Decaying vortex and wave turbulence in rotating shallow water model, as follows from high-resolution direct numerical simulations

作者：Lahaye Noe^*; Zeitlin Vladimir

来源：Physics of Fluids, 2012, 24(11): 115106.

DOI：10.1063/1.4767723

• flow simulation
• numerical analysis
• shallow water equations
• shock waves
• statistical analysis
• turbulence
• vortices

We report results of direct numerical simulations of decaying turbulence in an inviscid rotating shallow water model. We use a new-generation high-resolution well-balanced shock-capturing finite-volume scheme with several types of initializations: "classical" ones with random velocity and/or height fields, or an initialization with randomly oriented coherent vortex dipoles. Together with "full" turbulence simulations we also perform pure wave-turbulence ones, starting from an initial random wave field of small amplitude with zero potential vorticity anomaly and a given initial spectrum. Statistical properties of the rotating shallow water turbulence, as well as the development of coherent structures and their interactions are studied in detail. For all "full" turbulence simulations we find a tendency to form coherent structures with clear cyclone-anticyclone asymmetry and very steep energy spectra, with exponents close to -6. We also observe a decorrelation of the vortex and wave fields in time, even at significant Rossby numbers. However, we do not observe a universal power law in the evolution of coherent vortices, predicted by the "universal decay" theory for the 2D turbulence. A clear sensitivity to the initial conditions is thus established. For wave-turbulence simulations we observe a tendency to form very steep spectra different from the predictions of the so-called weak turbulence, and of both the turbulence of cusped nonlinear waves and the shock turbulence.

• 出版日期2012-11