Momentum Flux Profiles Research Articles

Coupled Numerical Modelling of Wind and Waves and the Theory of the Wave Boundary Layer

The description of a coupled wind and wave model in conformal coordinates is given. The wave model is based on potential equations for the flow with a free surface, extended with the algorithm of breaking dissipation. The wave boundary-layer (WBL) model is based on the Reynolds equations with the K − e closure scheme with the solutions for air and water matched through the interface. The structure of the WBL and vertical profiles of the wave-produced momentum flux (WPMF) in a long-term simulation of the coupled dynamics are investigated and parameterized. The shape of the β function connecting elevation and surface pressure is studied up to high nondimensional wave frequencies. The errors of a linear presentation of the surface pressure are estimated. The β function and the universal shape of the WPMF profile obtained in coupled simulations allow a formulation of the one-dimensional theory of the WBL, and the carrying out of a detailed study of the WBL structure including the dependence of the drag coefficient on the wind speed. It is shown that a wide scatter of the experimental data on the drag coefficient can be explained, taking into account the age of waves. It is suggested that a reduction of the drag coefficient at high wind speeds can be qualitatively explained by the high-frequency wave suppression.

Large-eddy simulation of katabatic winds. Part 1: Comparison with observations

Steady-state quasi-one-dimensional large-eddy simulations of slope winds over simple terrain are presented. The model results of up-slope flow are compared to previous simulations by Schumann (1990), and good agreement is found. Modelled downslope winds are compared to meteorological observations from two glaciers. The vertical profiles of velocity and buoyancy agree with the observations, whereas larger discrepancies are found between the modelled and the observed momentum and buoyancy flux profiles. Despite some discrepancies, the model captures the main characteristics of the observed downslope winds fairly well. The numerical model is used in a companion paper (Part II) to study how some external input parameters affect katabatic winds.

Turbulence Structure of the Hurricane Boundary Layer between the Outer Rainbands

Abstract As part of the Coupled Boundary Layers Air–Sea Transfer (CBLAST)-Hurricane program, flights were conducted to directly measure turbulent fluxes and turbulence properties in the high-wind boundary layer of hurricanes between the outer rainbands. For the first time, vertical profiles of normalized momentum fluxes, sensible heat and humidity fluxes, and variances of three-dimensional wind velocities and specific humidity are presented for the hurricane boundary layer with surface wind speeds ranging from 20 to 30 m s−1. The turbulent kinetic energy budget is estimated, indicating that the shear production and dissipation are the major source and sink terms, respectively. The imbalance in the turbulent kinetic energy budget indicates that the unmeasured terms, such as horizontal advection, may be important in hurricane boundary layer structure and dynamics. Finally, the thermodynamic boundary layer height, estimated based on the virtual potential temperature profiles, is roughly half of the boundary layer height estimated from the momentum flux profiles. The latter height where momentum and humidity fluxes tend to vanish is close to that of the inflow layer and also of the maximum in the tangential velocity profiles.

Analysis of Model Results for the Turning of the Wind and Related Momentum Fluxes in the Stable Boundary Layer

The turning of wind with height and the related cross-isobaric (ageostrophic) flow in the thermally stable stratified boundary layer is analysed from a variety of model results acquired in the first Global Energy and Water Cycle Experiment (GEWEX) Atmospheric Boundary Layer Study (GABLS1). From the governing equations in this particular simple case it becomes clear that the cross-isobaric flow is solely determined by the surface turbulent stress in the direction of the geostrophic wind for the quasi-steady state conditions under consideration. Most models indeed seem to approach this relationship but for very different absolute values. Because turbulence closures used in operational models typically tend to give too deep a boundary layer, the integrated total cross-isobaric mass flux is up to three times that given by research numerical models and large-eddy simulation. In addition, the angle between the surface and the geostrophic wind is typically too low, which has important implications for the representation of the larger-scale flow. It appears that some models provide inconsistent results for the surface angle and the momentum flux profile, and when the results from these models are removed from the analysis, the remaining ten models do show a unique relationship between the boundary-layer depth and the surface angle, consistent with the theory given. The present results also imply that it is beneficial to locate the first model level rather close to the surface for a proper representation of the turning of wind with height in the stable boundary layer.

