Flow over the summit of an isolated hill

Observations of the mean flow and turbulence statistics over the summit of an isolated, roughly circular hill, Nyland hill, are presented, Nyland hill rises 70 m above the surrounding terrain and has a base diameter of about 500 m. The summit of the hill is very smooth and allows representative measurements to be made close to the surface. The flow speed 8 m above the summit is increased by a factor of 2 over the upstream speed 8 m above level terrain, and flow separation occurs in the lee of the hill. The mean velocity profile over the summit shows an increase in velocity with height up to about 2 m and then a near constant velocity between 2 and 16 m. The flow perturbation relative to the upstream profile is thus a maximum at about 2 m. The measurements of turbulence structure show how the influence of the hill depends on the length scale of the turbulent eddies involved. Scales greater than the scale of the hill are modified through the flow speed-up whilst scales shorter than the hill suffer complex changes. The short-scale turbulence over the summit is only in local equilibrium in the lowest fraction of a metre. Above this equilibrium region, there is a complex adjustment towards the rapid distortion dynamics which appear to dominate at heights above about 8 m. The detailed results are compared with previous studies and available theories.     

Evaluation of an alternative method for numerically modeling nonhydrostatic flows over irregular terrain

Modeling nonhydrostatic atmospheric flow requires the solution of the vertical equation of motion and a prognostic or diagnostic equation for pressure. If the nonhydrostatic components of the flow are relatively small, they can be approximated and incorporated into a purely hydrostatic model, which usually is conceptually simpler and computationally more efficient. A method to do this for a linear model of local thermally-induced circulations is further developed and adapted to a non-linear numerical model of the neutral atmospheric boundary layer. A hydrostatic model and the quasi-nonhydrostatic version were used to simulate neutral flow over simple terrain features. One set of observations taken over a simple change in roughness and another set taken over a change in both roughness and terrain were simulated by both models to assess the capabilities of the quasi-nonhydrostatic technique.It is found that (as expected) the pressure deviation from the hydrostatic state is negligible for the roughness change, but it is an important aspect of neutral flow over terrain. Thus, for flow encountering a simple roughness change, the hydrostatic approximation is good, even for small horizontal scales. However, the quasi-nonhydrostatic model qualitatively produces the features in the observations for flow over a terrain change that the hydrostatic model cannot produce.Journal Paper No. J-12737 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 2779.     

A comparison of wind-tunnel experiments and numerical simulations of neutral and stratified flow over a hill

A comparison is made of numerical and experimental results for flow over two-dimensional hills in both neutral and stably stratified flow. The numerical simulations are carried out using a range of one-and-a-half order and second-order closure schemes. The performance of the various turbulence schemes in predicting both the mean and turbulent quantities over the hill is assessed by comparing the results with new wind-tunnel measurements. The wind-tunnel experiments include both neutral and stably stratified flow over two different hills with different slopes, one of which is steep enough to induce flow separation. The dataset includes measurements of the mean and turbulent parts of the flow using laser Doppler anemometry. Pressure measurements are also made across the surface of the hill. These features make the dataset an excellent test of the model performance. In general second-order turbulence schemes provide the best agreement with the experimental data, however, they can be numerically unstable for steep hills. Some modifications can be made to the standard one-and-a-half order closure scheme, which results in improved performance at a fraction of the computation cost of the second-order schemes.     

A new nonlinear analytical model for canopy flow over a forested hill

A new nonlinear analytical model for canopy flow over gentle hills is presented. This model is established based on the assumption that three major forces (pressure gradient, Reynolds stress gradient, and nonlinear canopy drag) within canopy are in balance for gentle hills under neutral conditions. The momentum governing equation is closed by the velocity-squared law. This new model has many advantages over the model developed by Finnigan and Belcher (Quart J Roy Meteorol Soc 130: 1–29 2004, hereafter referred to as FB04) in predicting canopy wind velocity profiles in forested hills in that: (1) predictions from the new model are more realistic because surface drag effects can be taken into account by boundary conditions, while surface drag effects cannot be accounted for in the algebraic equation used in the lower canopy layer in the FB04 model; (2) the mixing length theory is not necessarily used because it leads to a theoretical inconsistency that a constant mixing length assumption leads to a nonconstant mixing length prediction as in the FB04 model; and (3) the effects of height-dependent leaf area density (a(z)) and drag coefficient (C _d ) on wind velocity can be predicted, while both a(z) and C _d must be treated as constants in FB04 model. The nonlinear algebraic equation for momentum transfer in the lower part of canopy used in FB04 model is height independent, actually serving as a bottom boundary condition for the linear differential momentum equation in the upper canopy layer. The predicting ability of the FB04 model is largely restricted by using the height-independent algebraic equation in the bottom canopy layer. This study has demonstrated the success of using the velocity-squared law as a closure scheme for momentum transfer in forested hills in comparison with the mixing length theory used in FB04 model thus enhancing the predicting ability of canopy flows, keeping the theory consistent and simple, and shining a new light into land-surface parameterization schemes in numerical weather and climate models.     

