Cross-isobar Angle Research Articles

Formulation, Implementation and Validation of a 1D Boundary Layer Inflow Scheme for the QUIC Modeling System

AbstractRecent studies have highlighted the importance of accurate meteorological conditions for urban transport and dispersion calculations. In this work, we present a novel scheme to compute the meteorological input in the Quick Urban & Industrial Complex () diagnostic urban wind solver to improve the characterization of upstream wind veer and shear in the Atmospheric Boundary Layer (ABL). The new formulation is based on a coupled set of Ordinary Differential Equations (ODEs) derived from the Reynolds Averaged Navier–Stokes (RANS) equations, and is fast to compute. Building upon recent progress in modeling the idealized ABL, we include effects from surface roughness, turbulent stress, Coriolis force, buoyancy and baroclinicity. We verify the performance of the new scheme with canonical Large Eddy Simulation (LES) tests with the GPU-accelerated FastEddy"Equation missing" solver in neutral, stable, unstable and baroclinic conditions with different surface roughness. Furthermore, we evaluate QUIC calculations with and without the new inflow scheme with real data from the Urban Threat Dispersion (UTD) field experiment, which includes Lidar-based wind measurements as well as concentration observations from multiple outdoor releases of a non-reactive tracer in downtown New York City. Compared to previous inflow capabilities that were limited to a constant wind direction with height, we show that the new scheme can model wind veer in the ABL and enhance the prediction of the surface cross-isobaric angle, improving evaluation statistics of simulated concentrations paired in time and space with UTD measurements.

Structuring of turbulence and its impact on basic features of Ekman boundary layers

Abstract. The turbulent Ekman boundary layer (EBL) has been studied in a large number of theoretical, laboratory and modeling works since F. Nansen's observations during the Norwegian Polar Expedition 1893–1896. Nevertheless, the proposed analytical models, analysis of the EBL instabilities, and turbulence-resolving numerical simulations are not fully consistent. In particular, the role of turbulence self-organization into longitudinal roll vortices in the EBL and its dependence on the meridional component of the Coriolis force remain unclear. A new set of large-eddy simulations (LES) are presented in this study. LES were performed for eight different latitudes (from 1° N to 90° N) in the domain spanning 144 km in the meridional direction. Geostrophic winds from the west and from the east were used to drive the development of EBL turbulence. The emergence and growth of longitudinal rolls in the EBL was simulated. The simulated rolls are in good agreement with EBL stability analysis given in Dubos et al. (2008). The destruction of rolls in the westerly flow at low latitude was observed in simulations, which agrees well with the action of secondary instability on the rolls in the EBL. This study quantifies the effect of the meridional component of the Coriolis force and the effect of rolls in the EBL on the internal EBL parameters such as friction velocity, cross-isobaric angle, parameters of the EBL depth and resistance laws. A large impact of the roll development or destruction is found. The depth of the EBL in the westerly flow is about five times less than it is in the easterly flow at low latitudes. The EBL parameters, which depend on the depth, also exhibit large difference in these two types of the EBL. Thus, this study supports the need to include the horizontal component of the Coriolis force into theoretical constructions and parameterizations of the boundary layer in models.

Friction law and turbulent properties in a laboratory Ekman boundary layer

We use spin-up/spin-down laboratory experiments to study the neutrally stratified Ekman boundary layer. The experiments are performed in the 13 m diameter, 1 m deep Coriolis rotating tank of the LEGI in Grenoble, France. A global flow rotation is produced by an initial change in the tank rotation speed. It then slowly decays under the effect of Ekman friction, evolving from the turbulent state to the laminar state. It is checked that the Ekman layer itself remains in a quasi-steady state during this decay. The velocity is measured by Particle Imaging Velocimetry (PIV) at two scales: the global rotation in a horizontal plane, and the vertical profile inside the boundary layer, where the three velocity components are obtained by stereoscopic PIV. The friction law is obtained by relating the decay rate of the bulk velocity to the velocity itself. This method is justified by the fact that this bulk velocity is independent of height beyond the top of the boundary layer (a few cm), as expected from the Taylor-Proudman theorem for rotating fluids. The local measurements inside the boundary layer provide profiles of the mean velocity and Reynolds stress components, in particular the cross-isobar angle between the interior and near surface velocities. In the laminar regime, good agreement is obtained with the classical Ekman's theory, which validates the method. In the turbulent regime, the results are found consistent with the classical Atmospheric Boundary Layer (ABL) model based on the von Karman logarithmic layer. Our experiments therefore indicate that this theory, in principle valid for very large Reynolds numbers, is already relevant close to the transitional regimes. A fit of the empirical coefficients A and B appearing in this theory yields A = 3.3 and B = 3.0. Extrapolating the results to the atmospheric case gives a friction velocity u* about 12% higher than the traditional fit for the ABL. We may safely deduce that for the oceanic bottom boundary layer, corresponding to lower Reynolds numbers than the atmosphere, our result provides a correct estimate within 10%. The previous laboratory results of Caldwell et al. [“A laboratory study of the turbulent Ekman layer,” Geophys. Fluid Dyn. 3, 125–160 (1972)10.1080/03091927208236078] provided frictions velocities about 20% higher than in our experiments, and slightly higher cross-isobar angles. We attribute this difference to the higher vortical Rossby number Rot in those experiments, and maybe also to roughness effects. We take into account the effect of this vortical Rossby number within the framework of the Ekman layer (Rot → 0) by replacing the tank rotation rate by the fluid rotation rate.

