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Bowen Zhou and Fotini Katopodes Chow
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Bowen Zhou and Fotini Katopodes Chow

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This numerical study investigates the nighttime flow dynamics in Owens Valley, California. Nested high-resolution large-eddy simulation (LES) is used to resolve stable boundary layer flows within the valley. On 17 April during the 2006 Terrain-Induced Rotor Experiment, the valley atmosphere experiences weak synoptic forcings and is largely dominated by buoyancy-driven downslope and down-valley flows. Tower instruments on the valley floor record a continuous decrease in temperature after sunset, except for a brief warming episode. This transient warming event is modeled with good magnitude and temporal precision with LES. Analysis of the LES flow field confirms the event to be the result of a slope to valley flow transition, as previously suggested by researchers based on field observations. On the same night, a northerly cold airflow from the Great Basin is channeled through a pass on the eastern valley sidewall. The current plunges into the stable valley atmosphere, overshooting the altitude of its neutral buoyancy, and generating a large-scale oscillatory motion. The resulting cross-valley flow creates strong vertical shear with the down-valley flow in the lower layers of the atmosphere. A portion of the cross-valley flow is captured by a scanning lidar. The nested LES is in good agreement with the lidar-recorded radial velocity. Furthermore, the LES is able to resolve Kelvin–Helmholtz waves, and ejection and sweep events at the two-layer interface, which lead to top-down vertical mixing.

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Bowen Zhou and Fotini Katopodes Chow

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The nighttime stable atmospheric boundary layer over real terrain is modeled with nested high-resolution large-eddy simulations (LESs). The field site is located near Leon, Kansas, where the 1999 Cooperative Atmosphere–Surface Exchange Study took place. The terrain is mostly flat with an average slope of 0.5°. The main topographic feature is a shallow valley oriented in the east–west direction. The night of 5 October is selected to study intermittent turbulence under prevailing quiescent conditions. Brief turbulent periods triggered by shear-instability waves are modeled with good magnitude and temporal precision with a dynamic reconstruction turbulence closure. In comparison, conventional closures fail to excite turbulent motions and predict a false laminar flow. A plausible new intermittency mechanism, previously unknown owing to limited spatial coverage of field instruments at this site, is unveiled with the LESs. Turbulence can be generated through gravity wave breaking over a stagnant cold-air bubble in the valley upwind of the main tower. The bubble is preceded by the formation of a valley cold-air pool due to down-valley drainage flows during the evening transition. The bubble grows in depth by entraining cold down-valley and downslope flows from below and is eroded by shear-induced wave breaking on the top. The cyclic process of formation and erosion is repeated during the night, leading to sporadic turbulent bursting.

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Bowen Zhou and Fotini Katopodes Chow

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Large-eddy simulation (LES) of the stably stratified atmospheric boundary layer is performed using an explicit filtering and reconstruction approach with a finite difference method. Turbulent stresses are split into the resolvable subfilter-scale and subgrid-scale stresses. The former are recovered from a reconstruction approach, and the latter are represented by a dynamic eddy-viscosity model. The resulting dynamic reconstruction model (DRM) can sustain resolved turbulence with less stringent resolution requirements than conventional closure models, even under strong atmospheric stability. This is achieved by proper representation of subfilter-scale (SFS) backscatter of turbulent kinetic energy (TKE). The flow structure and turbulence statistics for the moderately stable boundary layer (SBL) are analyzed with high-resolution simulations. The DRM simulations show good agreement with established empirical formulations such as flux and gradient-based surface similarity, even at relatively coarse resolution. Similar results can be obtained with traditional closure models at the cost of higher resolution. SBL turbulence under strong stability is also explored. Simulations show an intermittent presence of elevated TKE below the low-level jet. Overall, the explicit filtering and reconstruction approach is advantageous for simulations of the SBL. At coarse resolution, it can extend the working range of LES to stronger stability, while maintaining agreement to similarity theory; at fine resolution, good agreement with theoretical formulations provides confidence in the results and allows for detailed investigation of the flow structure under moderate to strong stability conditions.

