scholarly journals Momentum Flux and Flux Divergence of Gravity Waves in Directional Shear Flows over Three-Dimensional Mountains

2012 ◽  
Vol 69 (12) ◽  
pp. 3733-3744 ◽  
Author(s):  
Xin Xu ◽  
Yuan Wang ◽  
Ming Xue
Keyword(s):  
Gravity Waves ◽  
Momentum Flux ◽  
Numerical Models ◽  
Surface Wind ◽  
Vertical Shear ◽  
Mean Flow ◽  
Turning Angle ◽  
Maximum Wind ◽  
Vertical Divergence ◽  
Wave Momentum

Abstract Linear mountain wave theory is used to derive the general formulas of the gravity wave momentum flux (WMF) and its vertical divergence that develop in directionally sheared flows with constant vertical shear. Height variations of the WMF and its vertical divergence are studied for a circular bell-shaped mountain. The results show that the magnitude of the WMF decreases with height owing to variable critical-level height for different wave components. This leads to continuous—rather than abrupt—absorption of surface-forced gravity waves, and the rate of absorption is largely determined by the maximum turning angle of the wind with height. For flows turning substantially with height, the wave momentum is primarily trapped in the lower atmosphere. Otherwise, it can be transported to the upper levels. The vertical divergence of WMF is oriented perpendicularly to the right (left) of the mean flow that veers (backs) with height except at the surface, where it vanishes. First, the magnitude of the WMF divergence increases with height until reaching its peak value. Then, it decreases toward zero above that height. The altitude of peak WMF divergence is proportional to the surface wind speed and inversely proportional to the vertical wind shear magnitude, increasing as the maximum wind turning angle increases. The magnitude of the peak WMF divergence also increases with the maximum wind turning angle, but it in general decreases as the ambient flow Richardson number increases. Implications of the findings for treating mountain gravity waves in numerical models are discussed.

The Influence of Vertical Wind Shear on the Evolution of Mountain-Wave Momentum Flux

2019 ◽  
Vol 76 (3) ◽  
pp. 749-756 ◽  
Author(s):  
Dale R. Durran ◽  
Maximo Q. Menchaca
Keyword(s):  
Momentum Flux ◽  
Large Scale ◽  
Vertical Wind Shear ◽  
Vertical Shear ◽  
Mean Flow ◽  
Mountain Wave ◽  
Flow Acceleration ◽  
Momentum Fluxes ◽  
Vertically Propagating ◽  
Wave Momentum

Abstract The influence of vertical shear on the evolution of mountain-wave momentum fluxes in time-varying cross-mountain flows is investigated by numerical simulation and analyzed using ray tracing and the WKB approximation. The previously documented tendency of momentum fluxes to be strongest during periods of large-scale cross-mountain flow acceleration can be eliminated when the cross-mountain wind increases strongly with height. In particular, the wave packet accumulation mechanism responsible for the enhancement of the momentum flux during periods of cross-mountain flow acceleration is eliminated by the tendency of the vertical group velocity to increase with height in a mean flow with strong forward shear, thereby promoting vertical separation rather than concentration of vertically propagating wave packets.

scholarly journals On strongly nonlinear gravity waves in a vertically sheared atmosphere

2020 ◽  
Vol 6 (1) ◽  
pp. 63-74
Author(s):  
Mark Schlutow ◽  
Georg S. Voelker
Keyword(s):  
Gravity Waves ◽  
Lower Layer ◽  
Vertical Shear ◽  
Horizontal Wind ◽  
Necessary Condition ◽  
Mean Flow ◽  
Individual Layer ◽  
Strongly Nonlinear ◽  
The Mean ◽  
The Stability

Abstract We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same order of magnitude as the background flow and hence the self-induced mean flow alters the modulation properties to leading order. In this theoretical study, we show that the stability of such a refracted wave depends on the classical modulation stability criterion for each individual layer, above and below the shearing. Additionally, the stability is conditioned by novel instability criteria providing bounds on the mean-flow horizontal wind and the amplitude of the wave. A necessary condition for instability is that the mean-flow horizontal wind in the upper layer is stronger than the wind in the lower layer.

scholarly journals Ageostrophic instability in rotating, stratified interior vertical shear flows

2014 ◽  
Vol 755 ◽  
pp. 397-428 ◽  
Author(s):  
Peng Wang ◽  
James C. McWilliams ◽  
Claire Ménesguen
Keyword(s):  
Energy Source ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Gravity Waves ◽  
Shear Flows ◽  
Vertical Shear ◽  
Mean Flow ◽  
Efficient Energy Transfer ◽  
The Mean ◽  
Inertia Gravity Waves

