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We describe a series of computational experiments that employ nonoscillatory finite volume methods to simulate the decay of high Reynolds number turbulence. These experiments cover a broad range of physical viscosities and numerical resolutions. We have extracted a data set from these experiments detailing the energy dissipation by physical viscosity and by the numerical algorithm. We offer a preliminary analysis of this data, including new insights into the (computational) transition between direct numerical simulation and large eddy simulation. [DOI: 10.1115/1.2176749]

Implicit turbulence modeling is the numerical simulation of high Reynolds fluid flow using nonoscillatory finite volume (NFV) schemes without any explicit subgrid scale model. Here we investigate the ability of a particular NFV scheme, MPDATA, to simulate decaying turbulence in a triply periodic cube for a variety of viscosities, comparing our results to analogous pseudo-spectral studies. In the regime of direct numerical simulation, MPDATA is shown to agree closely with the pseudo-spectral results. As viscosity is reduced, the two model results diverge. We study the MPDATA results in the inviscid limit, using a combination of mathematical analysis and computational experiment. We validate these results as representing the turbulent flow in the limit of very high Reynolds number. [DOI: 10.1115/1.1514210]

A wake is traditionally defined as the region of nearly stagnant flow downstream of a body in a uniform stream. In a stratified fluid, the motions and density surfaces downstream of an obstacle become primarily horizontal; the vertical component of the vorticity associated with the wake, coexisting with the stable vertical density stratification, implies that there is potential vorticity (PV) in the wake. Recent work has demonstrated that dissipation aloft, associated with a breaking mountain wave over an isolated peak, produces a dipole in PV downstream- the dipolar vertical vorticity of the wake is associated with the PV dipole. Although one may infer the existence of vorticity downstream, the PV argument is silent on the question, Where does the wake vorticity come from? To answer this question, a weakly nonlinear model for PV production and wake formation in the case of a small-amplitude mountain has been analyzed, and numerical simulations pertaining to the strongly nonlinear large-amplitude case have been carried out. The simple model indicates that even with dissipation in the system, the vertical vorticity of the wake arises through the tilting of baroclinically generated horizontal vorticity by the dissipating mountain wave. This analysis shows that there need not be any direct effect of friction in the vorticity equation to produce the vorticity of the wake; dissipation (due to friction and/or heating) enters indirectly through its effect on the tilting term. Analysis of numerical simulations of the large-amplitude case shows that the conclusions from the weakly nonlinear model regarding the source of wake vorticity continue to hold in the strongly nonlinear regime.

Considers three different sets of shallow water equations representing different levels of approximation. Comparison of numerical solutions of these different equations for flow past bottom topography in several different flow regimes; Level of approximation required for a particular flow.