Descripción: In this work we show that when an inviscid axisymmetric Rankine flow experiences a soft expansion, rotating Kelvin waves can be excited. Downstream of the region where the expansion occurs (the transition region) the resulting flow can be expressed as the addition of a Rankine and a Beltrami flow. The Beltrami constant is determined from the Rankine upstream flow, and the helix pitch of the n=1 mode results from the boundary conditions downstream. Finally, a discussion of the process leading to oscillatory flow and a conjecture about the topological background that sustains the Beltrami flow structure are offered. © 2008 American Institute of Physics.

Descripción: In a previous paper [R. González, L. G. Sarasua, and A. Costa, "Kelvin waves with helical Beltrami flow structure," Phys. Fluids20, 024106 (2008)] we analyzed the formation of Kelvin waves with a Beltrami flow structure in an ideal fluid. Here, taking into account the results of this paper, the topological analogy between the role of the magnetic field in Woltjer's theorem [L. Woltjer, "A theorem on force-free magnetic fields," Proc. Natl. Acad. Sci. U.S.A.44, 489 (1958)] and the role of the vorticity in the equivalent theorem is revisited. Via this analogy we identify the force-free equilibrium of the magnetohydrodynamics with the Beltrami flow equilibrium of the hydrodynamic. The stability of the last one is studied applying Arnold's theorem. We analyze the role of the enstrophy in the determination of the equilibrium and its stability. We show examples where the Beltrami flow equilibrium is stable under perturbations of the Beltrami flow type with the same eigenvalue as the basic flow one. The enstrophy variation results invariant with respect to a uniform rotating and translational frame and the stability is conserved when the flow experiences a transition from a Beltrami axisymmetric flow to a helical one of the same eigenvalue. These results are discussed in comparison with that given by Moffatt in 1986 [H. K. Moffatt, "Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 2. Stability considerations," J. Fluid Mech.166, 359 (1986)]. © 2010 American Institute of Physics.

Descripción: We define the beltramized flow as the sum of an uniform translation and an uniform rotation with a Beltrami flow. Some of their features are studied by solving the Euler equations, for different geometries, taking into account the boundary conditions, and for different symmetries. We show that the Kelvin waves are beltramized flows. Finally, we show that the variational principle found in a previous work, remains valid for the beltramized flow.

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: We examine the decomposition of forced Taylor-Green and Arn'old-Beltrami-Childress (ABC) flows into coherent and incoherent components using an orthonormal wavelet decomposition. We ask whether wavelet coefficient thresholding based on the Donoho-Johnstone criterion can extract a coherent vortex signal while leaving behind Gaussian random noise. We find that no threshold yields a strictly Gaussian incoherent component, and that the most Gaussian incoherent flow is found for data compression lower than that achieved with the fully iterated Donoho-Johnstone threshold. Moreover, even at such low compression, the incoherent component shows clear signs of large-scale spatial correlations that are signatures of the forcings used to drive the flows. © 2012 American Institute of Physics.

Descripción: We present numerical evidence on how three-dimensionalization is recovered at small scale in rotating turbulence with helical forcing provided by a Beltrami flow. The relevant ranges (large-scale inverse cascade of energy, anisotropic and isotropic direct cascades of energy and helicity, dissipative) are each moderately resolved. These results stem from large direct numerical simulations on grids of either 15363 or 30723 points. In the latter case, the scale at which the inertial wave time and the eddy turn-over time are equal is found to be more than one order of magnitude larger than the dissipation scale. We also examine how the presence of such an intermediate scale could affect truncation due to the use of a helical spectral Large Eddy Simulation procedure which can allow for extending the analysis to a wider range of parameters. Finally, the self-similarity of the direct cascade of energy to small scales for rotating flows, observed recently in numerical simulations as well as in several laboratory experiments, will be discussed briefly for its scaling properties and its conformal invariance.