AbstractThe linear instability of several rotating, stably stratified, interior vertical shear flows $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\overline{U}(z)$ is calculated in Boussinesq equations. Two types of baroclinic, ageostrophic instability, AI1 and AI2, are found in odd-symmetric $\overline{U}(z)$ for intermediate Rossby number ($\mathit{Ro}$). AI1 has zero frequency; it appears in a continuous transformation of the unstable mode properties between classic baroclinic instability (BCI) and centrifugal instability (CI). It begins to occur at intermediate $\mathit{Ro}$ values and horizontal wavenumbers ($k,l$) that are far from $l= 0$ or $k = 0$, where the growth rate of BCI or CI is the strongest. AI1 grows by drawing kinetic energy from the mean flow, and the perturbation converts kinetic energy to potential energy. The instability AI2 has inertia critical layers (ICL); hence it is associated with inertia-gravity waves. For an unstable AI2 mode, the coupling is either between an interior balanced shear wave and an inertia-gravity wave (BG), or between two inertia-gravity waves (GG). The main energy source for an unstable BG mode is the mean kinetic energy, while the main energy source for an unstable GG mode is the mean available potential energy. AI1 and BG type AI2 occur in the neighbourhood of $A-S= 0$ (a sign change in the difference between absolute vertical vorticity and horizontal strain rate in isentropic coordinates; see McWilliams et al., Phys. Fluids, vol. 10, 1998, pp. 3178–3184), while GG type AI2 arises beyond this condition. Both AI1 and AI2 are unbalanced instabilities; they serve as an initiation of a possible local route for the loss of balance in 3D interior flows, leading to an efficient energy transfer to small scales.

Characterization of Momentum Transport Associated with Organized Moist Convection and Gravity Waves

2010 ◽  
Vol 67 (10) ◽  
pp. 3208-3225 ◽  
Author(s):  
Todd P. Lane ◽  
Mitchell W. Moncrieff
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Tropical Convection ◽  
Momentum Transport ◽  
Moist Convection ◽  
Convective Systems ◽  
Convective Momentum Transport ◽  
Convective Organization ◽  
Wave Momentum

Abstract Tropical convection is inherently multiscalar, involving complex fields of clouds and various regimes of convective organization ranging from small disorganized cumulus up to large organized convective clusters. In addition to being a crucial component of the atmospheric water cycle and the global heat budget, tropical convection induces vertical fluxes of horizontal momentum. There are two main contributions to the momentum transport. The first resides entirely in the troposphere and is due to ascent, descent, and organized circulations associated with precipitating convective systems. The second resides in the troposphere, stratosphere, and farther aloft and is caused by vertically propagating gravity waves. Both the convective momentum transport and the gravity wave momentum flux must be parameterized in general circulation models; yet in existing parameterizations, these two processes are treated independently. This paper examines the relationship between the convective momentum transport and convectively generated gravity wave momentum flux by utilizing idealized simulations of multiscale tropical convection in different wind shear conditions. The simulations produce convective systems with a variety of regimes of convective organization and therefore different convective momentum transport properties and gravity wave spectra. A number of important connections are identified, including a consistency in the sign of the momentum transports in the lower troposphere and stratosphere that is linked to the generation of gravity waves by tilted convective structures. These results elucidate important relationships between the convective momentum transport and the gravity wave momentum flux that will be useful for interlinking their parameterization in the future.

Application of the IDEMIX Concept for Internal Gravity Waves in the Atmosphere

2020 ◽  
Vol 77 (10) ◽  
pp. 3601-3618
Author(s):  
B. Quinn ◽  
C. Eden ◽  
D. Olbers
Keyword(s):  
Energy Balance ◽  
Wave Field ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Middle Atmosphere ◽  
Internal Gravity Waves ◽  
Wave Drag ◽  
Mean Flow ◽  
The Mean

AbstractThe model Internal Wave Dissipation, Energy and Mixing (IDEMIX) presents a novel way of parameterizing internal gravity waves in the atmosphere. IDEMIX is based on the spectral energy balance of the wave field and has previously been successfully developed as a model for diapycnal diffusivity, induced by internal gravity wave breaking in oceans. Applied here for the first time to atmospheric gravity waves, integration of the energy balance equation for a continuous wave field of a given spectrum, results in prognostic equations for the energy density of eastward and westward gravity waves. It includes their interaction with the mean flow, allowing for an evolving and local description of momentum flux and gravity wave drag. A saturation mechanism maintains the wave field within convective stability limits, and a closure for critical-layer effects controls how much wave flux propagates from the troposphere into the middle atmosphere. Offline comparisons to a traditional parameterization reveal increases in the wave momentum flux in the middle atmosphere due to the mean-flow interaction, resulting in a greater gravity wave drag at lower altitudes. Preliminary validation against observational data show good agreement with momentum fluxes.

scholarly journals Momentum Flux Spectrum of Convectively Forced Internal Gravity Waves and Its Application to Gravity Wave Drag Parameterization. Part I: Theory