Weakly nonlinear oscillatory flow over an isolated seamount

Abstract

Numerical models can show large errors in the modelling of flow around tall topography. We present a weakly nonlinear analytical solution of barotropic oscillatory flow over a tall axisymmetric seamount and compare the results to a numerical tidal model. The comparison is formulated for a flat topped seamount with parabolic sides and for a standing wave boundary condition in order to make the problem analytically tractable and to reduce it to a series of ordinary differential equations. The comparison shows reasonable agreement within the confines of the analytical formulation confirming that the numerical model can exploit tall topography. Comparisons to a Gaussian seamount and Kelvin wave forcing illustrate the generality of the results.

The analytical formulation produces an equation relating relative errors in the comparison to discontinuities in topographical slope; the numerical model should have smaller errors over smoother topography. Residual velocities are found to be proportional to the aspect ratio of the topography.     

A model of atmospheric boundary-layer flow above an isolated two-dimensional ‘hill’; an example of flow above ‘gentle topography’

A numerical model is developed for two-dimensional turbulent boundary-layer flow above gentle topography — defined as not giving rise to mean flow separation. Although the model is formulated in a framework of mixing length and turbulent energy equation models for the surface layer of the atmospheric boundary layer, it could be modified to include higher-order closure hypotheses and/or extended to model gentle topography for the planetary boundary layer or on the sea bed. Results are presented for flow above a specific shape of hill and the effects of surface roughness and hill height are investigated.     

On the parameterization of drag over small-scale topography in neutrally-stratified boundary-layer flow

Predictions of the surface drag in turbulent boundary-layer flow over two-dimensional sinusoidal topography from various numerical models are compared. For simple 2D terrain, the model results show that the drag increases associated with topography are essentially proportional to (slope)² up to the steepness at which the flow separates. For the purposes of boundary-layer parameterisation within larger-scale models, we propose a representation of the effects of simple 2D topography via an effective roughness length, z ₀ ^eff. The form of the varation of z ₀ ^eff with terrain slope and topographic wavelength is established for small slopes from the model results and a semi-empirical formula is proposed.     

A mixed spectral finite-difference model for pollutant concentrations over a hill

Given incident logarithmic profiles of wind and pollutant concentration above a rough, absorbing surface, the three-dimensional distribution of pollutant concentration over a hill of gentle slope is determined from a linearized model. The model is applied in neutrally stratified flow, without chemistry, and is integrated using spectral methods in the horizontal and a finite-difference scheme in the vertical. This approach allows for flexibility in choosing a closure scheme and a variety of surface boundary conditions. This was not possible in the analytic approach of Padro (1987) who added pollutant concentration and flux to the MS3DJH/1 model of Walmsley et al. (1980). The present model requires as input the turbulent kinetic energy, E, dissipation, , and the perturbation vertical velocity, w, from the three-dimensional boundary-layer flow model of Beljaars et al. (1987), hereinafter referred to as MSFD, The latter model also supplies wind velocity perturbations at the upper boundary, as input to upper boundary conditions on the pollutant flux perturbations.The present study describes applications of the model to idealized terrain features: isolated two- and three-dimensional hills and ridges and an infinite series of ridges. (Application to real terrain, however, presents no difficulties.) Comparisons were made with different (though uniform) surface roughnesses. Tests were performed to examine the effect of upstream terrain features in the periodic domain and to illustrate the importance of the vertical resolution of the output for interpreting results from the sinusoidal terrain case.     