FORMATION OF PROTOSTELLAR JETS AS TWO-COMPONENT OUTFLOWS FROM STAR-DISK MAGNETOSPHERES

Axisymmetric magnetohydrodynamic (MHD) simulations have been applied to investigate the interrelation of a central stellar magnetosphere and stellar wind with a surrounding magnetized disk outflow and how the overall formation of a large scale jet is affected. The initial magnetic field distribution applied is a superposition of two components - a stellar dipole and a surrounding disk magnetic field, in both either parallel or anti-parallel alignment. Correspondingly, the mass outflow is launched as stellar wind plus a disk wind. Our simulations evolve from an initial state in hydrostatic equilibrium and an initially force-free magnetic field configuration. Due to initial differential rotation and induction of a strong toroidal magnetic field the stellar dipolar field inflates and is disrupted on large scale. Stellar and disk wind may evolve in a pair of collimated outflows. The existence of a reasonably strong disk wind component is essential for collimation. A disk jet as known from previous numerical studies will become de-collimated by the stellar wind. In some simulations we observe the generation of strong flares triggering a sudden change in the outflow mass loss rate by a factor of two and also a re-distribution in the radial profile of momentum flux and jet velocity across the jet. We discuss the hypothesis that these flares may trigger internal shocks in the asymptotic jets which are observed as knots.

Meteor wind radar observations of gravity wave momentum fluxes and their forcing toward the Mesospheric Semiannual Oscillation

Wind measurements from continuous meteor radar observations during June 2004–May 2007 are used to estimate the gravity wave momentum fluxes in the Mesosphere Lower Thermosphere (MLT) region over Trivandrum (8.5°N, 76.9°E), a low‐latitude station in India. The radial velocity variances in the 82–98 km height region, which are mainly caused by gravity waves, measured by the meteor radar are used to determine the gravity wave momentum fluxes. Using a novel method proposed by Hocking (2005), altitude profiles of momentum fluxes of short period (less than 2–3 h) gravity waves are estimated for three continuous years. Seasonal variation in the gravity wave momentum fluxes showed semi annual variation with equinoctial maximum and solstitial minimum. By using estimated gravity wave momentum fluxes, an attempt is made to quantify their contribution in driving the Mesospheric Semi Annual Oscillation (MSAO). The mean flow acceleration estimated from the divergence of gravity wave momentum fluxes is compared with the observed mean flow acceleration computed from monthly mean zonal winds during six MSAO cycles over three years. This comparison reveled that the gravity wave contribution toward the westerly phase of MSAO varies from ∼20–60% while that toward the easterly phase varies from ∼30–70%. Variations are observed from cycle‐to‐cycle in the gravity wave forcing toward both phases of MSAO. The significance of the present study lies in estimating the gravity wave momentum fluxes in the MLT region and quantifying their contribution toward the generation of MSAO over the low‐latitude for the first time.

The vertical structure of turbulent momentum flux in the lower part of the atmospheric boundary layer

The acoustic sounder (sodar) can be used to measure the parameters of turbulence in the lower part of the atmospheric boundary layer. We suggest a new method to estimate the vertical structure of the momentum flux up to the height of several hundred meters above the surface. The method uses sodar-measured profiles of mean wind and of the variance of vertical wind component σ 2 w . The field experiment have shown a good agreement of sodar-derived momentum flux values with those measured in situ. We obtained the typical profiles of momentum flux with the method.

A quantitative study on the role of gravity waves in driving the tropical Stratospheric Semiannual Oscillation

Using a coordinated experimental observation under Middle Atmospheric Dynamics (MIDAS) program, an extensive study is carried out to quantify the role of gravity waves in driving the tropical Stratospheric Semiannual Oscillation (SSAO). Rayleigh lidar observations of middle atmospheric temperature over Gadanki (13.5°N, 79.2°E) and rocketsonde wind measurements over Trivandrum (8.5°N, 76.9°E) during the period November 2002 to June 2005 are used for the present study. Gravity waves with periods ranging from 2–4 hours and 0.5–1 hour are found to be dominant in the middle atmosphere throughout the observational period. The altitude profiles of momentum fluxes of gravity waves having these time periods are estimated and their seasonal variations are studied, which showed semiannual variation with maximum around equinoxes and minimum around solstitial months. The mean flow acceleration estimated from the divergence of momentum flux of gravity waves is compared with the mean flow acceleration observed using rocket measured zonal winds during three different cycles of SSAO. This comparison provided an opportunity to quantify the contribution of gravity waves toward generation of SSAO, which is found to be ∼30–50% of the observed acceleration during the evolution of the westerly phase of the SSAO. The present observations showed that the contribution of the gravity waves toward the westerly phase of SSAO varies significantly from cycle to cycle. The significance of the present results lies in quantifying the gravity wave–mean flow interaction during both easterly and westerly phases of SSAO for the first time over this tropical latitude.