2005 ◽  
Vol 62 (1) ◽  
pp. 107-124 ◽  
Author(s):  
In-Sun Song ◽  
Hye-Yeong Chun
Keyword(s):  
Gravity Waves ◽  
Momentum Flux ◽  
Three Dimensional ◽  
Internal Gravity Waves ◽  
Buoyancy Frequency ◽  
Spectral Structure ◽  
Two Dimensional ◽  
Resonance Factor ◽  
Flux Spectrum ◽  
Wave Momentum

Abstract The phase-speed spectrum of momentum flux by convectively forced internal gravity waves is analytically formulated in two- and three-dimensional frameworks. For this, a three-layer atmosphere that has a constant vertical wind shear in the lowest layer, a uniform wind above, and piecewise constant buoyancy frequency in a forcing region and above is considered. The wave momentum flux at cloud top is determined by the spectral combination of a wave-filtering and resonance factor and diabatic forcing. The wave-filtering and resonance factor that is determined by the basic-state wind and stability and the vertical configuration of forcing restricts the effectiveness of the forcing, and thus only a part of the forcing spectrum can be used for generating gravity waves that propagate above cumulus clouds. The spectral distribution of the wave momentum flux is largely determined by the wave-filtering and resonance factor, but the magnitude of the momentum flux varies significantly according to spatial and time scales and moving speed of the forcing. The wave momentum flux formulation in the two-dimensional framework is extended to the three-dimensional framework. The three-dimensional momentum flux formulation is similar to the two-dimensional one except that the wave propagation in various horizontal directions and the three-dimensionality of forcing are allowed. The wave momentum flux spectrum formulated in this study is validated using mesoscale numerical model results and can reproduce the overall spectral structure and magnitude of the wave momentum flux spectra induced by numerically simulated mesoscale convective systems reasonably well.

scholarly journals Mesospheric gravity wave activity estimated via airglow imagery, multistatic meteor radar, and SABER data taken during the SIMONe–2018 campaign

2020 ◽  
Author(s):  
Fabio Vargas ◽  
Jorge L. Chau ◽  
Harikrishnan Charuvil Asokan ◽  
Michael Gerding
Keyword(s):  
Gravity Waves ◽  
Momentum Flux ◽  
Large Scale ◽  
Lower Thermosphere ◽  
Small Scale ◽  
Meteor Radar ◽  
Mean Flow ◽  
Horizontal Scale ◽  
Momentum Fluxes ◽  
Mesosphere And Lower Thermosphere

Abstract. We describe in this study the analysis of small and large horizontal scale gravity waves from datasets composed of images from multiple mesospheric nightglow emissions as well as multistatic specular meteor radar (MSMR) winds collected in early November 2018, during the SIMONe–2018 campaign. These ground-based measurements are supported by temperature and neutral density profiles from TIMED/SABER satellite in orbits near Kühlungsborn, northern Germany (54.1° N, 11.8° E). The scientific goals here include the characterization of gravity waves and their interaction with the mean flow in the mesosphere and lower thermosphere and their relationship to dynamical conditions in the lower and upper atmosphere. We obtain intrinsic parameters of small and large horizontal scale gravity waves and characterize their impact in the mesosphere region via momentum flux and flux divergence estimations. We have verified that a small percent of the detected wave events are responsible for most of the momentum flux measured during the campaign from oscillations seen in the airglow brightness and MSMR winds. From the analysis of small-scale gravity waves in airglow images, we have found wave momentum fluxes ranging from 0.38 to 24.74 m2/s2 (0.88 ± 0.73 m2/s2 on average), with a total of 586.96 m2/s2 (sum over all 362 detected waves). However, small horizontal scale waves with flux > 3 m2/s2 (11 % of the events) transport 50 % of the total measured flux. Likewise, wave events having flux > 10 m2/s2 (2 % of the events) transport 20 % of the total flux. The examination of two large-scale waves seen simultaneously in airglow keograms and MSMR winds revealed relative amplitudes > 35 %, which translates into momentum fluxes of 21.2–29.6 m/s. In terms of gravity wave–mean flow interactions, these high momentum flux waves could cause decelerations of 22–41 m/s/day (small-scale waves) and 38–43 m/s/day (large-scale waves) if breaking or dissipating within short distances in the mesosphere and lower thermosphere region. The dominant large-scale waves might be the result of secondary gravity excited from imbalanced flow in the stratosphere caused by primary wave breaking.

scholarly journals Surface Wave Effects on the Translation of Wind Stress across the Air–Sea Interface in a Fetch-Limited, Coastal Embayment

