Magnitude Of Shear Research Articles

Formation and development of a breaker bar under regular waves. Part 1: Model description and hydrodynamics

In this work a detailed hydrodynamic model is presented, which is used for the study of cross-shore sediment transport and morphodynamics in two dimensions. The model is described in the framework of the generally unstructured, finite volume method. Considerable emphasis is put on those subtleties in the morphological formulation, which are required to achieve mass conservation for the amount of sediment in the bed and in suspension.In this first part of two, the hydrodynamic description over the cross-shore profile is presented. The model is validated against an experiment with detailed measurements of the free surface and turbulence over a fixed breaker bar profile. A test matrix covering a large interval of the surf similarity parameter is simulated, and the phase lag between the breakpoint and the initiation of the setup is described. The relation of this phase lag to a cross-shore delay in dissipation of organised energy into turbulence is described. The relation of this phase lag to the distribution of the location of maxima in bed shear stresses and magnitude of the undertow is also described.Furthermore, processes in the hydrodynamics, which will have a smoothing effect on the mean cross-shore sediment transport and morphodynamic response are considered.All simulations are presented for regular waves and for values of the deep-water surf similarity parameter, ζ0, in the range from 0.08 to 1.19, i.e. covering both spilling and plunging breakers.

Characterizaton of the Vessel Geometry, Flow Mechanics and Wall Shear Stress in the Great Arteries of Wildtype Prenatal Mouse

IntroductionAbnormal fluid mechanical environment in the pre-natal cardiovascular system is hypothesized to play a significant role in causing structural heart malformations. It is thus important to improve our understanding of the prenatal cardiovascular fluid mechanical environment at multiple developmental time-points and vascular morphologies. We present such a study on fetal great arteries on the wildtype mouse from embryonic day 14.5 (E14.5) to near-term (E18.5).MethodsUltrasound bio-microscopy (UBM) was used to measure blood velocity of the great arteries. Subsequently, specimens were cryo-embedded and sectioned using episcopic fluorescent image capture (EFIC) to obtain high-resolution 2D serial image stacks, which were used for 3D reconstructions and quantitative measurement of great artery and aortic arch dimensions. EFIC and UBM data were input into subject-specific computational fluid dynamics (CFD) for modeling hemodynamics.ResultsIn normal mouse fetuses between E14.5–18.5, ultrasound imaging showed gradual but statistically significant increase in blood velocity in the aorta, pulmonary trunk (with the ductus arteriosus), and descending aorta. Measurement by EFIC imaging displayed a similar increase in cross sectional area of these vessels. However, CFD modeling showed great artery average wall shear stress and wall shear rate remain relatively constant with age and with vessel size, indicating that hemodynamic shear had a relative constancy over gestational period considered here.ConclusionOur EFIC-UBM-CFD method allowed reasonably detailed characterization of fetal mouse vascular geometry and fluid mechanics. Our results suggest that a homeostatic mechanism for restoring vascular wall shear magnitudes may exist during normal embryonic development. We speculate that this mechanism regulates the growth of the great vessels.

Shear-induced endothelial mechanotransduction: the interplay between reactive oxygen species (ROS) and nitric oxide (NO) and the pathophysiological implications

Hemodynamic shear stress, the blood flow-generated frictional force acting on the vascular endothelial cells, is essential for endothelial homeostasis under normal physiological conditions. Mechanosensors on endothelial cells detect shear stress and transduce it into biochemical signals to trigger vascular adaptive responses. Among the various shear-induced signaling molecules, reactive oxygen species (ROS) and nitric oxide (NO) have been implicated in vascular homeostasis and diseases. In this review, we explore the molecular, cellular, and vascular processes arising from shear-induced signaling (mechanotransduction) with emphasis on the roles of ROS and NO, and also discuss the mechanisms that may lead to excessive vascular remodeling and thus drive pathobiologic processes responsible for atherosclerosis. Current evidence suggests that NADPH oxidase is one of main cellular sources of ROS generation in endothelial cells under flow condition. Flow patterns and magnitude of shear determine the amount of ROS produced by endothelial cells, usually an irregular flow pattern (disturbed or oscillatory) producing higher levels of ROS than a regular flow pattern (steady or pulsatile). ROS production is closely linked to NO generation and elevated levels of ROS lead to low NO bioavailability, as is often observed in endothelial cells exposed to irregular flow. The low NO bioavailability is partly caused by the reaction of ROS with NO to form peroxynitrite, a key molecule which may initiate many pro-atherogenic events. This differential production of ROS and RNS (reactive nitrogen species) under various flow patterns and conditions modulates endothelial gene expression and thus results in differential vascular responses. Moreover, ROS/RNS are able to promote specific post-translational modifications in regulatory proteins (including S-glutathionylation, S-nitrosylation and tyrosine nitration), which constitute chemical signals that are relevant in cardiovascular pathophysiology. Overall, the dynamic interplay between local hemodynamic milieu and the resulting oxidative and S-nitrosative modification of regulatory proteins is important for ensuing vascular homeostasis. Based on available evidence, it is proposed that a regular flow pattern produces lower levels of ROS and higher NO bioavailability, creating an anti-atherogenic environment. On the other hand, an irregular flow pattern results in higher levels of ROS and yet lower NO bioavailability, thus triggering pro-atherogenic effects.

