Analytical and phenomenological studies of rotating turbulence (original) (raw)

The decay of turbulence in rotating flows

Physics of Fluids, 2011

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 k 4 . 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.

Some developments in the theory of turbulence

Journal of Fluid Mechanics, 1981

This is in no way intended as a review of turbulence-the subject is far too big for adequate treatment within a reasonably finite number of pages; the monumental ' closure ' scheme brings no guarantee of better predictions outside the range of geometries and parameters previously documented, then it is of little value to the user. Sometimes a user may suffer from the delusion that a more ' advanced ' closure scheme must, merely by virtue of its complexity, provide a better representation of the effects

Nonextensivity in turbulence in rotating two-dimensional and three-dimensional flows

Physica D: Nonlinear Phenomena, 2003

Our experiments on turbulent flow in a rotating annulus yield probability distribution functions (PDFs) for velocity increments δv( ), where is the separation between points. We fit these PDFs to a form derived for turbulent flows by Beck, who used the Tsallis nonextensive statistical mechanics formalism. For slow rotation rates, we find that the fit parameter q is 1.25 for small . At large , q decreases to unity, the value corresponding to the usual Boltzmann-Gibbs statistics. These results agree with those previously measured in experiments on Couette-Taylor turbulence. However, with rapid rotation of the annulus, the turbulent flow becomes strongly two-dimensional (2D) rather than three-dimensional (3D), and we find q = 1.32 ± 0.04, independent of . This suggests that the coherent structures (vortices), which are a source of intermittency, are important at all length scales in the 2D case.

Energy transfer in rotating turbulence

Journal of Fluid Mechanics, 1997

The influence of rotation on the spectral energy transfer of homogeneous turbulence is investigated in this paper. Given the fact that linear dynamics, e.g. the inertial waves regime found in an RDT (rapid distortion theory) analysis, cannot affect a homogeneous isotropic turbulent flow, the study of nonlinear dynamics is of prime importance in the case of rotating flows. Previous theoretical (including both weakly nonlinear and EDQNM theories), experimental and DNS (direct numerical simulation) results are collected here and compared in order to give a self-consistent picture of the nonlinear effects of rotation on turbulence.

Transport Coefficients in Rotating Weakly Compressible Turbulence

ICASE/LaRC Interdisciplinary Series in Science and Engineering, 1999

Analytical studies of compressible turbulence have found that compressible velocity fluctuations create both effective fluid transport properties and an effective equation of state. This paper investigates the effects of rotation on compressible turbulence. It is shown that rotation modifies the transport properties of compressible turbulence by replacing the turbulence time scale by a rotational time scale, much as rotation modifies the transport properties of incompressible turbulence. But thermal equilibrium properties are modified in a more complex manner. Two regimes are possible: one dominated by incompressible fluctuations, in which the sound speed is modified as it is in non-rotating turbulence, and a rotation dominated regime in which the sound speed enhancement is rotation dependent. The dimensionless parameter which discriminates between regimes is identified. In general, rotation is found to suppress the effects of compressibility. A novel feature of the present analysis is the use of a non-Kolmogorov steady state as the reference state of turbulence. introduction of such steady states expands the power and utility of analytical turbulence closures to a wider range of problems.

Rotational effects in turbulence driven by convection

1997

We analyze rotational effects in turbulence driven by convectionintheouterregionsofanaccretiondisk,whereopac- ityismainlygivenbyice.Theseeffectsareexplicitlyconsidered through the introduction of an efciency factor which takes into account inverse energy cascade processes and through the con- sideration of a centrifugally supported basic state. By adopting a procedure which assigns some dynamics to the anisotropy factor, we obtain an equation that describes how the turbu- lent structures behave

On the sensitization of turbulence models to rotation and curvature

Aerospace Science and Technology, 1997

Spalart P. R., Shur M., Aerospace Scierzce and Technology, 1997, no 4, 297-302. Empirical alterations of eddy-viscosity turbulence models to account for system rotation and streamline curvature are discussed. Except in a narrow class of flows, the streamline curvature itself is an inadequate entry into a model, because it is not Galilean-invariant.

On the energy spectrum of rapidly rotating forced turbulence

Physics of Fluids, 2018

In this paper, we investigate the statistical features of a fully developed, forced, rapidly rotating, turbulent system using numerical simulations and model the energy spectrum that fits well with the numerical data. Among the wavenumbers (k) larger than the Kolmogorov dissipation wavenumber, the energy is distributed such that the suitably non-dimensionalized energy spectrum isĒ(k) ≈ exp(−0.05k), where the overbar denotes appropriate non-dimensionalization. For the wavenumbers smaller than that of forcing, the energy in a horizontal plane is much more than that along the vertical rotation-axis. For such wavenumbers, we find that the anisotropic energy spectrum, E(k ⊥ , k), follows the power law scaling, k −5/2 ⊥ k −1/2 , where "⊥" and " ," respectively, refer to the directions perpendicular and parallel to the rotation axis; this result is in line with the Kuznetsov-Zakharov-Kolmogorov spectrum predicted by the weak inertial-wave turbulence theory for the rotating fluids.

On the decrease of intermittency in decaying rotating turbulence

Physics of Fluids, 2008

The scaling of the longitudinal velocity structure functions, Sq(r)=⟨∣δu(r)∣q⟩∼rζq, is analyzed up to order q=8 in a decaying rotating turbulence experiment from a large particle image velocimetry dataset. The exponent of the second order structure function ζ2 increases throughout the self-similar decay regime, up to the Ekman time scale. The normalized higher-order exponents ζq∕ζ2 are close to those of the intermittent nonrotating case at small times, but show a marked departure at larger times, on a time scale Ω−1 (Ω is the rotation rate), although a strictly nonintermittent linear law ζq∕ζ2=q∕2 is not reached.