2017 ◽  
Vol 47 (8) ◽  
pp. 1921-1939 ◽  
Author(s):  
Alexander W. Fisher ◽  
Lawrence P. Sanford ◽  
Malcolm E. Scully ◽  
Steven E. Suttles
Keyword(s):  
Surface Wave ◽  
Wave Field ◽  
Chesapeake Bay ◽  
Wind Stress ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Breaking Waves ◽  
Wave Direction ◽  
Mean Flow ◽  
Surface Wave Field

AbstractThe role of surface gravity waves in structuring the air–sea momentum flux is examined in the middle reaches of Chesapeake Bay. Observed wave spectra showed that wave direction in Chesapeake Bay is strongly correlated with basin geometry. Waves preferentially developed in the direction of maximum fetch, suggesting that dominant wave frequencies may be commonly and persistently misaligned with local wind forcing. Direct observations from an ultrasonic anemometer and vertical array of ADVs show that the magnitude and direction of stress changed across the air–sea interface, suggesting that a stress divergence occurred at or near the water surface. Using a numerical wave model in combination with direct flux measurements, the air–sea momentum flux was partitioned between the surface wave field and the mean flow. Results indicate that the surface wave field can store or release a significant fraction of the total momentum flux depending on the direction of the wind. When wind blew across dominant fetch axes, the generation of short gravity waves stored as much as 40% of the total wind stress. Accounting for the storage of momentum in the surface wave field closed the air–sea momentum budget. Agreement between the direction of Lagrangian shear and the direction of the stress vector in the mixed surface layer suggests that the observed directional difference was due to the combined effect of breaking waves producing downward sweeps of momentum in the direction of wave propagation and the straining of that vorticity field in a manner similar to Langmuir turbulence.

scholarly journals Sampling Errors in Observed Gravity Wave Momentum Fluxes from Vertical and Tilted Profiles

Atmosphere ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 57 ◽  
Author(s):  
Simon B. Vosper ◽  
Andrew N. Ross
Keyword(s):  
Gravity Waves ◽  
Sampling Error ◽  
Numerical Models ◽  
Vertical Profiles ◽  
Sampling Errors ◽  
Mountain Wave ◽  
Mountain Waves ◽  
Momentum Fluxes ◽  
Aircraft Data ◽  
Wave Momentum

Observations from radiosondes or from vertically pointing remote sensing profilers are often used to estimate the vertical flux of momentum due to gravity waves. For planar, monochromatic waves, these vertically integrated fluxes are equal to the phase averaged flux and equivalent to the horizontal averaging used to deduce momentum flux from aircraft data or in numerical models. Using a simple analytical solution for two-dimensional hydrostatic gravity waves over an isolated ridge, it is shown that this equivalence does not hold for mountain waves. For a vertical profile, the vertically integrated flux estimate is proportional to the horizontally integrated flux and decays with increasing distance of the profile location from the mountain. For tilted profiles, such as those obtained from radiosonde ascents, there is a further sampling error that increases as the trajectory extends beyond the localised wave field. The same sampling issues are seen when the effects of the Coriolis force on the gravity waves are taken into account. The conclusion of this work is that caution must be taken when using radiosondes or other vertical profiles to deduce mountain wave momentum fluxes.

Some Aspects of Great Lakes Physics of Importance to Biological and Chemical Processes

1974 ◽  
Vol 31 (5) ◽  
pp. 689-730 ◽  
Author(s):  
F. M. Boyce
Keyword(s):  
Great Lakes ◽  
Large Scale ◽  
Numerical Models ◽  
Thermal Structure ◽  
Mechanical Energy ◽  
Surface Wind ◽  
Heat Fluxes ◽  
Dynamical Structure ◽  
Mean Flow ◽  
Advection Diffusion Equation

This is a discussion of some aspects of the physical behavior of the Great Lakes written for scientists with backgrounds in disciplines other than physics. The basic physical characteristics of Great Lakes basins are summarized. These characteristics are determined by the facts that (i) the basins are closed, (ii) the basins are large enough so that the Coriolis force is an important component of their dynamics, (iii) the principal source of mechanical energy is the wind, and (iv) the basins are vertically stratified in summer. Discussion of large-scale horizontal motions includes both currents and diffusion. The advection–diffusion equation is used as a framework for a discussion which includes a summary of the basic problem confronting hydrodynamic modellers, the parameterization of turbulence phenomena in terms of mean flow variables. Vertical transfer processes are considered, notably the measurement of vertical fluxes of heat and momentum and the computation of eddy diffusion coefficients, the prediction of thermal structure in terms of net surface wind stresses and heat fluxes, and the interactions of waves, currents, and turbulence in the thermocline. The dynamical structure of the coastal zone is outlined, and the review concludes with recommendations for future work on the understanding of vertical turbulent transports, the climatology of Great Lakes coastal zones, and an operational approach to verifying and improving numerical models of lake circulation.

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