on the drag: either these variations are assumed to be infinitely abrupt (Leutbecher, ; Teixeira et al ., ; ), or they are assumed to be so slow that no wave reflections can occur (VanZandt and Fritts, ; Teixeira and Miranda, ; Yu and Teixeira, ). Since reality is somewhere in between, it is worthwhile assessing the limitations of these assumptions.…”

Section: Discussionmentioning

confidence: 99%

“…They assumed that there are abrupt variations of the wind shear and/or static stability at discrete levels. In the first case, only wave refraction effects are considered and wave reflections are neglected by design, whereas in the second case wave reflections are explicitly considered (Wurtele et al ., ; Durran, ; Miranda and Valente, ; Wang and Lin, ; Leutbecher, ; Teixeira et al ., ; ; Yu and Teixeira, ).…”

Section: Introductionmentioning

confidence: 99%

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The dependence of mountain wave reflection on the abruptness of atmospheric profile variations

Teixeira

Argaín

2020

Quart J Royal Meteoro Soc

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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.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The dependence of mountain wave reflection on the abruptness of atmospheric profile variations

Teixeira

Argaín

2020

Quart J Royal Meteoro Soc

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“…These almost coincide with the values of l 2 a used in Figure (except for the case with l 2 a =5, where trapped lee waves are very weak). Hence, as long as the waves are able to propagate vertically in the lower layer, they become stronger as trapped lee waves when a larger faction of them is evanescent in the upper layer, which happens when the value of l 2 a is sufficiently low (an aspect noted by Teixeira et al () and Yu and Teixeira ()). This is of course expected, since all waves would become evanescent in the upper layer (and thus trapped) in the limit

l_{2} \to 0

(but this limit is not realistic in the atmosphere).…”

Section: Resultsmentioning

confidence: 99%

Drag associated with 3D trapped lee waves over an axisymmetric obstacle in two‐layer atmospheres

Teixeira

Miranda

2017

Quart J Royal Meteoro Soc

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Mountain‐wave drag is evaluated explicitly using linear theory and verified against numerical simulations for the flow of idealized two‐layer atmospheres with piecewise‐constant stratification over an axisymmetric mountain. Static stability is either higher in the bottom layer and lower in the top layer (Scorer's atmosphere) or neutral in the bottom layer and positive in the top layer, separated by a sharp temperature inversion (Vosper's atmosphere). The drag receives contributions from long mountain waves propagating vertically in the upper layer and from short trapped lee waves propagating downstream, either in the lower layer or at the inversion. This trapped lee‐wave drag, which is typically not represented in parametrizations, acts on the atmosphere at low levels. As in flow over a 2D ridge, this drag has several maxima as a function of the height of the interface between the two layers for Scorer's atmosphere and is maximized by a marked Scorer parameter contrast between those layers. In Vosper's atmosphere, there is a single trapped lee‐wave drag maximum for Froude numbers near one, when the wind speed matches the phase speed of the dominant interfacial waves, and this drag is maximized for relatively low interface elevations, for which waves at the inversion have higher amplitude. The 3D flow geometry allows resonant wave modes to have various horizontal orientations and a continuous spectrum, forming a dispersive ‘Kelvin ship wave’ pattern, and expanding the regions in parameter space where the drag is non‐zero relative to 2D flow, but it also decreases the drag magnitude dispersively. Nevertheless, the trapped lee‐wave drag on an axisymmetric obstacle can still equal or exceed the drag associated with vertically propagating waves and the reference hydrostatic drag valid for a uniformly stratified atmosphere.

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“…This work adapts the TLM for flow profiles that vary with altitude, and studies how these variations change the interaction between the ABL flow and gravity waves. A common approach in gravity wave theory is to use a piecewise representation of the upper atmosphere, where the profiles of the stratification and the wind speed are split up in a discrete number of layers (Tolstoy, 1973;Gossard and Hooke, 1975;Baines, 1998;Smith et al, 2002;Teixeira et al, 2013;Yu and Teixeira, 2015). We generalize this approach by allowing for an arbitrarily large amount of layers, so that any atmospheric profile can be accurately analyzed.…”

Section: Introductionmentioning

confidence: 99%

Extending the applicability of a wind-farm gravity-wave model to vertically non-uniform atmospheres

Devesse

Lanzilao

Jamaer

et al. 2022

Preprint

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Abstract. Recent research suggests that atmospheric gravity waves can affect off-shore wind farm performance. A fast wind-farm boundary-layer model has been proposed to simulate the effects of these gravity waves on wind-farm operation by Allaerts and Meyers (2019). The current work extends the applicability of that model to free atmospheres in which wind and stability vary with altitude. We validate the model using reference cases from literature on mountain waves. Analysis of two reference flows shows that internal gravity wave resonance caused by the atmospheric non-uniformity can prohibit perturbations in the ABL at the wavelengths where it occurs. To determine the overall impact of the vertical variations in the atmospheric conditions on wind farm operation, we consider one year of operation of the Belgian–Dutch wind-farm cluster with the extended model. We find that this impact on individual flow cases is often of the same order of magnitude as the total flow perturbation. In 16.5 % of the analysed flows, the relative difference in upstream velocity reduction between uniform and non-uniform free atmospheres is more than 30 %. However, this impact is small when averaged over all cases. This suggests that variations in the atmospheric conditions should be taken into account when simulating wind-farm operation in specific atmospheric conditions.

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Impact of non‐hydrostatic effects and trapped lee waves on mountain‐wave drag in directionally sheared flow

Cited by 9 publications

References 35 publications

The dependence of mountain wave reflection on the abruptness of atmospheric profile variations

The dependence of mountain wave reflection on the abruptness of atmospheric profile variations

Drag associated with 3D trapped lee waves over an axisymmetric obstacle in two‐layer atmospheres

Extending the applicability of a wind-farm gravity-wave model to vertically non-uniform atmospheres

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