Momentum Fluxes of Gravity Waves Generated by Variable Froude Number Flow over Three-Dimensional Obstacles

2010 ◽  
Vol 67 (7) ◽  
pp. 2260-2278 ◽  
Author(s):  
Stephen D. Eckermann ◽  
John Lindeman ◽  
Dave Broutman ◽  
Jun Ma ◽  
Zafer Boybeyi
Keyword(s):  
Froude Number ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Mesoscale Model ◽  
Three Dimensional ◽  
Wave Drag ◽  
Analytical Relation ◽  
Far Field ◽  
Pressure Drag ◽  
Momentum Fluxes

Abstract Fully nonlinear mesoscale model simulations are used to investigate the momentum fluxes of gravity waves that emerge at a “far-field” height of 6 km from steady unsheared flow over both an axisymmetric and elliptical obstacle for nondimensional mountain heights ĥm = Fr−1 in the range 0.1–5, where Fr is the surface Froude number. Fourier- and Hilbert-transform diagnostics of model output yield local estimates of phase-averaged momentum flux, while area integrals of momentum flux quantify the amount of surface pressure drag that translates into far-field gravity waves, referred to here as the “wave drag” component. Estimates of surface and wave drag are compared to parameterization predictions and theory. Surface dynamics transition from linear to high-drag (wave breaking) states at critical inverse Froude numbers Frc−1 predicted to within 10% by transform relations. Wave drag peaks at Frc−1 < ĥm ≲ 2, where for the elliptical obstacle both surface and wave drag vacillate owing to cyclical buildup and breakdown of waves. For the axisymmetric obstacle, this occurs only at ĥm = 1.2. At ĥm ≳ 2–3 vacillation abates and normalized pressure drag assumes a common normalized form for both obstacles that varies approximately as ĥm−1.3. Wave drag in this range asymptotes to a constant absolute value that, despite its theoretical shortcomings, is predicted to within 10%–40% by an analytical relation based on linear clipped-obstacle drag for a Sheppard-based prediction of dividing streamline height. Constant wave drag at ĥm ∼ 2–5 arises despite large variations with ĥm in the three-dimensional morphology of the local wave momentum fluxes. Specific implications of these results for the parameterization of subgrid-scale orographic drag in global climate and weather models are discussed.

Effects of Nonlinearity on Convectively Forced Internal Gravity Waves: Application to a Gravity Wave Drag Parameterization

2008 ◽  
Vol 65 (2) ◽  
pp. 557-575 ◽  
Author(s):  
Hye-Yeong Chun ◽  
Hyun-Joo Choi ◽  
In-Sun Song
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Lower Thermosphere ◽  
Internal Gravity Waves ◽  
Wave Drag ◽  
Scale Factor ◽  
Wide Range ◽  
Flux Spectrum ◽  
Diabatic Forcing

Abstract In the present study, the authors propose a way to include a nonlinear forcing effect on the momentum flux spectrum of convectively forced internal gravity waves using a nondimensional numerical model (NDM) in a two-dimensional framework. In NDM, the nonlinear forcing is represented by nonlinear advection terms multiplied by the nonlinearity factor (NF) of the thermally induced internal gravity waves for a given specified diabatic forcing. It was found that the magnitudes of the waves and resultant momentum flux above the specified forcing decrease with increasing NF due to cancellation between the two forcing mechanisms. Using the momentum flux spectrum obtained by the NDM simulations with various NFs, a scale factor for the momentum flux, normalized by the momentum flux induced by diabatic forcing alone, is formulated as a function of NF. Inclusion of the nonlinear forcing effect into current convective gravity wave drag (GWD) parameterizations, which consider diabatic forcing alone by multiplying the cloud-top momentum flux spectrum by the scale factor, is proposed. An updated convective GWD parameterization using the scale factor is implemented into the NCAR Whole Atmosphere Community Climate Model (WACCM). The 10-yr simulation results, compared with those by the original convective GWD parameterization considering diabatic forcing alone, showed that the magnitude of the zonal-mean cloud-top momentum flux is reduced for wide range of phase speed spectrum by about 10%, except in the middle latitude storm-track regions where the cloud-top momentum flux is amplified. The zonal drag forcing is determined largely by the wave propagation condition under the reduced magnitude of the cloud-top momentum flux, and its magnitude decreases in many regions, but there are several areas of increasing drag forcing, especially in the tropical upper mesosphere and lower thermosphere.

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.

