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J. C. Weil

Abstract

A Lagrangian stochastic model of particle trajectories is used to investigate the asymmetry in vertical diffusion from area sources at the bottom and top of an inhomogeneous turbulent boundary layer. Such an asymmetry was discovered in the large-eddy simulations (LES) of the convective boundary layer (CBL) by Wyngaard and Brost (1984) and Moeng and Wyngaard (1984).

For inhomogeneous Gaussian turbulence, a diffusion asymmetry results from the vertical asymmetry in the vertical velocity variance about the midplane of the boundary layer. For small turbulence time scales, this is predictable from eddy-diffusion (K) theory. However, for large time scales, K theory is inapplicable as evidenced by countergradient flux regions and K singularities. The fundamental causes of the K model breakdown are the memory (large time scale) and vertical inhomogeneity of the turbulence, which lead to a mean vertical acceleration of particles away from the source and a “drift” velocity.

A positive skewness in vertical velocity enhances the drift velocity for a bottom source and suppresses it for a top source, thus leading to a greater diffusion asymmetry than in Gaussian turbulence; this is independent of the variance profile. The asymmetry due to skewness is caused by the bias in the probability density function of vertical velocity (w)—larger positive w values and smaller negative ones than in Gaussian turbulence. The results for inhomogeneous skewed turbulence are in good agreement with the LES results for the CBL.

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C-H. Moeng, J. C. McWilliams, R. Rotunno, P. P. Sullivan, and J. Weil

Abstract

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.

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Peter P. Sullivan, James C. McWilliams, Jeffrey C. Weil, Edward G. Patton, and Harindra J. S. Fernando

Abstract

Turbulent flow in a weakly convective marine atmospheric boundary layer (MABL) driven by geostrophic winds U g = 10 m s−1 and heterogeneous sea surface temperature (SST) is examined using fine-mesh large-eddy simulation (LES). The imposed SST heterogeneity is a single-sided warm or cold front with temperature jumps Δθ = (2, −1.5) K varying over a horizontal distance between [0.1, −6] km characteristic of an upper-ocean mesoscale or submesoscale regime. A Fourier-fringe technique is implemented in the LES to overcome the assumptions of horizontally homogeneous periodic flow. Grid meshes of 2.2 × 109 points with fine-resolution (horizontal, vertical) spacing (δx = δy, δz) = (4.4, 2) m are used. Geostrophic winds blowing across SST isotherms generate secondary circulations that vary with the sign of the front. Warm fronts feature overshoots in the temperature field, nonlinear temperature and momentum fluxes, a local maximum in the vertical velocity variance, and an extended spatial evolution of the boundary layer with increasing distance from the SST front. Cold fronts collapse the incoming turbulence but leave behind residual motions above the boundary layer. In the case of a warm front, the internal boundary layer grows with downstream distance conveying the surface changes aloft and downwind. SST fronts modify entrainment fluxes and generate persistent horizontal advection at large distances from the front.

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Peter P. Sullivan, James C. McWilliams, Jeffrey C. Weil, Edward G. Patton, and Harindra J. S. Fernando

Abstract

Turbulent flow in a weakly convective marine atmospheric boundary layer (MABL) driven by geostrophic winds V g = 10 m s−1 and heterogeneous sea surface temperature (SST) is examined using fine-mesh large-eddy simulation (LES). The imposed SST heterogeneity is a single-sided warm or cold front with jumps Δθ = (2, −1.5) K varying over a horizontal x distance of 1 km characteristic of an upper-ocean mesoscale or submesoscale front. The geostrophic winds are oriented parallel to the SST isotherms (i.e., the winds are alongfront). Previously, Sullivan et al. examined a similar flow configuration but with geostrophic winds oriented perpendicular to the imposed SST isotherms (i.e., the winds were across-front). Results with alongfront and across-front winds differ in important ways. With alongfront winds, the ageostrophic surface wind is weak, about 5 times smaller than the geostrophic wind, and horizontal pressure gradients couple the SST front and the atmosphere in the momentum budget. With across-front winds, horizontal pressure gradients are weak and mean horizontal advection primarily balances vertical flux divergence. Alongfront winds generate persistent secondary circulations (SC) that modify the surface fluxes as well as turbulent fluxes in the MABL interior depending on the sign of Δθ. Warm and cold filaments develop opposing pairs of SC with a central upwelling or downwelling region between the cells. Cold filaments reduce the entrainment near the boundary layer top that can potentially impact cloud initiation. The surface-wind–SST-isotherm orientation is an important component of atmosphere–ocean coupling. The results also show frontogenetic tendencies in the MABL.