Remote determination of momentum-flux profiles in the lower atmospheric boundary layer

An acoustic locator—a sodar—is a unique instrument for getting the objective characteristics of the current state of the atmospheric boundary layer (ABL) owing to a combination of such properties as remoteness, mobility, resolution, and information content. This study demonstrates the capabilities of a sodar to obtain data on the second moments of the field of wind-velocity fluctuations, in particular, the profiles of momentum flux in the lower ABL, which are very important in practical applications. A corresponding method is described, and the results of its experimental verification and some examples of its application under the conditions of different ABL stratification are presented.

Mountain-Wave Momentum Flux in an Evolving Synoptic-Scale Flow

Abstract The evolution of mountain-wave-induced momentum flux is examined through idealized numerical simulations during the passage of a time-evolving synoptic-scale flow over an isolated 3D mountain of height h. The dynamically consistent synoptic-scale flow U accelerates and decelerates with a period of 50 h; the maximum wind arrives over the mountain at 25 h. The synoptic-scale static stability N is constant, so the time dependence of the nonlinearity parameter, ɛ(t) = Nh/U(t), is symmetric about a minimum value at 25 h. The evolution of the vertical profile of momentum flux shows substantial asymmetry about the midpoint of the cycle even though the nonlinearity parameter is symmetric. Larger downward momentum fluxes are found during the accelerating phase, and the largest momentum fluxes occur in the mid- and upper troposphere before the maximum background flow arrives at the mountain. For a period of roughly 15 h, this vertical distribution of momentum flux accelerates the lower-tropospheric zonal-mean winds due to low-level momentum flux convergence. Conservation of wave action and Wentzel–Kramers–Brillouin (WKB) ray tracing are used to reconstruct the time–altitude dependence of the mountain-wave momentum flux in a semianalytic procedure that is completely independent of the full numerical simulations. For quasi-linear cases, the reconstructions show good agreement with the numerical simulations, implying that the basic asymmetry obtained in the full numerical simulations may be interpreted using WKB theory. These results demonstrate that even slow variations in the mean flow, with a time scale of 2 days, play a dominant role in regulating the vertical profile of mountain-wave-induced momentum flux. The time evolution of cross-mountain pressure drag is also examined in this study. For almost-linear cases, the pressure drag is well predicted under steady-state linear theory by using the instantaneous incident flow. Nevertheless, for mountains high enough to preserve a moderate degree of nonlinearity when the synoptic-scale incident flow is strongest, the evolution of cross-mountain pressure drag is no longer symmetric about the time of maximum wind. A higher drag state is found when the cross-mountain flow is accelerating. These results suggest that the local character of the topographically induced disturbance cannot be solely determined by the instantaneous value of the nonlinearity parameter ɛ.

Comparison of gravity wave momentum fluxes estimated by different methods using mesosphere‐stratosphere‐troposphere radar

Mesosphere‐stratosphere‐troposphere radar measurements have been used to estimate momentum flux of gravity waves in a 2–6 hour period in the lower atmosphere over Gadanki (13.5°N, 79.2°E), a tropical station. Different methods have been adopted to compute momentum flux profiles, and a comparative study shows that momentum flux estimates produced by a hybrid method (Worthington and Thomas, 1996) which measures the vertical wind with a vertical beam and the horizontal wind with a pair of radial beams and those obtained by direct computation of spatial covariances ( and ) show satisfactory agreement. The symmetric beam radar method of Vincent and Reid (1983) has the unique advantage since it does not require vertical beam measurement, and it is found to produce momentum flux estimates compatible with other methods except in high wind shear zones. It is observed that the result of momentum flux obtained by the symmetric beam method shows excellent matching with other methods when the average of vertical winds derived from E‐W and N‐S beams is used in the formula for both zonal and meridional fluxes.