Flow past a sphere moving vertically in a stratified diffusive fluid

2000 ◽  
Vol 417 ◽  
pp. 211-236 ◽  
Author(s):  
C. R. TORRES ◽  
H. HANAZAKI ◽  
J. OCHOA ◽  
J. CASTILLO ◽  
M. VAN WOERT
Keyword(s):  
Froude Number ◽  
Rear Surface ◽  
Wave Drag ◽  
Thin Layers ◽  
Original Position ◽  
Linear Wave ◽  
Frictional Drag ◽  
Pressure Drag ◽  
Lee Wave ◽  
Vertical Jet

Numerical studies are described of the flows generated by a sphere moving vertically in a uniformly stratified fluid. It is found that the axisymmetric standing vortex usually found in homogeneous fluids at moderate Reynolds numbers (25 [les ] Re [les ] 200) is completely collapsed by stable stratification, generating a strong vertical jet. This is consistent with our experimental visualizations. For Re = 200 the complete collapse of the vortex occurs at Froude number F ≃ 19, and the critical Froude number decreases slowly as Re increases. The Froude number and the Reynolds number are here defined by F = W/Na and Re = 2Wa/v, with W being the descent velocity of the sphere, N the Brunt–Väisälä frequency, a the radius of the sphere and v the kinematic viscosity coefficient. The inviscid processes, including the generation of the vertical jet, have been investigated by Eames & Hunt (1997) in the context of weak stratification without buoyancy effects. They showed the existence of a singularity of vorticity and density gradient on the rear axis of the flow and also the impossibility of realizing a steady state. When there is no density diffusion, all the isopycnal surfaces which existed initially in front of the sphere accumulate very near the front surface because of density conservation and the fluid in those thin layers generates a rear jet when returning to its original position. In the present study, however, the fluid has diffusivity and the buoyancy effects also exist. The density diffusion prevents the extreme piling up of the isopycnal surfaces and allows the existence of a steady solution, preventing the generation of a singularity or a jet. On the other hand, the buoyancy effect works to increase the vertical velocity to the rear of the sphere by converting the potential energy to vertical kinetic energy, leading to the formation of a strong jet. We found that the collapse of the vortex and the generation of the jet occurs at much weaker stratifications than those necessary for the generation of strong lee waves, showing that jet formation is independent of the internal waves. At low Froude numbers (F [les ] 2) the lee wave patterns showed good agreement with the linear wave theory and the previous experiments by Mowbray & Rarity (1967). At very low Froude numbers (F [les ] 1) the drag on a sphere increases rapidly, partly due to the lee wave drag but mainly due to the large velocity of the jet. The jet causes a reduction of the pressure on the rear surface of the sphere, which leads to the increase of pressure drag. High velocity is induced also just outside the boundary layer of the sphere so that the frictional drag increases even more significantly than the pressure drag.

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 Consistency between Fourier transform and small-volume few-wave decomposition for spectral and spatial variability of gravity waves above a typhoon

2012 ◽  
Vol 5 (7) ◽  
pp. 1637-1651 ◽  
Author(s):  
C. I. Lehmann ◽  
Y.-H. Kim ◽  
P. Preusse ◽  
H.-Y. Chun ◽  
M. Ern ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Momentum Flux ◽  
Wide Spectrum ◽  
Three Dimensional ◽  
Phase Speed ◽  
Analysis Technique ◽  
Momentum Fluxes ◽  
Different Types ◽  
Wave Decomposition ◽  
First Time

Abstract. Convective gravity wave (GW) sources are spatially localized and emit at the same time waves with a wide spectrum of phase speeds. Any wave analysis therefore compromises between spectral and spatial resolution. Future satellite borne limb imagers will for a first time provide real 3-D volumes of observations. These volumes will be however limited which will impose further constraints on the analysis technique. In this study a three dimensional few-wave approach fitting sinusoidal waves to limited 3-D volumes is introduced. The method is applied to simulated GWs above typhoon Ewiniar and GW momentum flux is estimated from temperature fluctuations. Phase speed spectra as well as average profiles of positive, negative and net momentum fluxes are compared to momentum flux estimated by Fourier transform as well as spatial averaging of wind fluctuations. The results agree within 10–20%. The few-wave method can also reveal the spatial orientation of the GWs with respect to the source. The relevance of the results for different types of measurements as well as its applicability to model data is discussed.

scholarly journals Stratospheric Gravity Waves Generated by Typhoon Saomai (2006): Numerical Modeling in a Moving Frame Following the Typhoon

2010 ◽  
Vol 67 (11) ◽  
pp. 3617-3636 ◽  
Author(s):  
So-Young Kim ◽  
Hye-Yeong Chun
Keyword(s):  
Gravity Waves ◽  
Momentum Flux ◽  
Mesoscale Model ◽  
Horizontal Resolution ◽  
Moving Frame ◽  
Mature Stage ◽  
Small Scale ◽  
Background Wind ◽  
Spiral Bands ◽  
Typhoon Saomai