Neutral surface-layer flow over isolated roughness strips

Numerical simulations are used to study neutral surface-layer flow which passes over isolated or widely separated strips of modified roughness embedded in an otherwise homogeneous surface.Simple power laws are given for the maximum height and horizontal extent of turbulent momentum and horizontal mean velocity wakes with an assessment of the range of validity of this proposal. Furthermore, it is indicated, how vertical profiles of energy budget and horizontal mean velocity are distorted by a roughness strip.     

A new parameterization of eddy diffusivities for nocturnal boundary-layer modeling

Exchange coefficients and mixing lengths under stable stratification have been studied through measurements of mean wind velocity and temperature in the nocturnal boundary layer. For values of the gradient Richardson number lower than 0.15, our measurements fit well the relation of Delage (1974). Beyond Ri = 0.15, the decrease of mixing length is much slower. So a new parameterization of turbulent exchanges is suggested. When introduced in a model of the nocturnal boundary layer, it results in a thickening of the turbulent and inversion layers.     

The onset of separation in neutral,turbulent flow over hills

The onset of separation in turbulent, neutrally stratified, boundary-layer flow over hills is considered. Since the flows are fully turbulent, the occurrence of intermittent separation, in the sense of any reversal of near surface flow, will depend strongly on the detailed structure and behaviour of the turbulent eddies. Very little is known about such intermittent separation and the phenomenon cannot be studied with numerical models employing standard turbulence closures; eddy-resolving models are required. Therefore, here, as elsewhere in the literature, the arguably less physically significant process of mean flow separation is studied. Numerical simulations of flow over idealised two- and three-dimensional hills are examined in detail to determine the lowest slope, _crit, for which the mean flow separates.Previous work has identified this critical slope as that required to produce a zero surface stress somewhere over the hill. This criterion, when a mixing-length turbulence closure is applied, reduces to requiring the near-surface vertical velocity shear to vanish at some point on the hill's surface. By applying results from a recent linear analysis for the flow perturbations to this condition, a new expression for _crit is obtained. The expression is approximate but its relative simplicity makes it practically applicable without the need for use of a computer or for detailed mapping of the hill. The approach suggested differs from previous ones in that it applies linear results to a non-linear expression for the surface stress. In the past, a linear expression for the surface stress has been used. The proposed expression for _crit leads to critical angles that are about twice previous predictions. It is shown that the present expression gives good agreement with the numerical results presented here, as well as with other numerical and experimental results. It is also consistent with atmospheric observations.     

The Kettles Hill Project: Field observations,wind-tunnel simulations and numerical model predictions for flow over a low hill

Field observations of the influence of topography on steady, neutrally-stratified boundary-layer flow were carried out in February 1981 and March 1984 on Kettles Hill near Pincher Creek, Alberta, Canada. The primary measurements were of wind speed at 3,6, and 10 m levels at stations in linear arrays along and across the major axis of this gentle, 1 km long and 100 m high, elliptical hill. Wind profile measurements up to heights of 200 m were made with TALA kites and tethersondes on the hilltop and at a reference site located about 3.7 km west of the hilltop. In addition, AIRsondes were flown and tracked from the reference site to provide additional data. The field observations provided the basic data for a comparison with wind-tunnel and numerical model simulations of the same flow. The wind-tunnel investigation was carried out in the Atmospheric Environment Service Boundary-Layer Wind Tunnel while the numerical model used was MS3DJH. For horizontal profiles of normalized mean wind speed at given heights above the prototype terrain, model results agree reasonably well with the field data. The wind-tunnel predictions are slightly high in most cases. For vertical profiles of wind speed up to 200 m above the hilltop, the numerical and wind-tunnel values are higher than were observed. The sensitivity of the normalized wind speed at the hilltop to deviations from non-logarithmic upwind profiles is demonstrated with data from the March 1984 experiment. A comparison of prototype with numerical-model mean-wind-direction perturbations at the 10 m level shows reasonable agreement except near the summit of the hill.Contractor: 24 Heslop Drive, Toronto.     