Rainfall asymmetries of tropical cyclones prior to, during, and after making landfall in South China and Southeast United States

This study examines rainfall asymmetries of tropical cyclones (TCs) prior to, during, and after making landfall in South China and the Southeast United States from 1998 to 2011 based on TRMM rainfall products. The climatological TC rainfall asymmetries are then linked to various potential environmental factors. These factors include TC intensity and motion, vertical wind shear, topography, sea surface temperature (SST), and total precipitable water (TPW). All these factors are examined in combination, as it is in the real world. Results show that effects of the deep vertical wind shear (200–850hPa) dominate the rainfall asymmetries producing maxima on the downshear and downshear-left sides. This wind shear effect is still dominant even during TCs making landfall, or after landfall, or interacting with mountains. The magnitude of the rainfall asymmetry increases with shear magnitude, but decreases with increasing TC intensity. Furthermore, the shear effect is less efficient for TCs over relatively cool SST and low TPW oceans when TCs produce less precipitation. On the other hand, effects of storm motion (producing rainfall maxima at front quadrants) are not evident in this study, mainly due to opposing vertical wind shear effects. However, landfalling TCs experience a significant increase in the rainfall percentage toward the right quadrants relative to the coast, likely due to surface frictional gradient between land and sea. There is no evident signature of precipitation enhancement over the windward slope of mountains (400–600m) in SCHN and SECHN.

Rheological Behavior of a Suspension of Escherichia Coli with Varying Motor Characteristics

We determine the rheological response of a suspension of E. coli for varying cell densities and shear rates. Experiments were performed at moderate to high shear rates with five different strains of E. coli varying in motor characteristics like duration of run and tumble. Irrespective of the strains, at low densities and at a fixed shear rate, the viscosity increased linearly with cell density akin to a dilute suspension of passive rods. The strains with low run speeds, short durations of run, and high rotary diffusivities exhibit lower viscosities compared to strains with high run speeds and large run duration. Interestingly, the latter exhibit a sharp decrease in viscosity at a critical volume fraction signaling the presence of strongly coordinated motion. The presence of such coordinated motion and the influence of shear rate and cell density on their lifetimes and length scales were confirmed by visualizing the motion of tracer particles in sheared suspensions. Reduction in correlated motion is observed for both increase in shear rate and decrease in cell density.The critical density depends not only on the magnitude of shear but also the motor characteristics of cells.View Large Image | View Hi-Res Image | Download PowerPoint Slide

Distant optical detection of small rotations and displacements by means of chiral liquid crystals

The paper describes novel chiral viscoelastic liquid crystalline mixtures and their application for the detection of small rotational displacements of two plates confining cholesteric liquid crystals (CLC). The mixtures are characterized by extremely high viscosities and stability of the selective reflection band (SRB) at ambient temperatures. Even a small rotation applied to the chiral liquid crystal (CLC) cell results in dramatic changes of the reflective properties of sandwiched CLC films. The angle and direction of rotation as well as the magnitude of CLC's shear deformation can be determined for a variety of experimental geometries, each of which is characterized by its own response function. The proposed model explains changes in the reflection spectra for different experimental geometries and relates them to the angle of rotation and magnitude of shear. The method was tested for a detection of small rotations from a distance of up to 50 m and allows for resolving small rotations of the order of fractions of degrees.