A Study of the Stable Boundary Layer Based on a Single-Column K-Theory Model

We document numerical experiments with a single-column, high-resolution model of the stable boundary layer. The model resolves the logarithmic layer, and does not require inverting the Monin–Obukhov similarity functions in order to calculate the surface fluxes. The turbulence closure is based on the K-theory approach, with a new form of stability functions of the Richardson number, evaluated by using the Surface Heat Budget of the Arctic Ocean (SHEBA) and the Cooperative Atmosphere-Surface Exchange Study (CASES-99) data. A comparison with two, high-resolution large-eddy simulation models shows very good agreement. The reported numerical experiments test the effects of shear, surface cooling, the Coriolis parameter, subsidence, and baroclinicity. The time evolution of the drag coefficient, the heat-transfer coefficient, and the cross-isobar angle is also evaluated.

Neutrally Stratified Turbulent Ekman Boundary Layer: Universal Similarity for a Transitional Rough Surface

The geostrophic Ekman boundary layer for large Rossby number (Ro) has been investigated by exploring the role played by the mesolayer (intermediate layer) lying between the traditional inner and outer layers. It is shown that the velocity and Reynolds shear stress components in the inner layer (including the overlap region) are universal relations, explicitly independent of surface roughness. This universality of predictions has been supported by observations from experiment, field and direct numerical simulation (DNS) data for fully smooth, transitionally rough and fully rough surfaces. The maxima of Reynolds shear stresses have been shown to be located in the mesolayer of the Ekman boundary layer, whose scale corresponds to the inverse square root of the friction Rossby number. The composite wall-wake universal relations for geostrophic velocity profiles have been proposed, and the two wake functions of the outer layer have been estimated by an eddy viscosity closure model. The geostrophic drag and cross-isobaric angle predictions yield universal relations, which are also supported by extensive field, laboratory and DNS data. The proposed predictions for the geostrophic drag and the cross-isobaric angle compare well with data for Rossby number Ro ≥ 105. The data show low Rossby number effects for Ro < 105 and higher-order effects due to the mesolayer compare well with the data for Ro ≥ 103.

Universal dependences between turbulent and mean flow parameters instably and neutrally stratified Planetary Boundary Layers

Abstract. We consider the resistance law for the planetary boundary layer (PBL) from the point of view of the similarity theory. In other words, we select the set of the PBL governing parameters and search for an optimal way to express through these parameters the geostrophic drag coefficient Cg=u* /Ug and the cross isobaric angle α (where u* is the friction velocity and Ug is the geostrophic wind speed). By this example, we demonstrate how to determine the "parameter space" in the most convenient way, so that make independent the dimensionless numbers representing co-ordinates in the parameter space, and to avoid (or at least minimise) artificial self-correlations caused by the appearance of the same factors (such as u*) in the examined dimensionless combinations (e.g. in Cg=u* /Ug) and in dimensionless numbers composed of the governing parameters. We also discuss the "completeness" of the parameter space from the point of view of large-eddy simulation (LES) modeller creating a database for a specific physical problem. As recognised recently, very large scatter of data in prior empirical dependencies of Cg and α on the surface Rossby number Ro=Ug| fz0|-1 (where z0 is the roughness length) and the stratification characterised by µ was to a large extent caused by incompactness of the set of the governing parameters. The most important parameter overlooked in the traditional approach is the typical value of the Brunt-Väisälä frequency N in the free atmosphere (immediately above the PBL), which involves, besides Ro and µ, one more dimensionless number: µN=N/ | f |. Accordingly, we consider Cg and α as dependent on the three (rather then two) basic dimensionless numbers (including µN) using LES database DATABASE64. By these means we determine the form of the dependencies under consideration in the part of the parameter space representing typical atmospheric PBLs, and provide analytical expressions for Cg and α.

