Peter P. Sullivan

A comparison of shear- and buoyancy-driven planetary boundary layer flows

Abstract Planetary boundary layer (PBL) flows are known to exhibit fundamental differences depending on the relative combination of wind shear and buoyancy forces. These differences are not unexpected in that shear instabilities occur locally, while buoyancy force sets up vigorous thermals, which result in nonlocal transport of heat and momentum. At the same time, these two forces can act together to modify the flow field. In this study, four large-eddy simulations (LESs) spanning the shear and buoyancy flow regimes were generated; two correspond to the extreme cases of shear and buoyancy-driven PBLs, while the other two represent intermediate PBLs where both forces are important. The extreme cases are used to highlight and quantify the basic differences between shear and convective PBLs in 1) flow structures, 2) overall statistics, and 3) turbulent kinetic energy (TKE) budget distributions. Results from the two intermediate LES cases are used to develop and verify a velocity scaling and a TKE budget mode...

Langmuir turbulence in the ocean

Solutions are analysed from large-eddy simulations of the phase-averaged equations for oceanic currents in the surface planetary boundary layer (PBL), where the averaging is over high-frequency surface gravity waves. These equations have additional terms proportional to the Lagrangian Stokes drift of the waves, including vortex and Coriolis forces and tracer advection. For the wind-driven PBL, the turbulent Langmuir number, La tur = ( U ∗/ U s ) 1/2 , measures the relative influences of directly wind-driven shear (with friction velocity U ∗) and the Stokes drift U s . We focus on equilibrium solutions with steady, aligned wind and waves and a realistic La tur = 0.3. The mean current has an Eulerian volume transport to the right of the wind and against the Stokes drift. The turbulent vertical fluxes of momentum and tracers are enhanced by the presence of the Stokes drift, as are the turbulent kinetic energy and its dissipation and the skewness of vertical velocity. The dominant coherent structure in the turbulence is a Langmuir cell, which has its strongest vorticity aligned longitudinally (with the wind and waves) and intensified near the surface on the scale of the Stokes drift profile. Associated with this are down-wind surface convergence zones connected to interior circulations whose horizontal divergence axis is rotated about 45° to the right of the wind. The horizontal scale of the Langmuir cells expands with depth, and there are also intense motions on a scale finer than the dominant cells very near the surface. In a turbulent PBL, Langmuir cells have irregular patterns with finite correlation scales in space and time, and they undergo occasional mergers in the vicinity of Y-junctions between convergence zones.

A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows

A long-standing problem in large-eddy simulations (LES) of the planetary boundary layer (PBL) is that the mean wind and temperature profiles differ from the Monin-Obukhov similarity forms in the surface layer. This shortcoming of LES has been attributed to poor grid resolution and inadequate sub-grid-scale (SGS) modeling. We study this deficiency in PBL LES solutions calculated over a range of shear and buoyancy forcing conditions. The discrepancy from similarity forms becomes larger with increasing shear and smaller buoyancy forcing, and persists even with substantial horizontal grid refinement. With strong buoyancy forcing, however, the error is negligible.In order to achieve better agreement between LES and similarity forms in the surface layer, a two-part SGS eddy-viscosity model is proposed. The model preserves the usual SGS turbulent kinetic energy formulation for the SGS eddy viscosity, but it explicitly includes a contribution from the mean flow and a reduction of the contributions from the turbulent fluctuations near the surface. Solutions with the new model yield increased fluctuation amplitudes near the surface and better correspondence with similarity forms out to a distance of 0.1–0.2 times the PBL depth, i.e., a typical surface-layer depth. These results are also found to be independent of grid anisotropy. The new model is simple to implement and computationally inexpensive.