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Bowen Zhou, Ming Xue, and Kefeng Zhu

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The model gray zone refers to the range of grid spacings comparable to the dominant length scale of the flow. In the gray zone, the flow is partially resolved and partially subgrid scale (SGS). Neither ensemble-averaging-based parameterizations nor turbulence closures are appropriate for parameterizing the effects of SGS motions on the resolved flow. The gray zone of the convective boundary layer (CBL) is in the range of CBL depth, typically O(1) km. A new approach that seeks explicit resolution of the unstable surface layer through a nest layer of fine grid spacing is proposed to improve CBL parameterization in the gray zone. To provide the theoretical basis for the approach, a linear analytic model is presented, and one-way nested simulations are performed to investigate the dynamical coupling between the surface layer and the mixed layer. The analytic model shows that at the onset of thermal instability, the vertical and horizontal structures of the mixed layer are set by surface-layer forcings. The nested 3D simulations extend the findings from the analytic model and further reveal potential improvements in high-order statistics and resolved convective structures both including and extending above the nest region compared to the stand-alone gray-zone simulations. This study suggests that when the most energetic scales of CBL convection are resolved in the surface layer, the overall simulation of the CBL improves at gray-zone resolutions.

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Bowen Zhou, Ming Xue, and Kefeng Zhu

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A grid-refinement-based method is implemented in a community atmospheric model to improve the representation of convective boundary layer (CBL) turbulence on gray-zone [i.e., ~O(1) km] grids. At this resolution, CBL convection is partially resolved and partially subgrid scale (SGS), such that neither traditional mesoscale planetary boundary layer (PBL) schemes nor SGS closures for large-eddy simulations (LESs) are appropriate. The proposed method utilizes two-way interactive nesting to refine the horizontal resolution of the unstable surface layer of the daytime CBL. SGS turbulent mixing in the fine nest and coarse parent grids are parameterized by an LES turbulence closure and a PBL scheme, respectively. The method does not rely on predetermined empirical functions to introduce grid (scale) dependency and in theory works with any PBL scheme. Compared to the stand-alone gray-zone simulation, the proposed approach shows improvements in terms of higher-order statistics, the timing of the onset of resolved convection, and the convective structures. A deficiency of the method exists when the nest domain is limited to the surface layer; the convective structures become gradually contaminated by spurious convection on the parent gray-zone grid. A deeper nest domain alleviates the issue at increased computational costs.

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Bowen Zhou, Kefeng Zhu, and Ming Xue

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Compared to the representation of vertical turbulent mixing through various planetary boundary layer (PBL) schemes, the treatment of horizontal turbulent mixing in the boundary layer has received much less attention. In mesoscale and convective-scale models, subgrid-scale horizontal turbulent mixing has traditionally been associated with mesoscale circulations or eddies. Its parameterization most often adopts the gradient-diffusion model, where the horizontal mixing coefficients are usually set constant, or through the 2D Smagorinsky formulation, or in some cases based on the 1.5-order turbulence kinetic energy (TKE) closure. For horizontal turbulent mixing associated with boundary layer eddies, the traditional schemes are shown to perform poorly. This work investigates the characteristic turbulence velocity and length scales based on analysis of a well-resolved, wide-domain large-eddy simulation of a convective boundary layer (CBL). To improve the representation of horizontal turbulent mixing by CBL eddies, a class of schemes is proposed with different levels of sophistication. The first two schemes can be used together with first-order PBL schemes, while the third uses TKE to define its characteristic velocity scale and can be used together with TKE-based higher-order PBL schemes. The proposed parameterizations are tested a posteriori in idealized simulations of turbulent dispersion of a passive scalar. Comparisons show improved horizontal dispersion by the proposed schemes and further demonstrate the weakness of the existing schemes.

