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Li Ding and Robert L. Street

Abstract

A numerical study of the wake structure behind a three-dimensional hill is presented. Large eddy simulation is used to investigate the source of the wake vorticity and the variations of the wake structure with U /Nh. Here, U is the freestream velocity, N is the Brunt–Väisälä frequency, and h is the hill height. The simulation shows that when U /Nh ∼ 1, the wake vorticity originates from baroclinic processes at the initial stage of the wake development. Even though contributions from friction effects increase during the later stage of the wake development, the production of the wake vorticity from baroclinicity remains significant. The wake consists of a pair of vertically oriented vortices, which form vertical lateral boundaries for the wake. When U /Nh ≤ 0.2, the vortical structure of the wake has a horseshoe shape, and the change of the wake width with height reflects the change of the radius of the hill with height. All evidence indicates that the wake at U ≤ 0.2 follows the two-dimensional wake assumption, and thus the wake vorticity comes mainly from surface friction instead of baroclinicity.

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F. L. Ludwig and Robert L. Street

Abstract

Multiresolution feature analysis (MFA), as originally proposed for estimating the fractal dimension of two-dimensional scalar fields, is described. MFA applies specified correlation filters to a data field (such as a gray-scale image) at different resolutions and examines the scaling of the intensities of the spatial peaks in the filter outputs at the different scales. These scaling properties can be related to different types of fractal dimension. One attractive aspect of MFA is that it gives the analyst flexibility to choose physically significant features for filtering. This paper describes the original MFA technique and then extends the technique from two-dimensional scalar fields to two-dimensional vector fields. In principle, the three-dimensional vector applications allow the estimation of the fractal dimension of the support for turbulent fluctuations but there are limitations on the applicability of the methodology, which are discussed. MFA requires definition of physically significant features, which take the form of small-scale patterns of motion when the technique is applied to three-dimensional flows. The authors describe statistical techniques (similar to principal component analysis) that can be applied to small subvolumes of data to identify those motion patterns that explain the most variance. These small-scale patterns of spatial variability then serve as the features in the version of MFA described here. Possible applications, modifications, and extensions of the methodology that has been developed are given.

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Angelos N. Findikakis and Robert L. Street

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Some aspects of the large eddy simulation method as applied to stratified flows are discussed and an algebraic model for subgrid-scale (SGS) turbulence is proposed. Differential equations for the SGS Reynolds stresses and turbulent heat fluxes are derived and new terms, which appear as a result of filtering nonlinear terms, are discussed. With the introduction of certain simplifying assumptions, the set of differential equations is reduced to a system of algebraic equations. The behavior of the solution of this system is studied for the special case of a locally two-dimensional structure for the large-scale field. Under certain assumptions the form of the algebraic equations for the SGS quantities is similar to the form of the equations for the corresponding “conventional” turbulent quantities. This allows comparison of the predictions made by the present SGS model to the results from “conventional” models and experimental data. The proposed model predicts that, for highly stratified flows, SGS turbulence is totally suppressed if the large-scale field is characterized by pure shear. In the presence of stretching, SGS turbulence approaches a constant level asymptotically as the intensity of stratification increases.

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Robert L. Street and Woodruff Miller Jr.

Abstract

The thicknesses of the viscous and thermal sublayers in the water beneath an air-water interface are obtained by an application of the theory of rough-wall flows to results obtained in a laboratory wind, water-wave research facility. For fully rough flow the dimensionless viscous sublayer thickness δv+ is proportional to the square root of the roughness Reynolds number h + based on mean roughness height, i.e., δv+ = 0.37h + frac12;. In addition, if Pr is the (molecular) Prandtl number, the dimensionless thermal sublayer thickness δt+ = 0.37h + −frac12;.

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Robert L. Street and A. Woodruff Miller Jr.

Abstract

No abstract available.

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Fotini Katopodes Chow and Robert L. Street

Abstract

The evaluation of turbulence closure models for large-eddy simulation (LES) has primarily been performed over flat terrain, where comparisons with theory and observations are simplified. The authors have previously developed improved closure models using explicit filtering and reconstruction, together with a dynamic eddy-viscosity model and a near-wall stress term. This dynamic reconstruction model (DRM) is a mixed model, combining scale-similarity and eddy-viscosity components. The DRM gave improved results over standard eddy-viscosity models for neutral boundary layer flow over flat but rough terrain, yielding the expected logarithmic velocity profiles near the wall. The results from the studies over flat terrain are now extended to flow over full-scale topography. The test case is flow over Askervein Hill, an isolated hill in western Scotland, where a field campaign was conducted in 1983 with the purpose of capturing wind data representing atmospheric episodes under near-neutral stratification and steady wind conditions. This widely studied flow provides a more challenging test case for the new turbulence models because of the sloping terrain and separation in the lee of the hill. Since an LES formulation is used, a number of simulation features are different than those typically used in the Askervein literature. The simulations are inherently unsteady, the inflow conditions are provided by a separate turbulent flow database, and (uniquely herein) ensemble averages of the turbulent flow results are used in comparisons with field data. Results indicate that the DRM can improve the predictions of flow speedup and especially turbulent kinetic energy (TKE) over the hill when compared with the standard TKE-1.5 model. This is the first study, to the authors’ knowledge, in which explicit filtering and reconstruction (scale similarity) and dynamic turbulence models have been applied to full-scale simulations of the atmospheric boundary layer over terrain. Simulations with the lowest level of reconstruction are straightforward. Increased levels of reconstruction, however, present difficulties when used with a dynamic eddy-viscosity model. An alternative mixed model is proposed to avoid the complexities associated with the dynamic procedure and to allow higher levels of reconstruction; this mixed model combines a standard TKE-1.5 eddy-viscosity closure with velocity reconstruction to form a simple and efficient turbulence model that gives good results for both mean flow and turbulence over Askervein Hill. The results indicate that significant improvements in LES over complex terrain can be obtained by the use of mixed models that combine scale-similarity and eddy-viscosity components.

