This paper gives a comprehensive numerical analysis of a multiscale method for equilibrium Navier Stokes equations. The method includes pressure regularization and eddy viscosity stabilizations both acting only on the finest scales. This method allows for equal order velocity-pressure spaces as well as the linear constant pair and the usual (Pk, Pk−1) pair. We show the method is optimal in a na...

We measure the eddy viscosity in the outermost layers of the solar convection zone by comparing the rotation law computed with the Reynolds stress resulting from f-plane simulations of the angular momentum transport in rotating convection with the observed differential rotation pattern. The simulations lead to a negative vertical and a positive horizontal angular momentum transport. The consequ...

In recent years field experiments have been undertaken in the lower atmosphere to perform a priori tests of subgrid-scale (SGS)models for large-eddy simulations (LES). The experimental arrangements and data collected have facilitated studies of variables such as the filtered strain rate, SGS stress and dissipation, and the eddy viscosity coefficient. However, the experimental set-ups did not pe...

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...

This study presents an alternative way to perform large eddy simulation based on a targeted numerical dissipation introduced by the discretization of the viscous term. It is shown that this regularisation technique is equivalent to the use of spectral vanishing viscosity. The flexibility of the method ensures high-order accuracy while controlling the level and spectral features of this purely n...

This paper presents a CFD modelling study of the bubble driven hydrodynamics in aluminium reduction cells. A time-averaged (steady state) bubble driven flow model has been developed using a full scale air-water model of part of an aluminium reduction cell as a test-bed. Simulated results have been compared with experimental data taken under similar conditions using Particle Image Velocimetry (P...

Exact asymptotic expressions for eddy diffusivity and eddy viscosity are ob tained as the lead ing terms of in finite-series representations of integral equations which express the act ion of turbulence on an infinitesimal mean field. The series are transformed term by te rm from Euler ian to Lagrangian form. The latter is more suitable for constructing approximations to the exact asymptotic ex...

Aims. We investigate the confinement and long-term dynamics of the magnetised solar tachocline. Methods. Starting from first principles, we derive the values of turbulent transport coefficients in the magnetised solar tachocline and then explore the implications for the confinement and long-term dynamics of the tachocline. Results. For reasonable parameter values, the turbulent eddy viscosity i...

This report extends a recent method that calculates an ensemble of solutions of the Navier-Stokes equations efficiently to higher Reynolds number flows. To do so herein we develop and analyze two ensemble eddy viscosity models that do not obviate the good algorithmic properties of the ensemble method. The combined approach of ensemble time stepping and ensemble eddy viscosity modelling has othe...