Airflow patterns over and around a large three-dimensional hill

Summary Surface wind patterns and air flows within the planetary boundary layer over a large three-dimensional hill of moderate slope are grouped according to Froude number classes. An evolution of flow patterns is shown to occur as the Froude number increases.Separation of the surface flow begins at the base of the lee side of the mountain near the centerline, moving upward on the lee slope as the Froude number increases. Recirculating eddies follow the separation of the lee flow. Eventually the separation line moves forward to the windward side as the Froude number becomes very large. The recirculating eddy becomes unsteady, with indication of an intermittent counterrolating eddy near the lee surface in neutral flow. The lee-side turbulence is enhanced with respect to the windward side due to the large eddies in high Froude number regimes.The concept of a critical height for the approach flow is generally supported. The integral form of the Froude number does not appear to be superior to a bulk Froude calculation in representing a particular airflow pattern.With 6 FiguresDeceased.     

Temperature fluctuations inside a cloud-laden airstream flowing over a hill station

Observations of temperature in a cloud-laden monsoon airstream at a height of 12 m above ground at a hill station, Mahabaleshwar (elevation 1390 m asl), were obtained for ten hours using a linearised thermistor (YSI Part 44202) as a temperature sensor, and analysed. It was found that the frequency distributions of temperatures were multimodal. The horizontal temperature gradients in the air stream were symmetrically distributed. The temperature spectra in the frequency range (0.001 to 0.1 Hz) studied can be classified into a lower frequency regime and a higher frequency regime separated approximately at the frequency 0.01 Hz or the wave number 3 km^–1. The spectra in the higher range conform to Kolmogorov's power law for the inertial subrange and those in the lower range exhibit a steeper negative slope of the order of -1.3. There is very little variation of air temperature associated with rainfall intensities greater than 4 mm hr^–1; for lower intensities, the smaller the intensity, the greater the variation.     

Some observations of airflow over a large hill of moderate slope

Measurements are presented of mean windspeed and turbulence over Great Dun Fell, which is rather larger than hills investigated in the past, viz., 847 m high, which is comparable to the boundary-layer depth. The Fell is well suited for study, being covered by rough grass with no trees and few other obstructions. It was found that the speed-up of the wind is dominated by the elevated stratification and generally agrees closely with the predictions of the model of Carruthers and Choularton (1982) except when the flow is blocked. On the hill summit, the turbulence is approximately in local equilibrium in at least the lowest 10 m and the turbulence measurements are similar to those obtained within the inner layer at other sites. The transverse and longitudinal components show spectral lags at wavelengths greater than 30 m. This suggests an inner-layer depth of about 1/3 that predicted by Jackson and Hunt (1975). At reduced frequencies (>0.1), a recovery in spectral energy is observed due to gravity wave activity. A large variation in the streamline tilt at the summit is observed depending on whether the airflow regime is supercritical or subcritical.     

Bulk parameterization for a vegetated surface and its application to a simulation of nocturnal drainage flow

Two simple models are presented for describing the surface energy budget above vegetated surfaces. One is the traditional single-source model that includes only one energy budget equation for the entire canopy-soil system, and the other is the double-source model that includes separate energy budget equations for the vegetation canopy and the underlying soil surface. In both models, the bulk transfer coefficients needed to solve the energy budget equations are parameterized as functions of leaf area index, leaf transfer coefficients, and soil surface roughnesses to obtain the best fit to values calculated by a standard multilayer-canopy model. The validity of these models was tested by comparing their performance with that of the multilayer-canopy model for simulation of the surface energy balance and nocturnal drainage flow above vegetation. Results show that the double-source model gives reliable estimations for all cases ranging from sparse to dense vegetation covers; the single-source model is only applicable to dense, fully-covered vegetation. It is also shown that sparse vegetation weakens nocturnal drainage flow, since it isolates the cool underlying soil surface from the atmosphere above the canopy. This phenomenon cannot be described by a traditional single-source model incorporated commonly in many atmospheric models; however, the double-source model adequately describes this process.     

Effects of shear and sharp gradients in static stability on two-dimensional flow over an isolated mountain ridge