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Bowen Zhou, Yuhuan Li, and Kefeng Zhu

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Based on a priori analysis of large-eddy simulations (LESs) of the convective atmospheric boundary layer, improved turbulent mixing and dissipation length scales are proposed for a turbulence kinetic energy (TKE)-based planetary boundary layer (PBL) scheme. The turbulent mixing length incorporates surface similarity and TKE constraints in the surface layer, and makes adjustments for lateral entrainment effects in the mixed layer. The dissipation length is constructed based on balanced TKE budgets accounting for shear, buoyancy, and turbulent mixing. A nongradient term is added to the TKE flux to correct for nonlocal turbulent mixing of TKE. The improved length scales are implemented into a PBL scheme, and are tested with idealized single-column convective boundary layer (CBL) cases. Results exhibit robust applicability across a broad CBL stability range, and are in good agreement with LES benchmark simulations. It is then implemented into a community atmospheric model and further evaluated with 3D real-case simulations. Results of the new scheme are of comparable quality to three other well-established PBL schemes. Comparisons between simulated and radiosonde-observed profiles show favorable performance of the new scheme on a clear day.

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Bowen Zhou, Shiwei Sun, Jianning Sun, and Kefeng Zhu

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The vertical turbulent velocity variance normalized by the convective velocity squared as a function of the boundary layer depth–normalized height [i.e., ] in the convective boundary layer (CBL) over a homogeneous surface exhibits a near-universal profile, as demonstrated by field observations, laboratory experiments, and numerical simulations. The profile holds over a wide CBL stability range set by the friction velocity, CBL depth, and surface heating. In contrast, the normalized horizontal turbulent velocity variance increases monotonically with decreasing stability. This study investigates the independence of the profile to changes in CBL stability, or more precisely, wind shear. Large-eddy simulations of several convective and neutral cases are performed by varying surface heating and geostrophic winds. Analysis of the turbulent kinetic energy budgets reveals that the conversion term between and depends almost entirely on buoyancy. This explains why does not vary with shear, which is a source to only. Further analysis through rotational and divergent decomposition suggests that the near-universal profile of is fundamentally related to the dynamics and interactions of local and nonlocal CBL turbulence. Specifically, the preferential interactions between local wavenumbers and the downscale energy cascade of CBL turbulence offer plausible explanations to the universal profile of .

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Shiwei Sun, Bowen Zhou, Ming Xue, and Kefeng Zhu

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In numerical simulations of deep convection at kilometer-scale horizontal resolutions, in-cloud subgrid-scale (SGS) turbulence plays an important role in the transport of heat, moisture, and other scalars. By coarse graining a 50 m high-resolution large-eddy simulation (LES) of an idealized supercell storm to kilometer-scale grid spacings ranging from 250 m to 4 km, the SGS fluxes of heat, moisture, cloud, and precipitating water contents are diagnosed a priori. The kilometer-scale simulations are shown to be within the “gray zone” as in-cloud SGS turbulent fluxes are comparable in magnitude to the resolved fluxes at 4 km spacing, and do not become negligible until ~500 m spacing. Vertical and horizontal SGS fluxes are of comparable magnitudes; both exhibit nonlocal characteristics associated with deep convection as opposed to local gradient-diffusion type of turbulent mixing. As such, they are poorly parameterized by eddy-diffusivity-based closures. To improve the SGS representation of turbulent fluxes in deep convective storms, a scale-similarity LES closure is adapted to kilometer-scale simulations. The model exhibits good correlations with LES-diagnosed SGS fluxes, and is capable of representing countergradient fluxes. In a posteriori tests, supercell storms simulated with the refined similarity closure model at kilometer-scale resolutions show better agreement with the LES benchmark in terms of SGS fluxes than those with a turbulent-kinetic-energy-based gradient-diffusion scheme. However, it underestimates the strength of updrafts, which is suggested to be a consequence of the model effective resolution being lower than the native grid resolution.

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