Measurements of the budgets of the subgrid-scale stress and temperature flux in a convective atmospheric surface layer

Abstract

AbstractThe dynamics of the subgrid-scale (SGS) stress and scalar flux in the convective atmospheric surface layer are studied through the budgets of the SGS turbulence kinetic energy (TKE), the SGS stress and the SGS temperature flux using field measurements from the Advection Horizontal Array Turbulence Study (AHATS). The array technique, which employs sensor arrays to perform filter operations to obtain the SGS velocity and temperature, is extended to include pressure sensors to measure the fluctuating pressure, enabling separation of the resolvable- and subgrid-scale pressure, and therefore for the first time allowing for measurement of the pressure covariance terms and the full SGS budgets. The non-dimensional forms of the SGS budget terms are obtained as functions of the stability parameter $z/ L$ and the ratio of the wavelength of the spectral peak of the vertical velocity to the filter width, ${\Lambda }_{w} / {\Delta }_{f} $. The results show that the SGS TKE budget is a balance among the production, transport and dissipation. The SGS shear stress budget and the SGS temperature flux budgets are dominated by the production and pressure destruction, with the latter causing return to isotropy. The budgets of the SGS normal stress components are more complex. Most notably the pressure–strain-rate correlation includes two competing processes, return to isotropy and generation of anisotropy, the latter due to ground blockage of the large convective eddies. For neutral surface layers, return to isotropy dominates. For unstable surface layers return to isotropy dominates for small filter widths, whereas for large filter widths the ground blockage effect dominates, resulting in strong anisotropy. The results in the present study, particularly for the pressure–strain-rate correlation, have strong implications for modelling the SGS stress and flux using their transport equations in the convective atmospheric boundary layer.