One-Equation Turbulence Modelling for Atmospheric and Engineering Applications

A new algebraic turbulent length scale model is developed, based on previous one-equation turbulence modelling experience in atmospheric flow and dispersion calculations. The model is applied to the neutral Ekman layer, as well as to fully-developed pipe and channel flows. For the pipe and channel flows examined the present model results can be considered as nearly equivalent to the results obtained using the standard k–ɛ model. For the neutral Ekman layer, the model predicts satisfactorily the near-neutral Cabauw friction velocities and a dependence of the drag coefficient versus Rossby number very close to that derived from published (G. N. Coleman) direct numerical simulations. The model underestimates the Cabauw cross-isobaric angles, but to a less degree than the cross-isobar angle versus Rossby dependence derived from the Coleman simulation. Finally, for the Cabauw data, with a geostrophic wind magnitude of 10 ms−1, the model predicts an eddy diffusivity distribution in good agreement with semi-empirical distributions used in current operational practice.

Model predictions of coastal winds in a small scale

Details of surface winds across a flat and non-curved coastline have been considered, mostly in the 1–10 km scale, by looking at some published observed cases and simulating with a high-resolution numerical model. Stability conditions were emphasized by having the land and sea at slightly different temperatures, but sea breeze conditions were excluded.A warm surface generally enhances momentum transfer and wind speed, and reduces the cross-isobar angle. This transforms to rapid acceleration and downstream veering of offshore winds as they enter a warm, smooth sea. Cold sea, on the other hand, strongly inhibits vertical momentum transfer. This leads to offshore winds temporarily backing downstream off the coast, accelerating only slowly and even decreasing in speed in some cases. These observed facts were well simulated by the model.Onshore flow on to cold land brought along rapid deceleration and strong inland backing of winds. The deceleration was weaker and more gradual over warm land with downstream veering instead. Smaller geostrophic wind speed accentuated these and all other stability effects as the wind shears then were weaker relative to the buoyancy effects (i.e. the absolute values of the local Richardson numbers were larger).For large-scale winds along the shore with land on the right, the induced coastal convergence and rising motion appears only above about 100 m height in the cold sea simulations (typical of early summer). Below, there is divergence and hence relatively weak coastal wind. The case is the opposite for winds with land on the left (e.g. westerlies along a south coast): then the coastal surface winds are relatively strong along a cold sea. For a warm sea (typical of autumn) these low-level features disappear and coastal 10 m winds tend to be close to the geostrophic wind in speed and direction for all onshore directions.

Evaluating Models of The Neutral, Barotropic Planetary Boundary Layer using Integral Measures: Part I. Overview

Data for the cross-isobaric angle α0, the geostrophic drag coefficient Cg, and the functions A and B of Rossby number similarity theory, obtained from meteorological field experiments, are used to evaluate a range of models of the neutral, barotropic planetary boundary layer. The data give well-defined relationships for α0, Cg, and the integrated dissipation rate over the boundary layer, as a function of the surface Rossby number. Lettau's first-order closure mixing-length model gives an excellent fit to the data; other simple models give reasonable agreement. However more sophisticated models, e.g., higher-order closure, large-eddy simulation, direct numerical simulation and laboratory models, give poor fits to the data. The simplemodels have (at least) one free parameter in their turbulence closure that is matched toatmospheric observations; the more sophisticated models either base their closure onmore general flows or have no free closure parameters. It is suggested that all of theatmospheric experiments that we could locate violate the strict simplifying assumptionsof steady, homogeneous, neutral, barotropic flow required by the sophisticated models.The angle α0 is more sensitive to violations of the assumptions than is Cg.

The Contribution of Organized Roll Vortices to the Surface Wind Vector in Baroclinic Conditions

Abstract Observations show that, for a given geostrophic forcing, baroclinity acting on the planetary boundary layer produces a nearly sinusoidal modification of the near-surface wind. Compared to barotropic conditions the speed is enhanced in the direction of the thermal wind and the cross-isobar angle increases (decreases) in cold (warm) advection. These modifications are asymmetric with respect to the thermal wind orientation. Two-layer similarity models that match a stratification-dependent surface layer to a stratification and baroclinity dependent Ekman layer simulate aspects of this asymmetric baroclinic modification if the cold advection conditions are more unstably stratified than the warm advection conditions. The authors demonstrate that roll vortices in a baroclinic planetary boundary layer produce an asymmetric surface wind modification in neutral stratification that can work in concert with the coupling between stratification and baroclinity to enhance the net effect of baroclinity on the su...