Probing dark energy through scale dependence

We consider the consequences of having no prior knowledge of the true dark energy model for the interpretation of cosmological observations. The magnitude of redshift-space distortions and weak-lensing shear is determined by the metric on the geodesics of which galaxies and light propagate. We show that, given precise enough observations, we can use these data to completely reconstruct the metric on our past lightcone and therefore to measure the scale- and time-dependence of the anisotropic stress and the evolution of the gravitational potentials in a model-independent manner. Since both dark matter and dark energy affect the visible sector only through the gravitational field they produce, they are inseparable without a model for dark energy: galaxy bias cannot be measured and therefore the distribution of dark matter determined; the peculiar velocity of dark matter can be identified with that of the galaxies only when the equivalence principle holds. Given these limitations, we show how one can nonetheless build tests for classes of dark energy models which depend on making measurements at multiple scales at a particular redshift. They are null tests on the model-independent observables, do not require modeling evolution in time and do not require any parametrization of the free functions of these models, such as the sound speed. We show how one can rule out or constrain the whole class of the most-general scalar-tensor theories even without assuming the quasi-static limit.

Numerical study on the development of asymmetric convection and vertical wind shear during tropical cyclone landfall

Idealized simulations on an f-plane of tropical cyclone (TC) landfall under a quiescent environment in the Southern Hemisphere are performed to investigate the effects of land–sea surface contrast on precipitation. In the control simulation, with realistic roughness and moisture over land to the south of the TC, the simulated vortex moves toward land due to a land-induced steering flow. The abrupt decrease (increase) of tangential wind at the surface leads to convergence (divergence) on the onshore (offshore) flow side. Enhanced convergence at the top of the planetary boundary layer is found on both onshore and offshore sides and is caused by advection from the surface and the enhanced offshore radial wind. The boundary-layer top convergence pattern is consistent with the rainfall distribution. Vertical wind shear develops during the landfall process associated with the low- and upper-level asymmetric flows across the model domain. The wavenumber-1-like low-level asymmetric flow is introduced by an asymmetric geopotential height field that is generated by the large area of frictionally induced convergence on the onshore side and divergence on the offshore side. The upper-level asymmetric flow is attributed to asymmetric convection and associated diabatic heating after landfall. Most rainfall is found in the down-shear right quadrant, which is consistent with previous studies that focused on the effect of environmental shear. Although the existence of feedback from the vertical wind shear to rainfall remains an open question, the relation between maximum rainfall and vertical wind shear is robust, especially when the shear magnitude is large after landfall.

American Society of Biomechanics Clinical Biomechanics Award 2012: Plantar shear stress distributions in diabetic patients with and without neuropathy

BackgroundThe exact pathology of diabetic foot ulcers remains to be resolved. Evidence suggests that plantar shear forces play a major role in diabetic ulceration. Unfortunately, only a few manuscripts exist on the clinical implications of plantar shear. The purpose of this study was to compare global and regional peak plantar stress values in three groups; diabetic patients with neuropathy, diabetic patients without neuropathy and healthy control subjects. MethodsFourteen diabetic neuropathic patients, 14 non-neuropathic diabetic control and 11 non-diabetic control subjects were recruited. Subjects walked on a custom-built stress plate that quantified plantar pressures and shear. Four stress variables were analyzed; peak pressure, peak shear, peak pressure-time and shear-time integral. FindingsGlobal peak values of peak shear (p=0.039), shear-time integral (p=0.002) and pressure-time integral (p=0.003) were significantly higher in the diabetic neuropathic group. The local peak shear stress and shear-time integral were also significantly higher in diabetic neuropathic patients compared to both control groups, in particular, at the hallux and central forefoot. The local peak pressure and pressure-time integral were significantly different between the three groups at the medial and lateral forefoot. InterpretationPlantar shear and shear-time integral magnitudes were elevated in diabetic patients with peripheral neuropathy, which indicates the potential clinical significance of these factors in ulceration. It is thought that further investigation of plantar shear would lead to a better understanding of ulceration pathomechanics, which in turn will assist researchers in developing more effective preventive devices and strategies.