Structure of the Entrainment Zone Capping the Convective Atmospheric Boundary Layer

The authors use large-eddy simulation (LES) to investigate entrainment and structure of the inversion layer of a clear convectively driven planetary boundary layer (PBL) over a range of bulk Richardson numbers, Ri. The LES code uses a nested grid technique to achieve fine resolution in all three directions in the inversion layer. Extensive flow visualization is used to examine the structure of the inversion layer and to illustrate the temporal and spatial interaction of a thermal plume and the overlying inversion. It is found that coherent structures in the convective PBL, that is, thermal plumes, are primary instigators of entrainment in the Ri range 13.6 # Ri # 43.8. At Ri 5 13.6, strong horizontal and downward velocities are generated near the inversion layer because of the plume‐interface interaction. This leads to folding of the interface and hence entrainment of warm inversion air at the plume’s edge. At Ri 5 34.5, the inversion’s strong stability prevents folding of the interface but strong horizontal and downward motions near the plume’s edge pull down pockets of warm air below the nominal inversion height. These pockets of warm air are then scoured off by turbulent motions and entrained into the PBL. The structure of the inversion interface from LES is in good visual agreement with lidar measurements in the PBL obtained during the Lidars in Flat Terrain field experiment. A quadrant analysis of the buoyancy flux shows that net entrainment flux (or average minimum buoyancy flux wu min) is identified with quadrant IV w2u1 , 0 motions, that is, warm air moving downward. Plumes generate both large negative quadrant II w1u2 , 0 and positive quadrant III w2u2 . 0 buoyancy fluxes that tend to cancel. The maximum vertical gradient in potential temperature at every (x, y) grid point is used to define a local PBL height, zi(x, y). A statistical analysis of zi shows that skewness of zi depends on the inversion strength. Spectra of zi exhibit a sensitivity to grid resolution. The normalized entrainment rate we/w * , where we and w * are entrainment and convective velocities, varies as ARi21 with A 0.2 in the range 13.6 # Ri # 43.8 and is in good agreement with convection tank measurements. For a clear convective PBL, the authors found that the finite thickness of the inversion layer needs to be considered in an entrainment rate parameterization derived from a jump condition.

Examining Two-Way Grid Nesting for Large Eddy Simulation of the PBL Using the WRF Model

The performance of two-way nesting for large eddy simulation (LES) of PBL turbulence is investigated using the Weather Research and Forecasting model framework. A pair of LES-within-LES experiments are performed where a finer-grid LES covering a smaller horizontal domain is nested inside a coarser-grid LES covering a larger horizontal domain. Both LESs are driven under the same environmental conditions, allowed to interact with each other, and expected to behave the same statistically. The first experiment of the free-convective PBL reveals a mean temperature bias between the two LES domains, which generates a nonzero mean vertical velocity in the nest domain while the mean vertical velocity averaged over the outer domain remains zero. The problem occurs when the horizontal extent of the nest domain is too small to capture an adequate sample of energy-containing eddies; this problem can be alleviated using a nest domain that is at least 5 times the PBL depth in both x and y. The second experiment of the neutral PBL exposes a bias in the prediction of the surface stress between the two LES domains, which is found due to the grid dependence of the Smagorinsky-type subgrid-scale (SGS) model. A new two-part SGS model is developed to solve this problem.

The Influence of Idealized Heterogeneity on Wet and Dry Planetary Boundary Layers Coupled to the Land Surface

Abstract This manuscript describes numerical experiments investigating the influence of 2–30-km striplike heterogeneity on wet and dry convective boundary layers coupled to the land surface. The striplike heterogeneity is shown to dramatically alter the structure of the convective boundary layer by inducing significant organized circulations that modify turbulent statistics. The impact, strength, and extent of the organized motions depend critically on the scale of the heterogeneity λ relative to the boundary layer height zi. The coupling with the land surface modifies the surface fluxes and hence the circulations resulting in some differences compared to previous studies using fixed surface forcing. Because of the coupling, surface fluxes in the middle of the patches are small compared to the patch edges. At large heterogeneity scales (λ/zi ∼18) horizontal surface-flux gradients within each patch are strong enough to counter the surface-flux gradients between wet and dry patches allowing the formation of...

The Effect of Mesh Resolution on Convective Boundary Layer Statistics and Structures Generated by Large-Eddy Simulation

AbstractA massively parallel large-eddy simulation (LES) code for planetary boundary layers (PBLs) that utilizes pseudospectral differencing in horizontal planes and solves an elliptic pressure equation is described. As an application, this code is used to examine the numerical convergence of the three-dimensional time-dependent simulations of a weakly sheared daytime convective PBL on meshes varying from 323 to 10243 grid points. Based on the variation of the second-order statistics, energy spectra, and entrainment statistics, LES solutions converge provided there is adequate separation between the energy-containing eddies and those near the filter cutoff scale. For the convective PBL studied, the majority of the low-order moment statistics (means, variances, and fluxes) become grid independent when the ratio zi/(CsΔf) > 310, where zi is the boundary layer height, Δf is the filter cutoff scale, and Cs is the Smagorinsky constant. In this regime, the spectra show clear Kolmogorov inertial subrange scaling...

