Eddy Diffusion

¶A time-dependent semi-geostrophic Ekman boundary-layer model (SG), including slowly varying eddy diffusivity with height and inertial term effects, is developed to investigate the diurnal wind variation in the planetary boundary layer (PBL). An approximate analytical solution of this model is derived by using the WKB method, which extends the Tan and Farahani (1998)’s solution by including the vertical variable eddy viscosity. The features of the diurnal wind variation in the PBL mainly depend on three factors: the latitude, horizontal momentum advection and eddy viscosity. The vertical variable eddy viscosity has little influence on diurnal wind variation in the PBL at the low latitude, however its effect may be exacerbated in the mid- and high latitudes. In comparing with the constant eddy viscosity case, the decreasing (increasing) with height eddy viscosity produces a large (small) maximum wind speed (MWS) in the PBL, however, the eddy viscosity that has a mid-layer peak in the vertical gives rise to a higher height of occurrence of MWS. For the boundary-layer wind structure, there is a singular point when the modified SG inertial oscillation frequency η equals the forcing frequency ω. The isotachs of boundary-layer wind speed have almost no tilt to left or right relative to time evolution and the occurrence time of the MWS is the earliest at the singular point. The feature will be enhanced in the decreasing with height eddy viscosity case and weakened in the eddy viscosity initially increasing with height case.

A large-domain large-eddy simulation of a tropical deep convection system is used as a benchmark to derive and test a mixed subgrid-scale (SGS) scheme for scalar and momentum fluxes in cloud-resolving models (CRMs). The benchmark simulation resolves a broad range of scales ranging from mesoscale organizations, through gravity waves and individual clouds, down to energy-containing turbulent eddies. A spectral analysis shows that the vertical-velocity kinetic energy peaks at scales from hundreds of meters in the lower cloud layer to several kilometers higher up; these scales are typical grid sizes of today’s CRMs. The analysis also shows that a significant portion of the scalar and momentum fluxes in the benchmark simulation are carried by motions smaller than several kilometers (i.e., smaller than a typical grid resolution of CRMs). The broad range of scales of the benchmark simulation is split into two components: filter scale (mimicking CRM resolvable scale) and subfilter scale (mi...

Eddies influence the surface heat budget both by modifying the surface heat flux and by the lateral transfer of heat within the surface mixed layer. It is shown that the presence of eddies modifies the surface heat flux in a model of the northwest Atlantic Ocean by more than 100 W m-2 over the Gulf Stream system. The diffusive effect of eddies is then illustrated by comparing two model runs, in the second of which the surface heat flux acts only on large spatial scales and interaction with the mesoscale eddies is suppressed. This second run exhibits finer-scale structure and tighter thermal fronts than in the fully interactive run. Finally, we estimate the surface eddy diffusivity associated with surface thermal damping from the fully interactive run. The estimated diffusivity takes large values (more than 103 m2 s-1) south of the Gulf Stream and smaller values elsewhere.

The mixing efficiency of a flow advecting a passive scalar sustained by steady sources and sinks is naturally defined in terms of the suppression of bulk scalar variance in the presence of stirring, relative to the variance in the absence of stirring. These variances can be weighted at various spatial scales, leading to a family of multi-scale mixing measures and efficiencies. We derive a priori estimates on these efficiencies from the advection–diffusion partial differential equation, focusing on a broad class of statistically homogeneous and ...

... A simple analytical estimate of T is obtained by using the large travel time, t ... NWP model profiles include analysed data as well as forecasts relevant to dispersion simulations of ... From Gifford's random-force theory, or Langevin model, of atmospheric diffusion (Gifford, 1982 and ...