Abstract
Direct numerical simulation is performed for the forced Navier–Stokes equation in four spatial dimensions. Well equilibrated, long time runs at sufficient resolution were obtained to reliably measure spectral quantities, the velocity derivative skewness, and the dimensionless dissipation rate. Comparisons to corresponding two- and three-dimensional results are made. Energy fluctuations are measured, and the results show a clear reduction moving from three to four dimensions. The dynamics show simplifications in four dimensions with a picture of increased forward energy transfer resulting in an extended inertial range with a smaller Kolmogorov scale. This enhanced forward transfer is linked to our finding of increased dissipative anomaly and velocity derivative skewness.
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