On ‘spurious’ eddies

Abstract

SUMMARYRecently, several papers have appeared in the CFD literature, proposing an idealized instability problem as a benchmark for discriminating among numerical algorithms for two-dimensional Navier-Stokes ows. The problem is a double shear layer simulated at coarse resolution and with a prescribed interface perturbation. A variety of second-order accurate schemes have been tested, with all results falling into one of two solution patterns-one pattern with two eddies and the other with three eddies. In the literature, there is no fast-and-ÿrm rule to predict the results of any particular algorithm. However, it is asserted that the two-eddy solution is correct. Our own research has led to two conclusions. First, the appearance of the third eddy is tied up with small details of the truncation error; we illustrate this point by prescribing small changes that lead to reversal of the appearance=disappearance of the third eddy in several schemes. Second, we discuss the realizability of the two solutions and suggest that the three-eddy solution is the more physical. Overall, we conclude that this problem is a poor choice of benchmark to discriminate among numerical algorithms.

The energetics of wave‐driven mean flow oscillations

“…This distinguishes the ux-form formulation from the semi-Lagrangian case, where unbalanced growth rates of background potential energy and kinetic energy lead to an overall increase of total energy. Our ÿndings are consistent with the conclusions in Reference [29]. The authors compared semiLagrangian and ux-form Eulerian simulations of a double shear layer with a prescribed interface perturbation, where the advective-form algorithm develops an unphysical growth of kinetic energy, followed by an increased dissipation rate.…”

On Spurious Vortical Structures

“…6 For k = 1/3, the scheme is strictly third order only for one-dimensional problems. 7 The reader interested in the morphology of highly resolved solutions and its implications for the mechanics of the spurious eddies is referred to [39]. 8 Note that larger δ leads to a thinner shear layer.…”

On numerical realizability of thermal convection

“…3 It is well known that the numerical realizations of simulated physical phenomena may depend critically on the algorithms employed. The literature documenting various forms of numerical artifacts disguised as physical effects is rich and interdisciplinary; see [32][33][34] for examples. Here, we report on a systematic investigation of numerical effects that influence the structure of simulated convection in the PBL.…”