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Investigation of the pressure–strain-rate correlation and pressure fluctuations in convective and near neutral atmospheric surface layers
- Mengjie Ding, Khuong X. Nguyen, Shuaishuai Liu, Martin J. Otte, Chenning Tong
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- Journal:
- Journal of Fluid Mechanics / Volume 854 / 10 November 2018
- Published online by Cambridge University Press:
- 31 August 2018, pp. 88-120
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The pressure–strain-rate correlation and pressure fluctuations in convective and near neutral atmospheric surface layers are investigated. Their scaling properties, spectral characteristics, the contributions from the different source terms in the pressure Poisson equation and the effects of the wall are investigated using high-resolution (up to $2048^{3}$) large-eddy simulation fields and through spectral predictions. The pressure–strain-rate correlation was found to have the mixed-layer and surface-layer scaling in the strongly convective and near neutral atmospheric surface layers, respectively. Its apparent surface-layer scaling in the moderately convective surface layer is due to the slow variations of the mixed-layer contribution, and is an inherent problem for single-point statistics in a multi-scale surface layer. In the strongly convective surface layer the pressure spectrum has an approximate $k^{-5/3}$ scaling range for small wavenumbers ($kz\ll 1$) due to the turbulent–turbulent contribution, and does not follow the surface-layer scaling, where $k$ and $z$ are the horizontal wavenumber and the distance from the surface respectively. The pressure–strain-rate cospectrum components have a $k^{-1}$ scaling range, consistent with our prediction using the surface layer parameters. It is dominated by the buoyancy contribution. Thus the anisotropy in the surface layer is due to the energy redistribution caused by the density fluctuations of the large eddies, rather than the turbulent–turbulent (inertial) effects. In the near neutral surface layer, the turbulent–turbulent and rapid contributions are primarily responsible for redistribution of energy from the streamwise velocity component to the vertical and spanwise components, respectively. The pressure–strain-rate cospectra peak near $kz\sim 1$, and have some similarities to those in the strongly convective surface layer for $kz\ll 1$. For the moderately convective surface layer, the pressure–strain-rate cospectra change signs at scales of the order of the Obukhov length, thereby imposing it as a horizontal length scale in the surface layer. This result provides strong support to the multipoint Monin–Obukhov similarity recently proposed by Tong & Nguyen (J. Atmos. Sci., vol. 72, 2015, pp. 4337–4348). We further decompose the pressure into the free-space (infinite domain), the wall reflection and the harmonic contributions. In the strongly convective surface layer, the free-space contribution to the pressure–strain-rate correlation is dominated by the buoyancy part, and is the main cause of the surface-layer anisotropy. The wall reflection enhances the anisotropy for most of the surface layer, suggesting that the pressure source has a large coherence length. In the near neutral surface layer, the wall reflection is small, suggesting a much smaller source coherence length. The present study also clarifies the understanding of the role of the turbulent–turbulent pressure, and has implications for understanding the dynamics and structure as well as modelling the atmospheric surface layer.
Investigation of the subgrid-scale fluxes and their production rates in a convective atmospheric surface layer using measurement data
- QINGLIN CHEN, SHUAISHUAI LIU, CHENNING TONG
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- Journal:
- Journal of Fluid Mechanics / Volume 660 / 10 October 2010
- Published online by Cambridge University Press:
- 19 July 2010, pp. 282-315
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The subgrid-scale (SGS) potential temperature flux and stress in the atmospheric surface layer are studied using field measurement data. We analyse the mean values of the SGS temperature flux, the SGS temperature flux production rate, the SGS temperature variance production rate, the SGS stress and the SGS stress production rate conditional on both the resolvable-scale velocity and temperature, which must be reproduced by SGS models for large-eddy simulation to reproduce the one-point resolvable-scale velocity–temperature joint probability density function (JPDF). The results show that the conditional statistics generally depend on the resolvable-scale velocity and temperature fluctuations, indicating that these conditional variables have strong influences on the resolvable-scale statistics. The dependencies of the conditional SGS stress and the SGS stress production rate, which are partly due to the effects of flow history and buoyancy, suggest that model predictions of the SGS stress also affect the resolvable-scale temperature statistics. The results for the conditional flux and the conditional flux production rate vectors have similar trends. These conditional vectors are also well aligned. The positive temperature fluctuations associated with updrafts are found to have a qualitatively different influence on the conditional statistics than the negative temperature fluctuations associated with downdrafts. The conditional temperature flux and the temperature flux production rate predicted using several SGS models are compared with measurements in statistical a priori tests. The predictions using the nonlinear model are found to be closely related to the predictions using the Smagorinsky model. Several potential effects of the SGS model deficiencies on the resolvable-scale statistics, such as the overprediction of the vertical mean temperature gradient and the underprediction of the vertical temperature flux, are identified. The results suggest that efforts to improve the LES prediction of a resolvable-scale statistic must consider all the relevant SGS components identified using the JPDF equation and the surface layer dynamics. This study also provides impetus for further investigations of the JPDF equation, especially analytical studies on the relationship between the JPDF and the SGS terms that govern its evolution.