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Ying Chen, Francis L. Ludwig, and Robert L. Street

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This paper describes observed and simulated interactions among atmospheric forcing, cold-pool development, and complex mountain terrain at the south end of the Salt Lake valley, near the Jordan Narrows and the Traverse Range. The Advanced Regional Prediction System (ARPS), a three-dimensional, nonhydrostatic compressible new-generation large-eddy simulation code in generalized terrain-following coordinates with advanced model parameterizations, was used. Past studies showed that a finer resolution produces more accurate simulations, and so this study used six one-way nested grids to resolve the complex topography. Horizontal grid spacing ranged from 20 km (initialized by Eta 40-km operational analyses) to 250 m; the finest grid had 200 vertically stretched levels between 5 m and 20 km above the surface. Two intense operating periods with weak synoptic forcing, stable stratification, and pronounced nighttime drainage were selected for simulation from the October 2000 Vertical Transport and Mixing (VTMX) experiment. Qualitative agreement between simulations and observations at four stations was good. Usually, the quantitative agreement was also good. Finer horizontal and vertical resolution improved agreement, capturing daytime and nighttime temperature structures, including inversion-layer strength. The simulations showed a complex flow near the Jordan Narrows, with hydraulic jumps and internal waves initiated by the Traverse Range to either side.

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Francis L. Ludwig, Fotini Katopodes Chow, and Robert L. Street

Abstract

This paper demonstrates the importance of high-quality subfilter-scale turbulence models in large-eddy simulations by evaluating the resolved-scale flow features that result from various closure models. The Advanced Regional Prediction System (ARPS) model was used to simulate neutral flow over a 1.2-km square, flat, rough surface with seven subfilter turbulence models [Smagorinsky, turbulent kinetic energy (TKE)-1.5, and five dynamic reconstruction combinations]. These turbulence models were previously compared with similarity theory. Here, the differences are evaluated using mean velocity statistics and the spatial structure of the flow field. Streamwise velocity averages generally differ among models by less than 0.5 m s−1, but those differences are often significant at a 95% confidence level. Flow features vary considerably among models. As measured by spatial correlation, resolved flow features grow larger and less elongated with height for a given model and resolution. The largest differences are between dynamic models that allow energy backscatter from small to large scales and the simple eddy-viscosity closures. At low altitudes, the linear extent of Smagorinsky and TKE-1.5 structures exceeds those of dynamic models, but the relationship reverses at higher altitudes. Ejection, sweep, and upward momentum flux features differ among models and from observed neutral atmospheric flows, especially for Smagorinsky and TKE-1.5 coarse-grid simulations. Near-surface isopleths separating upward fluxes from downward are shortest for the Smagorinsky and TKE-1.5 coarse-grid simulations, indicating less convoluted turbulent interfaces; at higher altitudes they are longest. Large-eddy simulation (LES) is a powerful simulation tool, but choices of grid resolution and subfilter model can affect results significantly. Physically realistic dynamic mixed models, such as those presented here, are essential when using LES to study atmospheric processes such as transport and dispersion—in particular at coarse resolutions.

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Yiannis Alex Papadimitrakis, En Yun Hsu, and Robert L. Street

Abstract

The structure of the velocity field over a propagating wave of fixed frequency is examined. The vertical and horizontal velocities were measured in a transformed Eulerian wave-following frame of reference in a wind-wave research facility at Stanford University. Experimental results are given for seven different wind speeds in the range 140–402 cm s−1, with 1 Hz, 2.54 cm nominal amplitude, mechanically-generated sinusoidal water waves.

The mean velocity profiles have a log-linear form with a wake free-stream characteristic. The constant C which characterizes these profiles decreases with increasing wind speed, as a result of the variation of surface roughness condition between the transition region and the fully rough regime. The wave-associated stresses with their main component at twice the fundamental wave frequency were found to be significant. Therefore, the nonlinear terms encountered in the wave-induced Navier-Stokes equations associated with these stresses cannot be neglected, and linearization of the above equations is not permissible. The wave-induced velocity field and the wave-perturbed turbulence were found to depend significantly on the ratio of the wave speed to the mean free-stream wind velocity, c/U δ0.

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Augustin Colette, Fotini Katopodes Chow, and Robert L. Street

Abstract

Numerical simulations of inversion-layer breakup in idealized steep valleys are performed using the Advanced Regional Prediction System (ARPS) to investigate the effects of valley width and depth, and topographic shade. Simulations of the diurnal pattern of slope winds under weak synoptic conditions are presented in a valley of depth 500 m and floor width 1200 m. Typical up- and downslope wind circulations are reproduced, and their influence on the stability in the valley is analyzed and characterized using the classifications of Whiteman. A systematic investigation of the inversion-layer characteristics in a set of 24 valleys of varying depth and width is conducted. For the narrow-valley cases, the depth and lifetime of the stable layer increase as the depth of the valley increases. For wide valleys, however, the stable-layer depth and lifetime converge toward a single value regardless of the valley depth. An original subroutine accounting for topographic shading is introduced and its effects on both the slope winds and the inversion breakup process are discussed. Results from tests in idealized valleys indicate that topographic shading can delay inversion-layer breakup and, therefore, should be included, when appropriate, in numerical simulations of flow over complex terrain.

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