Descripción: A subgrid-scale spectral model of rotating turbulent flows is tested against direct numerical simulations (DNSs). The case of Taylor-Green forcing is considered, a configuration that mimics the flow between two counter-rotating disks as often used in the laboratory. Computations are performed for moderate rotation down to Rossby numbers of 0.03, as can be encountered in the Earth's atmosphere. We provide several measures of the degree of anisotropy of the small scales and conclude that an isotropic model may suffice at moderate Rossby number. The model, developed previously [J. Baerenzung, H. Politano, Y. Ponty, and A. Pouquet, "Spectral modeling of turbulent flows and the role of helicity," Phys. Rev. E77, 046303 (2008)], incorporates eddy viscosity and eddy noise that depend dynamically on the index of the energy spectrum. We show that the model reproduces satisfactorily all large-scale properties of the DNS up to Reynolds numbers of ~104 and for long times after the onset of the inverse cascade of energy; it is also shown to behave better than either the Chollet-Lesieur eddy viscosity model [J. P. Chollet and M. Lesieur, "Parametrization of small scales of three-dimensional isotropic turbulence utilizing spectral closures," J. Atmos. Sci.38, 2747 (1981)] or an under-resolved DNS. © 2010 American Institute of Physics.

Descripción: Rapidly rotating turbulent flow is characterized by the emergence of columnar structures that are representative of quasi-two-dimensional behavior of the flow. It is known that when energy is injected into the fluid at an intermediate scale L f, it cascades towards smaller as well as larger scales. In this paper we analyze the flow in the inverse cascade range at a small but fixed Rossby number, Ro f≈0.05. Several numerical simulations with helical and nonhelical forcing functions are considered in periodic boxes with unit aspect ratio. In order to resolve the inverse cascade range with reasonably large Reynolds number, the analysis is based on large eddy simulations which include the effect of helicity on eddy viscosity and eddy noise. Thus, we model the small scales and resolve explicitly the large scales. We show that the large-scale energy spectrum has at least two solutions: one that is consistent with Kolmogorov-Kraichnan-Batchelor-Leith phenomenology for the inverse cascade of energy in two-dimensional (2D) turbulence with a ∼k⊥-5/3 scaling, and the other that corresponds to a steeper ∼k⊥-3 spectrum in which the three-dimensional (3D) modes release a substantial fraction of their energy per unit time to the 2D modes. The spectrum that emerges depends on the anisotropy of the forcing function, the former solution prevailing for forcings in which more energy is injected into the 2D modes while the latter prevails for isotropic forcing. In the case of anisotropic forcing, whence the energy goes from the 2D to the 3D modes at low wave numbers, large-scale shear is created, resulting in a time scale τ sh, associated with shear, thereby producing a ∼k -1 spectrum for the total energy with the horizontal energy of the 2D modes still following a ∼k⊥-5/3 scaling. © 2012 American Physical Society.