On 'spurious' eddies

Recently, 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 flows. 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-firm 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.