Physical mechanism of vertical gradient of pressure flux and its impact on turbulent flux estimation

Abstract

• Flux-variance method is an effective way to indirectly obtain pressure flux. • Pressure flux convergence/divergence is partially related to larger-scale eddies. • Ejection and sweep events lead to opposite vertical gradient of pressure flux. • There's a quadratic relation between pressure flux gradient and friction velocity. • Taking pressure transport into account refines estimation of turbulent flux in CBL. Using multi-layer pressure fluctuations and other conventional turbulence observational data over a nearly flat and homogeneous dune underlying surface, the temporal and spatial characteristics of pressure flux and its profile were analyzed to illustrate the physical mechanism of pressure flux convergence/divergence and the impact of pressure transport terms on the estimation of turbulent fluxes in this study. The flux-variance (FV) method is an effective approach to indirectly obtain pressure flux through momentum flux when no fast-response observations of pressure fluctuations are available. The fitted functions are w ′ p ′ ¯ = 0.16 · ( − F Z ( z ) · u ′ w ′ ¯ σ p σ u ) and u ′ p ′ ¯ = 0.55 · ( F X ( z ) · u ′ w ′ ¯ σ p σ w ) , where F Z ( z ) and F X ( z ) are the height normalized functions for vertical and horizontal directions. Under the circumstance of pressure flux divergence (FD), the transport efficiency of pressure and contribution of larger-scale eddies to pressure flux at higher levels are greater than those at lower levels, and flows in the atmospheric surface layer (ASL) are mainly dominated by the sweep events; while the pressure flux convergence (FC) cases are exactly the opposite situations. A good quadratic function relationship was found between the vertical gradient of pressure flux and friction velocity under different atmospheric stabilities: ∂ w ′ p ′ ¯ ∂ z = 0.01 u * ( 16 u * − 1 ) . Turbulence kinetic energy (TKE) and its vertical transport are greater in the FD cases than those in the FC cases. The momentum and sensible heat fluxes in the convective boundary layer (CBL) were overestimated by their common second-order diagnostic equations and Rotta model (pressure redistribution term parameterization) which neglect the diffusion terms. After adding the contribution of pressure transport terms into the diagnostic equations and Rotta model and modifying the original Rotta constants, the overestimations were well corrected and the estimated turbulent fluxes were more consistent with the observations. This work provides a novel direction and idea for the future improvement of the planetary boundary layer (PBL) parameterization schemes in many numerical weather and climate models.