Shock response of single crystal and nanocrystalline pentaerythritol tetranitrate: Implications to hotspot formation in energetic materials

We investigate shock response of single crystal and nanocrystalline pentaerythritol tetranitrate (PETN) with a coarse-grained model and molecular dynamics simulations, as regards mechanical hotspot formation in the absence or presence of grain boundaries (GBs). Single crystals with different orientations, and columnar nanocrystalline PETN with regular hexagonal, irregular hexagonal, and random GB patterns, are subjected to shock loading at different shock strengths. In single crystals, shock-induced plasticity is consistent with resolved shear stress calculations and the steric hindrance model, and this deformation leads to local heating. For regular-shaped hexagonal columnar nanocrystalline PETN, different misorientation angles lead to activation of different/same slip systems, different deformation in individual grains and as a whole, different GB friction, different temperature distributions, and then, different hotspot characteristics. Compared to their regular-shaped hexagonal counterpart, nanocrystalline PETN with irregular hexagonal GB pattern and that with random GBs, show deformation and hotspot features specific to their GBs. Driven by stress concentration, hotspot formation is directly related to GB friction and GB-initiated crystal plasticity, and the exact deformation is dictated by grain orientations and resolved shear stresses. GB friction alone can induce hotspots, but the hotspot temperature can be enhanced if it is coupled with GB-initiated crystal plasticity, and the slip of GB atoms has components out of the GB plane. The magnitude of shearing can correlate well with temperature, but the slip direction of GB atoms relative to GBs may play a critical role. Wave propagation through varying microstructure may also induce differences in stress states (e.g., stress concentrations) and loading rates, and thus, local temperature rise. GB-related friction and plasticity induce local heating or mechanical hotspots, which could be precursors to chemical hotspot formation related to initiation in energetic materials, in the absence of other, likely more effective, means for hotspot formation such as void collapse.

Plasma Response to a Varying Degree of Stress

We report experimental evidence of a seamless transition between three distinct modes in a magnetized plasma with a transverse sheared flow as the ratio of the ion gyroradius to the shear scale length (a measure of shear magnitude) is varied. This was achieved using a dual plasma configuration in a laboratory experiment, where a sheared flow oriented perpendicular to a background magnetic field is localized at the boundary of the plasmas. This confirms the basic theory that plasma is unstable to transverse velocity shear in a broad frequency and wavelength range. The experiment characterizes the compression or relaxation of boundary layers often generated in a variety of laboratory and space plasma processes.

Environmental Flow Impacts on Tropical Cyclone Structure Diagnosed from Airborne Doppler Radar Composites

Abstract Following a recent demonstration of multicase compositing of axisymmetric tropical cyclone (TC) structure derived from airborne Doppler radar measurements, the authors extend the analysis to the asymmetric structure using an unprecedented database from 75 TC flights. In particular, they examine the precipitation and kinematic asymmetry forced by the TC's motion and interaction with vertical wind shear. For the first time they quantify the average magnitude and phase of the three-dimensional shear-relative kinematic asymmetry of observed TCs through a composite approach. The composite analysis confirms principal features of the shear-relative TC asymmetry documented in prior numerical and observational studies (e.g., downshear tilt, downshear-right convective initiation, and a downshear-left precipitation maximum). The statistical significance of the composite shear-relative structure is demonstrated through a stratification of cases by shear magnitude. The impact of storm motion on eyewall convective asymmetry appears to be secondary to the much greater constraint placed by vertical wind shear on the organization of convection, in agreement with prior studies using lightning and precipitation data.

Relating the Skill of Tropical Cyclone Intensity Forecasts to the Synoptic Environment

Abstract Prior knowledge of the performance of a tropical cyclone intensity forecast holds the potential to increase the value of forecasts for end users. The values of certain dynamical parameters, such as storm speed, latitude, current intensity, potential intensity, wind shear magnitude, and direction of the shear vector, are shown to be related to the error of an individual model forecast. The varying success of each model in the different environmental conditions represents a source of additional information on the reliability of an individual forecast beyond average forecast error. Three hurricane intensity models that were operational for the duration of the five hurricane seasons between 2006 and 2010, as well as the National Hurricane Center official forecast (OFCL), are evaluated for 24-, 48-, and 72-h forecasts in the Atlantic Ocean. The performance of each model is assessed by computing the mean absolute error, bias, and percent skill relative to a benchmark model. The synoptic variables are binned into physically meaningful ranges and then tested individually and in combinations to capture the different regimes that are conducive to forecasts with higher or lower error. The results address conventional wisdom about which environmental conditions lead to better forecasts of hurricane intensity and highlight the different strengths of each model. The statistical significance established between the different bins in each model as well as the corresponding bins for other models indicates there is the potential for error predictions to accompany tropical cyclone intensity forecasts.