Surface gravity wave effects in the oceanic boundary layer large-eddy : simulation with vortex force and stochastic breakers

The wind-driven stably stratified mid-latitude oceanic surface turbulent boundary layer is computationally simulated in the presence of a specified surface gravity-wave field. The gravity waves have broad wavenumber and frequency spectra typical of measured conditions in near-equilibrium with the mean wind speed. The simulation model is based on (i) an asymptotic theory for the conservative dynamical effects of waves on the wave-averaged boundary-layer currents and (ii) a boundary-layer forcing by a stochastic representation of the impulses and energy fluxes in a field of breaking waves. The wave influences are shown to be profound on both the mean current profile and turbulent statistics compared to a simulation without these wave influences and forced by an equivalent mean surface stress. As expected from previous studies with partial combinations of these wave influences, Langmuir circulations due to the wave-averaged vortex force make vertical eddy fluxes of momentum and material concentration much more efficient and non-local (i.e. with negative eddy viscosity near the surface), and they combine with the breakers to increase the turbulent energy and dissipation rate. They also combine in an unexpected positive feedback in which breaker-generated vorticity seeds the creation of a new Langmuir circulation and instigates a deep strong intermittent downwelling jet that penetrates through the boundary layer and increases the material entrainment rate at the base of the layer. These wave effects on the boundary layer are greater for smaller wave ages and higher mean wind speeds.

An Objective Method for Deriving Atmospheric Structure from Airborne Lidar Observations

Abstract Wavelet analysis is applied to airborne infrared lidar data to obtain an objective determination of boundaries in aerosol backscatter that are associated with boundary layer structure. This technique allows high-resolution spatial variability of planetary boundary layer height and other structures to be derived in complex, multilayered atmospheres. The technique is illustrated using data from four different lidar systems deployed on four different field campaigns. One case illustrates high-frequency retrieval of the top of a strongly convective boundary layer. A second case illustrates the retrieval of multiple layers in a complex, stably stratified region of the lower troposphere. The method is easily modified to allow for varying aerosol distributions and data quality. Two more difficult cases, data that contain a great deal of instrumental noise and a cloud-topped convective layer, are described briefly. The method is also adaptable to model analysis, as is shown via application to large eddy ...

Simulation of turbulent flow over idealized water waves

Turbulent flow over idealized water waves with varying wave slope ak and wave age c / u ∗ is investigated using direct numerical simulations at a bulk Reynolds number Re = 8000. In the present idealization, the shape of the water wave and the associated orbital velocities are prescribed and do not evolve dynamically under the action of the wind. The results show that the imposed waves significantly influence the mean flow, vertical momentum fluxes, velocity variances, pressure, and form stress (drag). Compared to a stationary wave, slow (fast) moving waves increase (decrease) the form stress. At small c / u ∗, waves act similarly to increasing surface roughness z o resulting in mean vertical velocity profiles with shorter buffer and longer logarithmic regions. With increasing wave age, z o decreases so that the wavy lower surface is nearly as smooth as a flat lower boundary. Vertical profiles of turbulence statistics show that the wave effects depend on wave age and wave slope but are confined to a region kz k is the wavenumber of the surface undulation and z is the vertical coordinate). The turbulent momentum flux can be altered by as much as 40% by the waves. A region of closed streamlines (or cats-eye pattern) centred about the critical layer height was found to be dynamically important at low to moderate values of c / u ∗. The wave-correlated velocity and flux fields are strongly dependent on the variation of the critical layer height and to a lesser extent the surface orbital velocities. Above the critical layer z cr the positions of the maximum and minimum wave-correlated vertical velocity w w occur upwind and downwind of the peak in z cr , like a stationary surface. The wave-correlated flux u w w w is positive (negative) above (below) the critical layer height.