Explicit filtering has the effect of reducing numerical or aliasing errors near the grid scale in large eddy simulation (LES). We use a differential filter, namely the inverse Helmholtz operator, which is readily applied to unstructured meshes. The filter is invertible, which allows the sub-filter scale (SFS) stresses to be exactly reconstructed in terms of the filtered solution. Unlike eddy vi...

Standard and anomalous transport in incompressible flow is investigated using multiscale techniques. Eddy-diffusivities emerge from the multiscale analysis through the solution of an auxiliary equation. From the latter it is derived an upper bound to eddy-diffusivities, valid for both static and time-dependent flow. The auxiliary problem is solved by a perturbative expansion in powers of the Pé...

Progress in understanding the general circulation of the atmosphere during the past 25 years is reviewed. The relationships of eddy generation, propagation and dissipation to eddy momentum fluxes and mean zonal winds are now sufficiently understood that intuitive reasoning about momentum based on firm theoretical foundations is possible. Variability in the zonal-flow can now be understood as a ...

The robustness of Nakamura’s effective diffusivity diagnostic for quantifying eddy diffusivities of tracers in a streamwise-average framework is carefully examined in an oceanographic context and the limits of its applicability are detailed. The nearsurface Southern Ocean geostrophic flow, obtained from altimetric observations, is chosen for particular examination. The temporal variability of t...

Experiments have been performed using a simplified, Newtonian forced, global circulation model to investigate how variability of the tropospheric jet can be characterized by examining the combined fluctuations of the two leading modes of annular variability. Eddy forcing of this variability is analyzed in the phase space of the leading modes using the vertically integrated momentum budget. The ...

A global ocean circulation model is formulated in terms of the “residual mean” and used to study eddy–mean flow interaction. Adjoint techniques are used to compute the three-dimensional eddy stress field that minimizes the departure of the coarse-resolution model from climatological observations of temperature. The resulting 3D maps of eddy stress and residual-mean circulation yield a wealth of...

The origin of low-frequency variability in the midlatitude jet is investigated using a two-level baroclinic channel model. The model state fields are separated into slow and fast components using intermediate timescale averaging. In the equation for the fast variables the nonlinear wave–wave interactions are parameterized as a stochastic excitation. The slowly varying ensemble mean eddy fluxes ...

The generation of large-scale magnetic field in the kinematic regime in the absence of an α-effect is investigated by following two different approaches, namely the testfield method and multiscale stability theory relying on the homogenisation technique. We show analytically that the former, applied for the evaluation of magnetic eddy diffusivities, yields results that fully agree with the latt...

As in the midlatitude atmosphere, midocean eddies are primarily generated by baroclinically unstable mean currents. In contrast to the atmosphere, however, oceanic currents are significantly nonzonal. Even weak nonzonal currents are linearly unstable since does not suppress growing meridional waves. Theories for the nonlinear equilibration of baroclinic instability, and hence theories for the a...

A stochastic barotropic model linearized about the 850-mb flow is used to investigate the relationship between wind variations associated with the Madden–Julian oscillation (MJO) and eddy kinetic energy variations in the Tropics. Such a model is successful in predicting the observed location of eddy kinetic energy maxima during the westerly phase of the MJO and the suppression of eddy activity ...