A Diagnostic Method for Computing the Surface Wind from the Geostrophic Wind Including the Effects of Baroclinity

Abstract A diagnostic procedure to compute the surface wind from the geostrophic wind including the effects of baroclinity is designed and tested. Expressions are derived to calculate the similarity functions A and B for use when only the surface geostrophic wind Vg0 and its vertical derivative ∂Vg/∂z are known (i.e., no atmospheric boundary-layer winds are available). The cross-isobaric angle of the surface wind has a maximum for δ=122° and a minimum for δ=300°, where δ is the angle counterclockwise from Vg0 to ∂Vg/∂z. The surface wind speed is highest for δ=30° and lowest for δ=210°. The results are compared to observations and the agreement is quite good.

A study of mixed-layer momentum evolution

Evolution of mixed-layer momentum is studied using a zeroth-order jump model of the mixed layer. The geostrophic Ekman number for the mixed layer is found to be an important parameter in determining the behavior of mixed-layer momentum. Two types of parameterizations of the surface momentum fluxes, viz. linear and quadratic friction relations, are compared. For the stationary case, the two models become identical when the linear friction factor r is chosen to give the same cross-isobaric angle predicted by the quadratic friction model. Theoretically the linear friction relation provides exponential decay of inertial oscillation while the quadratic friction model introduces damping inversely proportional to time. In actual numerical simulations, however, these model differences are not very significant, especially when r which is taken as a function of time, is appropriately estimated. From the case studies of Cabauw data (Driedonks, 1981) some important features of mixed-layer momentum evolution during daytime are revealed. Similar to the thermodynamic evolution of the mixed layer, the momentum field also experiences diurnal changes which are seen through the diurnal variations of the relative contributions of surface friction, entrainment of momentum and large-scale pressure gradient forcing in the mean kinetic energy budget and the diurnal variation of cross-isobaric angles of the mixed-layer winds. However, for the days when advection and other large-scale effects are present, the predictions of the model are not favorable.

Effects of local accelerations and baroclinity on the mean structure of the atmospheric boundary layer over the sea

Substitution of the geostrophic wind by the actual upper wind in the equations of motion for the boundary layer implies less sensitivity of the mean wind to inertial effects. This is confirmed by observations, although the problem of computing time or spatial derivatives from scattered data reduces the accuracy and the clarity of the results. It is found that acceleration (deceleration) increases (decreases) the cross-isobar angle whereas the geostrophic drag coefficient is a minimum (maximum) for crosswind acceleration (deceleration). On the other hand, cold air advection increases the cross-isobar angle whereas the geostrophic drag coefficient is a maximum when the thermal wind is parallel to the surface wind. The universal functions Am and Bm based on vertically averaged winds are also rather insensitive to inertial influences.

Simulations of Cold Surges over Oceans with Application to AMTEX'75

Comparative numerical experiments and observational verifications for cold surges over the ocean are conducted using a primitive equation planetary boundary layer (PBL) model. The comparative experiments illustrate the importance of large-scale environmental conditions on air mass transformation. Such factors as baroclinity, static stability, moisture content, upwind inversion strength and height exert strong controls on the downwind evolution of the PBL and clouds. Most results are obtained for clouds in the cumulus mode, but two comparisons are made with simpler stratocumulus simulations. The PBL flow is influenced by the synoptic geostrophic wind distribution and the PBL depth is also sensitive to large-scale vertical velocity. The responses of this advective PBL to stronger wind are found to be different from that of a horizontally homogeneous PBL. A simulation of an intense cold air outbreak observed during the Air Mass Transformation Experiment, 1975 (AMTEX'75) is performed. Downwind variations of dynamic and thermodynamic PBL properties and cloud distribution and type are well reproduced. The steep sea-surface temperature gradient produces strong PBL baroclinity and a strongly divergent PBL flow. The simulated large cross-isobar angle associated with intense cold air advection and vigorous momentum mixing is in favorable agreement with both observation and theory.

