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.

Descripción: We determine how the differences in the treatment of the subfilter-scale physics affect the properties of the flow for three closely related regularizations of Navier-Stokes. The consequences on the applicability of the regularizations as subgrid-scale (SGS) models are also shown by examining their effects on superfilter-scale properties. Numerical solutions of the Clark-α model are compared to two previously employed regularizations, the Lagrangian-averaged Navier-Stokes α-model (LANS-α) and Leray-α, albeit at significantly higher Reynolds number than previous studies, namely, Re≈3300, Taylor Reynolds number of Re≈790, and to a direct numerical simulation (DNS) of the Navier-Stokes equations. We derive the de Kármán-Howarth equation for both the Clark-α and Leray-α models. We confirm one of two possible scalings resulting from this equation for Clark-α as well as its associated k-1 energy spectrum. At subfilter scales, Clark-α possesses similar total dissipation and characteristic time to reach a statistical turbulent steady state as Navier-Stokes, but exhibits greater intermittency. As a SGS model, Clark-α reproduces the large-scale energy spectrum and intermittency properties of the DNS. For the Leray-α model, increasing the filter width α decreases the nonlinearity and, hence, the effective Reynolds number is substantially decreased. Therefore, even for the smallest value of α studied Leray-α was inadequate as a SGS model. The LANS-α energy spectrum ∼k1, consistent with its so-called "rigid bodies," precludes a reproduction of the large-scale energy spectrum of the DNS at high Re while achieving a large reduction in numerical resolution. We find, however, that this same feature reduces its intermittency compared to Clark-α (which shares a similar de Kármán-Howarth equation). Clark-α is found to be the best approximation for reproducing the total dissipation rate and the energy spectrum at scales larger than α, whereas high-order intermittency properties for larger values of α are best reproduced by LANS-α. © 2008 American Institute of Physics.

Descripción: We present a parametric space study of the decay of turbulence in rotating flows combining direct numerical simulations, large eddy simulations, and phenomenological theory. Several cases are considered: (1) the effect of varying the characteristic scale of the initial conditions when compared with the size of the box, to mimic "bounded" and "unbounded" flows; (2) the effect of helicity (correlation between the velocity and vorticity); (3) the effect of Rossby and Reynolds numbers; and (4) the effect of anisotropy in the initial conditions. Initial conditions include the Taylor-Green vortex, the Arn'old-Beltrami-Childress flow, and random flows with large-scale energy spectrum proportional to k4. The decay laws obtained in the simulations for the energy, helicity, and enstrophy in each case can be explained with phenomenological arguments that consider separate decays for two-dimensional and three-dimensional modes and that take into account the role of helicity and rotation in slowing down the energy decay. The time evolution of the energy spectrum and development of anisotropies in the simulations are also discussed. Finally, the effect of rotation and helicity in the skewness and kurtosis of the flow is considered. © 2011 American Institute of Physics.

Descripción: The subfilter-scale (SFS) physics of regularization models are investigated to understand the regularizations' performance as SFS models. Suppression of spectrally local SFS interactions and conservation of small-scale circulation in the Lagrangian-averaged Navier-Stokes α-model (LANS-α) is found to lead to the formation of rigid bodies. These contaminate the superfilter-scale energy spectrum with a scaling that approaches k +1 as the SFS spectra is resolved. The Clark-α and Leray-α models, truncations of LANS-α, do not conserve small-scale circulation and do not develop rigid bodies. LANS-α, however, is closest to Navier-Stokes in intermittency properties. All three models are found to be stable at high Reynolds number. Differences between L 2 and H 1 norm models are clarified. For magnetohydrodynamics (MHD), the presence of the Lorentz force as a source (or sink) for circulation and as a facilitator of both spectrally nonlocal large to small scale interactions as well as local SFS interactions prevents the formation of rigid bodies in Lagrangian-averaged MHD (LAMHD-α). LAMHD-α performs well as a predictor of superfilter-scale energy spectra and of intermittent current sheets at high Reynolds numbers. It may prove generally applicable as a MHD-LES. © 2010 Springer Science+Business Media, LLC.

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: Correlation anisotropy emerges dynamically in magnetohydrodynamics (MHD), producing stronger gradients across the large-scale mean magnetic field than along it. This occurs both globally and locally, and has significant implications in space and astrophysical plasmas, including particle scattering and transport, and theories of turbulence. Properties of local correlation anisotropy are further documented here by showing through numerical experiments that the effect is intensified in more localized estimates of the mean field. The mathematical formulation of this property shows that local anisotropy mixes second-order with higher order correlations. Sensitivity of local statistical estimates to higher order correlations can be understood in connection with the stochastic coordinate system inherent in such formulations. We demonstrate this in specific cases, and illustrate the connection to higher order statistics by showing the sensitivity of local anisotropy to phase randomization, after which the global measure of anisotropy is recovered at all scales of averaging. This establishes that anisotropy of the local structure function is not a measure of anisotropy of the energy spectrum. Evidently, the local enhancement of correlation anisotropy is of substantial fundamental interest and must be understood in terms of higher order correlations, specifically fourth-order and above. © 2012. The American Astronomical Society. All rights reserved.