Flow structure and turbulence characteristics of the daytime atmosphere in a steep and narrow Alpine valley

AbstractAircraft measurements, radio soundings and sonic data—obtained during the MAP‐Riviera field campaign in autumn 1999 in southern Switzerland—are used to investigate the flow structure, temperature profiles and turbulence characteristics of the atmosphere in a steep and narrow Alpine valley under convective conditions. On all predominantly sunny days of the intensive observation periods, a pronounced valley‐wind system develops. In the southern half of the valley, the daily up‐valley winds have a jet‐like structure and are shifted towards the eastern slope. These up‐valley winds advect potentially colder air, a process which appears to be balanced by vertical warm air advection from above. The profiles of potential temperature show that, with the onset of up‐valley winds, the mixed layer consistently stops growing or—on days with very strong up‐valley winds—even stabilizes almost throughout the entire valley atmosphere. This is probably due to a pronounced secondary circulation in the southern part of the valley, which induces advection of warm air from above. The secondary circulation appears to be a consequence of sharp curvature in the along‐valley topography.Turbulence variables are calculated from flight legs in the along‐valley direction. Turbulent kinetic energy (TKE) scales surprisingly well (i) if a TKE criterion (TKE >0.5 m2s−2) is employed as a definition of the boundary layer height and (ii) if the ‘surface fluxes’—which exhibit a substantial spatial variability—from the slope sites are used rather than those from directly beneath the profile considered. Significant site‐to‐site differences in incoming solar radiation seem to be the reason for this characteristic behaviour. Profiles of momentum flux—scaled with a surface friction velocity—reveal more scatter than the TKE profiles, but still show a consistent behaviour. A surprisingly strong shear in the cross‐valley direction can be observed and is probably a result of the secondary circulation. Copyright © 2004 Royal Meteorological Society

Flow behavior and regime transition in a high-density circulating fluidized bed riser

Flow behavior and flow regime transitions were determined in a circulating fluidized bed riser (0.203 m i.d. × 5.9 m high) of FCC particles ( d p = 70 μ m , ρ p = 1700 kg / m 3 ). A momentum probe was used to measure radial profiles of solids momentum flux at several heights and to distinguish between local net upward and downward flow. In the experimental range covered ( U g = 5 – 8 m / s ; G s = 22 – 345 kg / m 2 s ), the fast fluidization flow regime was observed to coexist with dense suspension upflow (DSU). At a constant gas velocity, net downflow of solids near the wall disappeared towards the bottom of the riser with increasing solids mass flux, with dense suspension upflow achieved where there was no refluxing of solids near the riser wall on a time-average basis. The transition to DSU conditions could be distinguished by means of variations of net solids flow direction at the wall, annulus thickness approaching zero and flattening of the solids holdup versus G s trend. A new flow regime map is proposed distinguishing the fast fluidization, DSU and dilute pneumatic transport flow regimes.

Flow structure and thickness of annular downflow layer in a circulating fluidized bed riser

Flow structures were determined in a circulating fluidized bed (CFB) riser (0.203 m i.d.×5.9 m high) of FCC particles ( d p=70 μm, ρ s=1700 kg/m 3). A momentum probe was used to measure radial momentum flux profiles at several levels and to distinguish between upward and downward flow regions. Time–mean dynamic pressure (Δ P m) decreases towards the wall in the range U g=5–8 m/s, G s=10–340 kg/m 2 s. The thickness of the annular downflow layer based on Δ P m=0 reaches a maximum with increasing height. The annular downflow layer disappears locally with increasing solids mass flux ( G s) at a constant gas velocity, with achievement of the dense suspension upflow (DSU) regime. A new correlation is developed to predict the time–mean thickness of solids down-flowing layer based on solids mass flux and momentum flux. It successfully accounts for the variation of the annular layer thickness with height and G s, and covers a wide G s range right up to near the onset of the DSU regime.

Investigating 2D Modeling of Atmospheric Convection in the PBL

The performance of a two-dimensional (2D) numerical model in representing three-dimensional (3D) planetary boundary layer (PBL) convection is investigated by comparing the 2D model solution to that of a 3D large- eddy simulation. The free convective PBL has no external forcing that would lead to any realizable 2D motion, and hence the 2D model represents a parameterization (not a simulation) of such a convective system. The present solutions show that the fluxes of conserved scalars, such as the potential temperature, are somewhat constrained and hence are not very sensitive to the model dimensionality. Turbulent kinetic energy (TKE), surface friction velocity, and velocity variances are sensitive to the subgrid-scale eddy viscosity and thermal diffusivity in the 2D model; these statistics result mostly from model-generated hypothetical 2D plumes that can be tuned to behave similarly to their 3D counterparts. These 2D plumes are comparable in scale with the PBL height due to the capping inversion. In the presence of shear, orienting the 2D model perpendicular to the mean shear is essential to generate a reasonable momentum flux profile, and hence mean wind profile and wind- related statistics such as the TKE and velocity variances.