Assessment of the separate effects of baroclinicity and thermal stability in the atmospheric boundary layer over the sea

Pibal soundings taken during the period 1929 to 1936 were analysed to augment our knowledge of boundary layer climatology. Use of the geostrophic departure method enables computation of surface stress and the cross-isobar angle as functions of stability and baroclinicity, the latter being assessed from the upper wind shear. The comparative effects of both terms are discussed and the importance of the often-neglected baroclinicity in explaining the scatter of the computed parameters is stressed. Use of similarity theory enables us to achieve some further order in the data and eventually to estimate the universal functions A and B freed from baroclinic effects. DOI: 10.1111/j.2153-3490.1982.tb01845.x

A Statistical Model for Wind Prediction at a Mountain and Valley Station Near Anderson Creek, California

Abstract Statistical models for surface-wind predictions at a mountain and a valley station near Anderson Creek, California, have been constructed. It is found that the surface wind speed depends primarily on the slope wind, cross-isobaric angle, surface thermal stability and geostrophic wind. The correlations between the calculated and observed surface wind speeds are found to be high for all time periods of the day and night. Because the variability of wind direction, which is greatly affected by topography, geostrophic wind and turbulent motion, is generally larger than that of the surface wind speed, statistical models for wind direction are more complicated than those for the wind speed. It is found that wind direction depends primarily on the geostrophic wind direction, aspect angle of the topography, up-canyon direction and cross-isobaric angle in the boundary layer.

熱帯海洋上の境界層の風の構造

Ship-based measurements of wind profiles in the boundary layer were carried out suc-cessfully in the tropical western Pacific, as a part of the observational program of the MONEX in Japan. A wind-finding procedure by use of pilot-balloon observation on board a ship is developed for the present study. Observed wind field in the boundary layer shows the characteristics of the mixed layer, that is, the layer of uniform wind speed and direction in the vertical. The depth of the layer almost corresponds with that of the mixed layer deter-mined from the thermodynamical structure of the boundary layer. The results seem to be in contrast with the general feature in the undisturbed trade winds where there appears appreciable vertical shear of wind speed in the thermodynamically determined mixed layer. A few estimations of cross-isobar angle and ratio of actual to geostrophic wind speed of the boundary layer wind are made, though roughly, in good agreement with climatological value in lower latitudes. An evidence is obtained that the depth of "a density current" by downdraft in front of the squall cell is about two hundred meters above the sea surface.

A Two-Layer First-Order Closure Model for the Study of the Baroclinic Atmospheric Boundary Layer

Abstract A steady-state two-layer model has been developed for the baroclinic boundary layer. The lower layer is the constant flux surface layer (SL) in which the eddy viscosity K varies with height and stability according to the Monin-Obukhov similarity theory; the upper one is the Ekman layer in which K is fixed at the value attained at the top of the SL. The equations of motion in the Ekman layer are solved using the Green's function approach. The lower boundary condition gives two equations from which the nondi-mensionalized friction velocity u*/Vg0 and the cross-isobaric angle α0 can be obtained in terms of the other known parameters. These equations are compared with the resistance laws. The boundary condition also is given a geometrical interpretation. It has been shown that if Vg(z) is linear, the variation of α0 and u*/Vg0 with θ, the angle between Vg(0) (surface isobars) and thermal wind (isotherms), is sinusoidal. Also, there is a phase difference of 90° between the variation of α0 and u*/Vg0, ...

On the dynamics and climatology of surface flow over the Equatorial oceans

The surface circulation over the Equatorial Atlantic and Eastern Pacific is investigated using 60-year average ship data with a one-degree square resolution. At the height of the Northern summer, a zonally oriented speed maximum extends across the Eastern part of the oceans at about 4–5 N, near where the cross-equatorial flow recurves from Southeast to Southwest. This separates a band of strong divergence immediately to the North of the Equator from the convergence belt further poleward. Strongest convergence occurs about 350 km South of the confluence between Northern and Southern Hemisphere trades, and within a region of high directional steadiness of wind. A negative wind stress curl induces upwelling and low sea surface temperature immediately South of the Equator, and downwelling to the North. In most of the Northeast trades and the Southeast trades of the Southern Hemisphere during July–August, frictional energy dissipation not offset by cross-isobaric flow produces a gradual slowing of the current and downstream convergence. As the Southern Hemisphere trades flow North from the Equator over the Eastern part of the oceans, the Coriolis acceleration increases acting to the right, enhancing the cross-isobaric angle and resulting in net kinetic energy generation, the aforementioned speed maximum and attendant zone of strong divergence. Continuation of this Coriolis effect recurves the flow from Southeast to Southwest, which further downstream diminishes the cross-isobaric angle, thus impairing kinetic energy generation and resulting in a band of maximum convergence. A positive relation is found between the latitude of the discontinuity separating Northern and Southern Hemisphere trades and the latitude and intensity of the zonally oriented convergence/divergence bands, both seasonally and on a year-to-year basis. DOI: 10.1111/j.2153-3490.1978.tb00859.x

地衡風抵抗及び地表風向と等圧線のなす角度の安定度依存性に関する数値的研究

地衡風抵抗及び地表風向と等圧線のなす角度の安定度依存性に関する数値的研究