Measurements of the Budget of the Subgrid-Scale Stress in Convective Atmospheric Surface Layers

Measurement data obtained in the atmospheric surface layer during the recent Advection Horizontal Array Turbulence Study (AHATS) field program are used to obtain the subgrid-scale (SGS) stress budget. The array technique used to obtain the SGS velocity was extended to include pressure sensors to measure the fluctuating pressure, enabling separation of the resolvable- and subgrid-scale pressure, and therefore allowing for all terms in the SGS stress budget to be computed. The budget terms are analyzed using two non-dimensional parameters: the surface layer stability, z/L, and the ratio of the wavelength corresponding to the peak of the vertical velocity spectrum to the filter size (i.e., the resolution of the LES field).

The results show that the budgets of the normal components of the SGS stress have more complex behaviors in unstable surface layers than in neutral surface layers due to the complex interactions among shear, buoyancy, pressure, and the presence of the ground. For neutral surface layers, energy gained by τ₁₁ from the mean flow is fed to τ₂₂ and τ₃₃ by the pressure-strain term, which diminishes with decreasing filter size as smaller eddies are increasingly more isotropic. For unstable surface layers, energy is gained by both τ₁₁ and τ₃₃. For large filter scales, the pressure-strain term feeds energy from τ₃₃ to τ₁₁ and τ₂₂ because the vertical motion of the large convective eddies are blocked by the ground. Thus, for large filter scales, the pressure-strain term contributes to the anisotropy of the SGS stress. As the filter scale decreases, the effects of the ground and buoyancy diminish while the anisotropy in the SGS stress becomes relatively more important. Here, the pressure-strain term reverses role and now acts to re-distribute energy from the horizontal to the vertical velocity component, driving the SGS stress tensor toward isotropy. For very small filter scales, the SGS stress becomes increasingly more isotropic, therefore the pressure strain term diminishes. These results have strong implications for using model transport equations for SGS stress, particularly in correctly parameterizing the pressure-strain-rate correlation.