A rapid-distortion model is developed to investigate the interaction of weak turbulence with a monochromatic irrotational surface water wave. The applicable when orbital velocity wave larger than intensity, and slope sufficiently high that straining by dominates over itself. suffers two distortions. Firstly, vorticity in modulated motions, which leads streamwise Reynolds stress attaining maxima at crests minima troughs; normal free develops troughs. Secondly, several cycles Stokes drift...

The drag and momentum fluxes produced by gravity waves generated in flow over orography are reviewed, focusing on adiabatic conditions without phase transitions or radiation effects, steady mean incoming flow. orographic wave is first introduced its simplest possible form, for inviscid, linearized, non-rotating with the Boussinesq hydrostatic approximations, constant wind static stability. Subsequently, contributions made previous authors (primarily using theory numerical simulations) to...

Abstract Trapped lee waves exert frictional forces on the atmosphere which, due to small scale of orography that causes waves, must be parametrised in coarser‐resolution weather and climate models. Because scarcity situ observations, numerical model data have been used previous climatological studies trapped which necessitates evaluation. While occurrence models has evaluated a systematic manner before, their characteristics not. To this end, wavelength orientation (UK) Met Office's...

Although various lee wave trapping mechanisms have been studied theoretically since Lyra (1940), not much is known about the relative occurrence of these in real world. For this purpose, vertical atmospheric profiles associated with trapped waves are clustered here using self-organising maps.Because in-situ observations scarce, extracted from Met Office’s convective-scale UKV model (which encompasses UK and Ireland). To demonstrate that accurately represents conditions relevant to...

Abstract The drag produced by 2D orographic gravity waves trapped at a temperature inversion and propagating in the stably stratified layer existing above are explicitly calculated using linear theory, for two-layer atmosphere with neutral static stability near surface, mimicking well-mixed boundary layer. For realistic values of flow parameters, trapped-lee-wave drag, which is given closed analytical expression, comparable to propagating-wave especially moderately strongly nonhydrostatic...

Abstract The surface drag force produced by trapped lee waves and upward propagating in non‐hydrostatic stratified flow over a mountain ridge is explicitly calculated using linear theory for two‐layer atmosphere with piecewise‐constant static stability wind speed profiles. behaviour of the normalized its hydrostatic single‐layer reference value investigated as function ratio Scorer parameters two layers l 2 /l 1 corresponding dimensionless interface height H , selected values width speeds...

We have calculated the equilibrium shape of axially symmetric meniscus along which a spherical bubble contacts flat liquid surface by analytically integrating Young-Laplace equation in presence gravity, limit large Bond numbers. This method has advantage that it provides semianalytical expressions for key geometrical properties terms number. Results are good overall agreement with experimental data and consistent fully numerical (Surface Evolver) calculations. In particular, we able to...

An analytical model is developed to predict the surface drag exerted by internal gravity waves on an isolated axisymmetric mountain over which there a stratified flow with velocity profile that varies relatively slowly height. The linear respect perturbations induced mountain, and solves Taylor–Goldstein equation variable coefficients using Wentzel–Kramers–Brillouin (WKB) approximation, formally valid for high Richardson numbers, Ri. WKB solution extended higher order than in previous...

Abstract The direct impact of mountain waves on the atmospheric circulation is due to deposition wave momentum at critical levels, or levels where break. first process treated analytically in this study within framework linear theory. variation flux with height investigated for relatively large shears, extending authors’ previous calculations surface gravity drag whole atmosphere. A Wentzel–Kramers–Brillouin (WKB) approximation used treat inviscid, steady, nonrotating, hydrostatic flow...

Abstract The characteristics of the boundary layer separating a turbulence region from an irrotational (or non-turbulent) flow are investigated using rapid distortion theory (RDT). is approximated as homogeneous and isotropic far away bounding turbulent/non-turbulent (T/NT) interface, which assumed to remain approximately flat. Inviscid effects resulting continuity normal velocity pressure at in addition viscous tangential shear stress, taken into account by considering sudden insertion T/NT...

Abstract Mountain-wave turbulence in the presence of directional wind shear over Rocky Mountains Colorado is investigated. Pilot reports (PIREPs) are used to select cases which moderate or severe encounters were reported combination with significant upstream sounding from Grand Junction, (GJT). For a selected case, semi-idealized numerical simulations carried out using WRF-ARW atmospheric model, initialized GJT and realistic but truncated orography profile. To isolate role causing wave...