Summary ?We have investigated the effects of shear and sharp gradients in static stability and demonstrated how a mountain wave and its associated surface winds can be strongly influenced. Linear theory for two-dimensional, nonrotating stratified flow over an isolated mountain ridge with positive shear and constant static stability shows that the horizontal wind speeds on both the lee and upslope surfaces are suppressed by positive shear. The critical F(=U/Nh where U is the basic wind speed, N the Brunt-Vaisala frequency, and h the mountain height) for the occurrence of wave breaking decreases when the strength of the positive shear increases, while the location for the wave-induced critical level is higher in cases with larger positive shear. The linear theory is then verified by a series of systematic nonlinear numerical experiments. Four different flow regimes are found for positive shear flow over a two-dimensional mountain. The values of critical F which separate the flow regimes are lower when the strength of the positive shear is larger. The location of stagnation aloft from numerical simulations is found to be quite consistent with those predicted by linear theory. We calculate the strongest horizontal wind speed on the lee surface (U _max), the smallest horizontal wind speed on the upslope surface (U _min), the reflection (Ref), and the transmission (Tran) coefficients for different combinations of the stability ratio between the upper and lower layers (i.e. and z ₁ (interface height) in a two-layer atmosphere from linear analytical solutions. Both Ref and Tran are found to be functions of log() but not the interface height (z ₁). Ref is larger when is much different from 1, no matter whether it is larger or smaller than 1. However, Tran decreases when log() increases and approaches 0 when log() is large. The magnitude of the largest U _max (smallest U _min) increases (decreases) as the absolute value of log() increases. It is found that the largest U _max occurs when the nondimensional z ₁ is near for cases with a less stable upper layer or when z ₁ is near for cases with a more stable upper layer. These results are confirmed by nonlinear numerical simulations. We find that linear theory is very useful in qualitative analysis of the possibility of high-drag state for different stability profiles. The location of stagnation aloft in a two-layer atmosphere from numerical simulations agrees very well with those predicted by linear theory. The above findings are applied to investigate the Boulder severe downslope windstorm of 11 January 1972. We find that the windstorm cannot develop if the near mountain-top inversion is located at a higher altitude (e.g.,  km). However, if there exists a less stable layer right below the tropopause, the windstorm can develop in the absence of a low-level inversion. These results indicate the importance of partial reflection due to the structured atmosphere in influencing the possibility of severe downslope windstorms, although partial reflection may not be the responsible mechanism for the generation of windstorms. Received September 25, 1999/Revised February 9, 2000     

Effects of surface flux parameterization on the numerically simulated intensity and structure of Typhoon Morakot (2009)

The effects of surface flux parameterizations on tropical cyclone(TC) intensity and structure are investigated using the Advanced Research Weather Research and Forecasting(WRF-ARW) modeling system with high-resolution simulations of Typhoon Morakot(2009).Numerical experiments are designed to simulate Typhoon Morakot(2009) with different formulations of surface exchange coefficients for enthalpy(C_K) and momentum(C_D) transfers,including those from recent observational studies based on in situ aircraft data collected in Atlantic hurricanes.The results show that the simulated intensity and structure are sensitive to C_K and C_D,but the simulated track is not.Consistent with previous studies,the simulated storm intensity is found to be more sensitive to the ratio of C_K/C_D than to C_K or C_D alone.The pressure-wind relationship is also found to be influenced by the exchange coefficients,consistent with recent numerical studies.This paper emphasizes the importance of C_D and C_K on TC structure simulations.The results suggest that C_D and C_K have a large impact on surface wind and flux distributions,boundary layer heights,the warm core,and precipitation.Compared to available observations,the experiment with observed C_D and C_K generally simulated better intensity and structure than the other experiments,especially over the ocean.The reasons for the structural differences among the experiments with different C_D and C_K setups are discussed in the context of TC dynamics and thermodynamics.     

The turbulent wind flow over an embankment

Under neutral conditions and with low winds, profiles of mean and turbulent wind components have been measured at various points across an embankment with aspect ratio 0.3. These measurements have been compared with and related to those of undisturbed flow in a horizontal homogeneous area on the windward side. The speed-up ratio, the turbulent and mean kinetic energy and the turbulent shear stress are examined. It is found that the flow stagnates on the windward side, accelerates above the crest, and separates behind the crest. The results show a remarkable dependence on the angle of attack. With an angle smaller than 90 °, the influence of the embankment on the mean wind field is reduced but is increased on the turbulent part, as lateral gustiness components are amplified. With the incoming flow normal to the embankment, maximum turbulence is found on the top of the ridge near the surface but at greater heights farther downwind. The same is true for the shear stress, but only for oblique flow, whereas for normal flow a minimum is found above the crest and a maximum on the windward side. Therefore, with varying angle of attack the embankment acts in different ways on mean wind, turbulent kinetic energy, and turbulent stress. Although the winds were low, all effects are clearly evident in the data.