Abstract Stratospheric gravity waves generated by Typhoon Saomai (2006) were simulated using a mesoscale model in a moving frame of reference following the typhoon. Waves with large amplitudes appear near the domain center because of strong convection in the eyewall of the typhoon. Convection bands propagating outward from the storm center also generate waves propagating to the stratosphere. Convective forcing is significant in various propagation directions, with maximum power in slowly moving eastward components due to convection in the eyewall. The forcing exhibits large amplitude at a speed of 8–16 m s−1 in the eastward direction in which spiral bands are mainly developed. Induced gravity waves in the stratosphere are dominant in the eastward, northeastward, and southeastward propagation directions, since westward waves are mostly filtered by the background wind below z = 25 km. While the typhoon moves northwestward for 78 h, the wave characteristics vary through time depending on the evolution of the eyewall and spiral bands. Horizontal wavelengths of waves are longer in the mature and decaying stages than in the developing stage of the typhoon, likely because of a more dominant concentric eyewall in the mature and decaying stages. The spectral peak of the waves is at ∼20 km (∼50 km) horizontal wavelength in the developing (mature) stage, and the wave amplitudes are larger in the developing stages. The dominant contribution to the momentum flux is from waves with horizontal wavelengths longer than 80 km. Positive momentum flux decreases with overall height and the resultant positive drag can cause deceleration of northeasterly background wind. Sensitivity of the model results to horizontal resolution reveals that small-scale waves resolved in the present simulations with 3-km resolution cannot be fully represented with 9- or 27-km resolutions.

scholarly journals Consistency between Fourier transform and small-volume few-wave decomposition for spectral and spatial variability of gravity waves above a typhoon

2012 ◽  
Vol 5 (1) ◽  
pp. 1763-1793
Author(s):  
C. I. Lehmann ◽  
Y.-H. Kim ◽  
P. Preusse ◽  
H.-Y. Chun ◽  
M. Ern ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Momentum Flux ◽  
Wide Spectrum ◽  
Three Dimensional ◽  
Phase Speed ◽  
Analysis Technique ◽  
Momentum Fluxes ◽  
Different Types ◽  
Wave Decomposition ◽  
First Time

Abstract. Convective gravity wave (GW) sources are spatially localized and emit at the same time waves with a wide spectrum of phase speeds. Any wave analysis therefore compromises between spectral and spatial resolution. Future satellite borne limb imagers will for a first time provide real 3d volumes of observations. These volumes will be however limited which will impose further constraints on the analysis technique. In this study a three dimensional few-wave appoach fitting sinusoidal waves to limited 3-D volumes is introduced. The method is applied to simulated GWs above typhoon Ewiniar and GW momentum flux is estimated from temperature fluctuations. Phase speed spectra as well as average profiles of positive, negative and net momentum fluxes are compared to momentum flux estimated by Fourier transform as well as spatial averaging of wind fluctuations. The results agree within 10–20%. The few-wave method can also reveal the spatial orientation of the GWs with respect to the source. The relevance of the results for different types of measurements as well as its applicability to model data is discussed.

scholarly journals Gravity wave reflection and its influence on the consistency of temperature- and wind-based momentum fluxes simulated above Typhoon Ewiniar

2012 ◽  
Vol 12 (2) ◽  
pp. 6263-6282 ◽  
Author(s):  
Y.-H. Kim ◽  
H.-Y. Chun ◽  
P. Preusse ◽  
M. Ern ◽  
S.-Y. Kim
Keyword(s):  
Gravity Wave ◽  
Momentum Flux ◽  
Wave Reflection ◽  
Mesoscale Model ◽  
Satellite Measurements ◽  
Stability Change ◽  
Propagating Waves ◽  
Momentum Fluxes ◽  
Flux Profile

Abstract. For a case study of Typhoon Ewiniar performed with a mesoscale model, we compare stratospheric gravity wave (GW) momentum flux determined from temperature variances by applying GW polarization relations and by assuming upward propagating waves with GW momentum flux calculated from model winds, which is considered as a reference. The temperature-based momentum-flux profile exhibits positive biases which fluctuate with altitude and have peak values of 17–39% at 20–40 km. We found that this deviation stems from the interference between upward and downward propagating waves. The downward propagating GWs are due mainly to partial reflections of upward propagating waves at altitudes where the background wind and stability change with height. When the upward and downward propagating waves are decomposed and their momentum fluxes are calculated separately from temperature perturbations, the fraction of the momentum flux arising from the downward propagating waves is about 4.5–8.2%. The net momentum flux of upward and downward propagating GWs agrees well with the reference from the model wind perturbations. Global distributions of GW momentum flux can be deduced from satellite measurements of temperatures also employing GW polarization relations but using different analysis methods. The implications of this study for the GW momentum-flux observations from satellites are discussed.

Sign in / Sign up

Export Citation Format

Share Document