The rapid-distortion model of Hunt & Graham (1978) for the initial distortion turbulence by a flat boundary is extended to account fully viscous processes. Two types are considered: solid wall and free surface. shown be formally valid provided two conditions satisfied. first condition that time short compared with decorrelation energy-containing eddies, so nonlinear processes can neglected. second layer near boundary, where tangential motions adjust condition, thin scales smallest...

Abstract An analytical model of orographic gravity wave drag due to sheared flow past elliptical mountains is developed. The extends the domain applicability well‐known Phillips wind profiles that vary relatively slowly in vertical, so they may be treated using a WKB approximation. illustrates how linear processes associated with profile shear and curvature affect force exerted by airflow on mountains, it crucial extend approximation second order small perturbation parameter for these...

Abstract Internal gravity waves generated in two-layer stratified shear flows over mountains are investigated here using linear theory and numerical simulations. The impact on the wave drag of wind profiles with constant unidirectional or directional up to a certain height zero above, without critical levels, is evaluated. This kind profile, which more realistic than extending indefinitely assumed many analytical studies, leads important modifications behavior due reflection at discontinuity...

A model for estimating the turbulent kinetic energy dissipation rate in oceanic boundary layer, based on insights from rapid‐distortion theory, is presented and tested. This provides a possible explanation very high levels found by numerous authors near surface. It conceived that turbulence, injected into water breaking waves, subsequently amplified due to its distortion mean shear of wind‐induced current straining Stokes drift surface waves. The partition stress shear‐induced part...

Abstract The analytical model proposed by Teixeira, Miranda, and Valente is modified to calculate the gravity wave drag exerted a stratified flow over 2D mountain ridge. found be more strongly affected vertical variation of background velocity than for an axisymmetric mountain. In hydrostatic approximation, corrections due this effect do not depend on detailed shape ridge as long exactly 2D. Besides drag, all perturbed quantities at surface, including pressure, may calculated analytically.

Abstract High‐drag states produced in stratified flow over a 2D ridge and an axisymmetric mountain are investigated using linear, hydrostatic, analytical model. A wind profile is assumed where the background velocity constant up to height z 1 then decreases linearly, internal gravity‐wave solutions calculated exactly. In ridge, normalized surface drag given by closed‐form expression, while it expression involving simple 1D integral. The found depend on two dimensionless parameters: formed...

We have studied a single vertical, two-dimensional liquid bridge spanning the gap between two flat, horizontal solid substrates of given wettabilities. For this simple geometry, Young–Laplace equation can be solved (quasi-)analytically to yield equilibrium shape under gravity. establish range widths (as described by Bond number ) for which exist, contact angles at top and bottom ( , respectively). In particular, we find that absolute maximum span is four capillary lengths, ; whereas no form,...

Mountain wave breaking, and the resulting potential for generation of turbulence in atmosphere, are investigated using numerical simulations idealized, nearly hydrostatic, atmospheric flows with directional wind shear over an axisymmetric isolated mountain. These simulations, which use WRF‐ARW model, differ degree flow nonlinearity intensity, quantified through dimensionless mountain height Richardson number incoming flow, respectively. The aim is to diagnose breaking based on large‐scale...

Abstract The momentum transport by orographic gravity waves (OGWs) plays an important role in driving the large-scale circulation throughout atmosphere and is subject to parameterization numerical models. Current schemes, which were originally developed for coarse-resolution models, commonly assume that unresolved OGWs are hydrostatic. With increase horizontal resolution of state-of-the-art smaller scale more influenced nonhydrostatic effects (NHE), thus challenging use hydrostatic...

In turbulent free shear flows such as jets and wakes, also in boundary layers, the region is bounded by a of irrotational flow where magnitude potential velocity fluctuations can be very high. This particularly true close to turbulent-nonturbulent interface layer (TNTI) that separates regions (rotational) nonturbulent (irrotational) fluid motion these flows. Previous works have shown for distances from TNTI x_{2} much bigger than integral scale L nearby (x_{2}≫L), variance 〈u_{i}^{2}〉...