Role of strain magnitude on the deformation response of geosynthetic-reinforced soil layers

ABSTRACT: This paper reports an investigation into the deformation response of geosynthetic-reinforced soil layers to evaluate the level of strain required to mobilize reinforcement mechanisms during surface loading. Specifically, an assessment of data from previous studies reporting surface settlements of reinforced and unreinforced soil layers during monotonic or cyclic loading to failure is complemented with new dynamic tests performed at small- and medium-strain magnitudes. A series of test sections with and without geosynthetic reinforcement were characterized using a Vibroseis shaker truck as a dynamic loading source. The behavior of uniform sand layers under relatively small strain magnitudes (shear strain magnitudes less than 0.2%) were characterized using embedded geophones. Shear and normal strain distributions within the test sections were measured as a function of depth during application of surface shear loading. The presence of geosynthetic reinforcement (either geogrid or geotextile) at a depth of 254 mm below the surface of the sand layer does not significantly alter the distributions of shear strain or vertical normal strain relative to an unreinforced control section for the magnitudes of shear and compressive strains applied to the soil surface. The behavior of aggregate base layers overlying sand layers under medium strain magnitudes (surface deflections up to 25 mm) were characterized using an array of LVDTs on the soil surface. Surface deflection basins were measured during application of several thousand cycles of compressive loading. The presence of a geogrid within the aggregate base layer or a woven geotextile beneath the aggregate base layer were observed not to lead to a change in the surface deflection basins up to a maximum deflection of 25 mm. These observations, together with results from the literature, indicate that reinforcement mechanisms such as lateral restraint and the tensioned-membrane effect may not be mobilized until reaching relatively large displacements in some soil layers.

High-accuracy characterization of the edge radial electric field at ASDEX Upgrade

The installation of a new poloidal charge exchange recombination spectroscopy (CXRS) diagnostic at ASDEX Upgrade (AUG) has enabled the determination of the radial electric field, Er, using the radial force balance of impurity ions. Er has been derived from charge exchange (CX) spectra measured on different impurity species, such as He2+, B5+, C6+ and Ne10+. The resulting Er profiles are found to be identical within the uncertainties regardless of the impurity species used, thus, demonstrating the validity of the diagnostic technique. The Er profile has been compared to the main ion pressure gradient term, which is found to be the dominant contribution at the plasma edge, thus, supporting that the Er well is created by the main ion species. The Er profile has been measured in different confinement regimes including L-, I- and H-mode. The depth of the Er well and the magnitude of the Er shear are correlated with the ion pressure at the pedestal top. The temporal evolution of the measured CX profiles and the resulting Er have been studied during an edge-localized mode (ELM) cycle. At the ELM crash, the Er minimum is less deep resulting in a reduction of the E × B shear. Within 2 ms after the ELM crash, the edge kinetic profiles have nearly recovered and the Er well is observed to recover simultaneously. In high density type-I ELM mitigated H-mode plasmas, obtained via externally applied magnetic perturbations (MPs) with toroidal mode number n = 2, no clear effect on Er due to the MPs has been observed.

Effects of Vertical Wind Shear on the Predictability of Tropical Cyclones

Abstract Through cloud-resolving simulations, this study examines the effect of vertical wind shear and system-scale flow asymmetry on the predictability of tropical cyclone (TC) intensity during different stages of the TC life cycle. A series of ensemble experiments is performed with varying magnitudes of vertical wind shear, each initialized with an idealized weak TC-like vortex, with small-scale, small-amplitude random perturbations added to the initial conditions. It is found that the environmental shear can significantly affect the intrinsic predictability of tropical cyclones, especially during the formation and rapid intensification stage. The larger the vertical wind shear, the larger the uncertainty in the intensity forecast, primarily owing to the difference in the timing of rapid intensification. In the presence of environmental shear, initial random noise may result in changes in the timing of rapid intensification by as much as 1–2 days through the randomness (and chaotic nature) of moist convection. Upscale error growth from differences in moist convection first alters the tilt amplitude and angle of the incipient tropical storms, which leads to significant differences in the timing of precession and vortex alignment. During the precession process, both the vertical tilt of the storm and the effective (local) vertical wind shear are considerably decreased after the tilt angle reaches 90° to the left of the environmental shear. The tropical cyclone intensifies immediately after the tilt and the effective local shear reach their minima. In some instances, small-scale, small-amplitude random noise may also limit the intensity predictability through altering the timing and strength of the eyewall replacement cycle.