SODAR-based estimation of TKE and momentum flux profiles in the atmospheric boundary layer: Test of a parameterization model

A simple parameterization for the estimation of turbulent kinetic energy (TKE) and momentum flux profiles under near-neutral stratification based on sodar measurements of the vertical velocity variance has been tested using data from the LINEX-2000 experiment. Measurements included operation of a phased-array Doppler sodar DSDPA.90 and of a sonic anemometer USA-1 mounted at a meteorological tower at a height of 90 m. Good agreement has been found between the TKE and momentum flux values derived from the sonic and sodar data (with correlation coefficients r > 0.90 and a slope of the regression lines of about 1.0 … 1.1) suggesting the possible use of sodar measurements of σ w 2 to derive turbulence parameter profiles above the tower range.

Momentum flux due to trapped lee waves forced by mountains

AbstractA simple, but general, horizontal momentum budget for inviscid flow is developed to understand how the vertical flux of horizontal momentum varies with height in a mountain‐forced trapped lee‐wave train. Taking a sinusoidal form for the wave field, from the analytical solution for a two‐layer Scorer‐parameter atmosphere, the constant Bernoulli functional on a streamline is used to diagnose the momentum flux. It is shown that in an inviscid, steady wave train the magnitude of the momentum flux decreases with height as a sinusoidal function. The present theory clearly shows how this profile of momentum flux with height is a direct consequence of the exact balance between the vertical derivative of momentum flux and the dynamic pressure difference across the mountain in steady state. The simple analytic profile of flux with height shows a remarkable qualitative similarity with numerical‐model results from idealized case‐studies of flow over an isolated mountain ridge. © Crown copyright, 2002.

Evapotranspiration and turbulent transport in an irrigated desert orchard

[1] Micrometeorological measurements were recorded in an irrigated pecan orchard for 2 weeks in the summer of 1996 near Las Cruces, NM. A vertical array of five sonic anemometers recorded three-dimensional wind and temperature data within and above the orchard. The measured energy budget closure error was only 3.2% of net radiation, indicating freedom from local edge advection. The effects of regional (oasis) advection and unsteady winds on evapotranspiration (ET) were considered by comparing the observed latent heat flux values to estimates of ET using the Penman–Monteith and Advection–Aridity approaches. Penman–Monteith underestimated observed ET values by 82%. The Advection–Aridity modifications of potential evapotranspiration (PET) underestimated ET by 11%. Profiles of turbulence statistics demonstrated vertical heterogeneity of turbulence within the canopy. Directly above the canopy, momentum flux profiles showed little divergence. However, at a level of two times the tree heights, sensible heat flux profiles did show divergence, confirming the presence of “oasis” advection resulting from warm, dry air moving above the internal boundary layer. Upward convection from the hot soil surface between the trees diluted the oasis condition to the point where a weak upward sensible heat flux was observed during the midday periods when the soil was not shaded. Convection ratios, and exuberance ratios, generated from quadrant analyses of the heat and momentum flux events, showed that turbulent motions moved freely up and down within this canopy with little attenuation due to the open spaces between the trees.

A theory for the estimation of surface fluxes in simple katabatic flows

The classical Prandtl model describes the basic dynamics of katabatic flows, but it fails in determining the gradients near the surface because the eddy diffusivity, K, is independent of height, z. An improvement is proposed to the Prandtl model by using the WKB method to solve the dynamic equation for any prescribed, reasonably smooth, K(z) profile. The surface fluxes are obtained by extrapolation from the katabatic jet down to the surface, thus the fluxes depend primarily on the jet which is well captured by the WKB method. The profiles of wind, temperature, momentum and heat fluxes, as well as the surface fluxes calculated using the model, are tested against observations from a meteorological field campaign on the Pasterze glacier, Austria, in 1994, and their numerical simulations. Generally there is a good agreement between observations and theory.

A theory for the estimation of surface fluxes in simple katabatic flows

AbstractThe classical Prandtl model describes the basic dynamics of katabatic flows, but it fails in determining the gradients near the surface because the eddy diffusivity, K, is independent of height, z. An improvement is proposed to the Prandtl model by using the WKB method to solve the dynamic equation for any prescribed, reasonably smooth, K(z) profile.The surface fluxes are obtained by extrapolation from the katabatic jet down to the surface, thus the fluxes depend primarily on the jet which is well captured by the WKB method. The profiles of wind, temperature, momentum and heat fluxes, as well as the surface fluxes calculated using the model, are tested against observations from a meteorological field campaign on the Pasterze glacier, Austria, in 1994, and their numerical simulations. Generally there is a good agreement between observations and theory.