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Peter P. Sullivan, Jeffrey C. Weil, Edward G. Patton, Harmen J. J. Jonker, and Dmitrii V. Mironov

Abstract

The nighttime high-latitude stably stratified atmospheric boundary layer (SBL) is computationally simulated using high–Reynolds number large-eddy simulation on meshes varying from 2003 to 10243 over 9 physical hours for surface cooling rates C r = [0.25, 1] K h−1. Continuous weakly stratified turbulence is maintained for this range of cooling, and the SBL splits into two regions depending on the location of the low-level jet (LLJ) and . Above the LLJ, turbulence is very weak and the gradient Richardson number is nearly constant: . Below the LLJ, small scales are dynamically important as the shear and buoyancy frequencies vary with mesh resolution. The heights of the SBL and Ri noticeably decrease as the mesh is varied from 2003 to 10243. Vertical profiles of the Ozmidov scale show its rapid decrease with increasing , with over a large fraction of the SBL for high cooling. Flow visualization identifies ubiquitous warm–cool temperature fronts populating the SBL. The fronts span a large vertical extent, tilt forward more so as the surface cooling increases, and propagate coherently. In a height–time reference frame, an instantaneous vertical profile of temperature appears intermittent, exhibiting a staircase pattern with increasing distance from the surface. Observations from CASES-99 also display these features. Conditional sampling based on linear stochastic estimation is used to identify coherent structures. Vortical structures are found upstream and downstream of a temperature front, similar to those in neutrally stratified boundary layers, and their dynamics are central to the front formation.

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Edward G. Patton, Peter P. Sullivan, Roger H. Shaw, John J. Finnigan, and Jeffrey C. Weil

Abstract

Large-eddy simulation of atmospheric boundary layers interacting with a coupled and resolved plant canopy reveals the influence of atmospheric stability variations from neutral to free convection on canopy turbulence. The design and implementation of a new multilevel canopy model is presented. Instantaneous fields from the simulations show that organized motions on the scale of the atmospheric boundary layer (ABL) depth bring high momentum down to canopy top, locally modulating the vertical shear of the horizontal wind. The evolution of these ABL-scale structures with increasing instability and their impact on vertical profiles of turbulence moments and integral length scales within and above the canopy are discussed. Linkages between atmospheric turbulence and biological control impact horizontal scalar source distributions. Decreasing spatial correlation between momentum and scalar fluxes with increasing instability results from ABL-scale structures spatially segregating momentum and scalar exchange at canopy top. In combination, these results suggest the need for roughness sublayer parameterizations to incorporate an additional length or time scale reflecting the influence of ABL-scale organized motions.

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T. W. Horst, J. Kleissl, D. H. Lenschow, C. Meneveau, C.-H. Moeng, M. B. Parlange, P. P. Sullivan, and J. C. Weil

Abstract

The Horizontal Array Turbulence Study (HATS) field program utilized horizontal, crosswind arrays of sonic anemometers to calculate estimates of spatially filtered and subfilter-scale (SFS) turbulence, corresponding to its partitioning in large-eddy simulations (LESs) of atmospheric flows. Measurements were made over a wide range of atmospheric stability and for zf nominally equal to 0.25, 0.5, 1.0, and 2.0, where z is height and Δf is the width of the spatial filter. This paper examines the viability of the crosswind array technique by analyzing uncertainties in the filtered turbulence fields. Aliasing in the crosswind direction, caused by the discrete spacing of the sonic anemometers, is found to be minimal except for the spatially filtered vertical velocity and for SFS second moments. In those cases, aliasing errors become significant when the sonic spacing is greater than the wavelength at the peak in the crosswind spectrum of vertical velocity. Aliasing errors are estimated to be of a similar magnitude for the crosswind gradients of filtered variables. Surrogate streamwise filtering is performed by assuming Taylor's hypothesis and using the mean wind speed U to interpret sonic time series as spatial data. The actual turbulence advection velocity U c is estimated from the cross correlation between data from HATS sonics separated in the streamwise direction. These estimates suggest that, for near-neutral stratification, the ratio U c/U depends on the turbulence variable and is typically between 1.0 and 1.2. Analysis of LES turbulence fields for a neutrally stratified boundary layer finds that the correlation between the true spatially filtered SFS stress component τ 13 and the same variable obtained with surrogate streamwise filtering exceeds 0.98 for zf > 0.25. Within the limits noted, it is concluded that the horizontal array technique is sufficient for the estimation of resolved and SFS turbulence variables.

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