An Experimental Study of Shear Stress Distribution in a Compound Meandering Channel

Naturally river flow can be characterized as compound meandering channel in which the shear stress characteristics are quite intricate. Reliable investigation of shear stress distribution in a compound meandering channel is essential in solving a variety of river hydraulics and engineering problems, designing stable channels and bank protection, understanding the mechanism of sediment transport. A laboratory experiment has been conducted in a compound meandering channel with symmetric cross-sections having floodplain width ratio of 1, 1.67, 2.33, 3 and depth ratio of 0.20, 0.30, 0.35, 0.40 using the large-scale open air facility in the Department of Water Resources Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh. Point velocity data have been collected using an ADV (Acoustic Doppler Velocity Meter) for different depth and width ratio at different locations of a compound meandering channel. Shear stress is calculated from the Prandtl-Von Karman Universal Velocity Distribution Law. The laboratory experimental investigation reveals that shear stress increases with the increase of depth and width ratio and low magnitude of boundary shear is observed in the outer bend as compare to the inner bend in a compound meandering channel.

The Role of Vortex and Environment Errors in Genesis Forecasts of Hurricanes Danielle and Karl (2010)

AbstractAn ensemble of Weather Research and Forecasting Model (WRF) forecasts initialized from a cycling ensemble Kalman filter (EnKF) system is used to evaluate the sensitivity of Hurricanes Danielle and Karl’s (2010) genesis forecasts to vortex and environmental initial conditions via ensemble sensitivity analysis. Both the Danielle and Karl forecasts are sensitive to the 0-h circulation associated with the pregenesis system over a deep layer and to the temperature and water vapor mixing ratio within the vortex over a comparatively shallow layer. Empirical orthogonal functions (EOFs) of the 0-h ensemble kinematic and thermodynamic fields within the vortex indicate that the 0-h circulation and moisture fields covary with one another, such that a stronger vortex is associated with higher moisture through the column. Forecasts of the pregenesis system intensity are only sensitive to the leading mode of variability in the vortex fields, suggesting that only specific initial condition perturbations associated with the vortex will amplify with time. Multivariate regressions of the vortex EOFs and environmental parameters believed to impact genesis suggest that the Karl forecast is most sensitive to the vortex structure, with smaller sensitivity to the upwind integrated water vapor and 200–850-hPa vertical wind shear magnitude. By contrast, the Danielle forecast is most sensitive to the vortex structure during the first 24 h, but is more sensitive to the 200-hPa divergence and vertical wind shear magnitude at longer forecast hours.

Rapid distortion analysis of high Mach number homogeneous shear flows: Characterization of flow-thermodynamics interaction regimes

In high-speed shear flows the nature of flow-thermodynamics interactions, and consequently the character of transition/turbulence, changes markedly with Mach number. We identify and characterize three different regimes of interactions in terms of acoustic frequency-to-shear magnitude ratio employing the linear rapid distortion analysis. We begin with an analysis of the pressure equation and demonstrate that acoustic frequency grows monotonically with time in this initial value problem whereas the shear magnitude is imposed to be constant. Initially when acoustic frequency is smaller than shear magnitude, fluctuations grow rapidly as the velocity field evolves unrestrained by pressure. This corresponds to Regime 1 wherein there is no significant flow-thermodynamics interaction. Flow-thermodynamics interactions commence in Regime 2 as acoustic frequency grows to the level of imposed shear rate. Dilatational velocity and pressure fields in the flow-normal direction are generated. The two fields are coupled as in a simple harmonic oscillator and consequently shear stresses oscillate about a near zero value. Thus production is drastically reduced leading to stabilization of perturbation kinetic energy growth rate. Further increase in acoustic frequency beyond shear magnitude leads to Regime 3. The solenoidal perturbations begin to dominate the flow statistics and the kinetic energy evolution bears much semblance to the incompressible shear flow. Overall, this work leads to improved insight into high-speed shear flow physics.

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

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.