Spectral imbalance and the normalized dissipation rate of turbulence

The normalized turbulent dissipation rate $C_\epsilon$ is studied in decaying and forced turbulence by direct numerical simulations, large-eddy simulations, and closure calculations. A large difference in the values of $C_\epsilon$ is observed for the two types of turbulence. This difference is found at moderate Reynolds number, and it is shown that it persists at high Reynolds number, where the value of $C_\epsilon$ becomes independent of the Reynolds number, but is still not unique. This difference can be explained by the influence of the nonlinear cascade time that introduces a spectral disequilibrium for statistically nonstationary turbulence. Phenomenological analysis yields simple analytical models that satisfactorily reproduce the numerical results. These simple spectral models also reproduce and explain the increase of $C_\epsilon$ at low Reynolds number that is observed in the simulations

Coriolis force in Geophysics: an elementary introduction and examples

We show how Geophysics may illustrate and thus improve classical Mechanics lectures concerning the study of Coriolis force effects. We are then interested in atmospheric as well as oceanic phenomena we are familiar with, and are for that reason of pedagogical and practical interest. Our aim is to model them in a very simple way to bring out the physical phenomena that are involved.Comment: Accepted for publication in European Journal of Physic

Field theory of the inverse cascade in two-dimensional turbulence

A two-dimensional fluid, stirred at high wavenumbers and damped by both viscosity and linear friction, is modeled by a statistical field theory. The fluid's long-distance behavior is studied using renormalization-group (RG) methods, as begun by Forster, Nelson, and Stephen [Phys. Rev. A 16, 732 (1977)]. With friction, which dissipates energy at low wavenumbers, one expects a stationary inverse energy cascade for strong enough stirring. While such developed turbulence is beyond the quantitative reach of perturbation theory, a combination of exact and perturbative results suggests a coherent picture of the inverse cascade. The zero-friction fluctuation-dissipation theorem (FDT) is derived from a generalized time-reversal symmetry and implies zero anomalous dimension for the velocity even when friction is present. Thus the Kolmogorov scaling of the inverse cascade cannot be explained by any RG fixed point. The beta function for the dimensionless coupling ghat is computed through two loops; the ghat^3 term is positive, as already known, but the ghat^5 term is negative. An ideal cascade requires a linear beta function for large ghat, consistent with a Pad\'e approximant to the Borel transform. The conjecture that the Kolmogorov spectrum arises from an RG flow through large ghat is compatible with other results, but the accurate k^{-5/3} scaling is not explained and the Kolmogorov constant is not estimated. The lack of scale invariance should produce intermittency in high-order structure functions, as observed in some but not all numerical simulations of the inverse cascade. When analogous RG methods are applied to the one-dimensional Burgers equation using an FDT-preserving dimensional continuation, equipartition is obtained instead of a cascade--in agreement with simulations.Comment: 16 pages, 3 figures, REVTeX 4. Material added on energy flux, intermittency, and comparison with Burgers equatio

Magnetic Fields and Passive Scalars in Polyakov's Conformal Turbulence

Polyakov has suggested that two dimensional turbulence might be described by a minimal model of conformal field theory. However, there are many minimal models satisfying the same physical inputs as Polyakov's solution (p,q)=(2,21). Dynamical magnetic fields and passive scalars pose different physical requirements. For large magnetic Reynolds number other minimal models arise. The simplest one, (p,q)=(2,13) makes reasonable predictions that may be tested in the astrophysical context. In particular, the equipartition theorem between magnetic and kinetic energies does not hold: the magnetic one dominates at larger distances.Comment: 12 pages, UR-1296, ER-745-4068

Decay of scalar variance in isotropic turbulence in a bounded domain

The decay of scalar variance in isotropic turbulence in a bounded domain is investigated. Extending the study of Touil, Bertoglio and Shao (2002; Journal of Turbulence, 03, 49) to the case of a passive scalar, the effect of the finite size of the domain on the lengthscales of turbulent eddies and scalar structures is studied by truncating the infrared range of the wavenumber spectra. Analytical arguments based on a simple model for the spectral distributions show that the decay exponent for the variance of scalar fluctuations is proportional to the ratio of the Kolmogorov constant to the Corrsin-Obukhov constant. This result is verified by closure calculations in which the Corrsin-Obukhov constant is artificially varied. Large-eddy simulations provide support to the results and give an estimation of the value of the decay exponent and of the scalar to velocity time scale ratio

Intermittency in the Joint Cascade of Energy and Helicity

The statistics of the energy and helicity fluxes in isotropic turbulence are studied using high resolution direct numerical simulation. The scaling exponents of the energy flux agree with those of the transverse velocity structure functions through refined similarity hypothesis, consistent with Kraichnan's prediction \cite{Kr74}. The helicity flux is even more intermittent than the energy flux and its scaling exponents are closer to those of the passive scalar. Using Waleffe's helical decomposition, we demonstrate that the existence of positive mean helicity flux inhibits the energy transfer in the negative helical modes, a non-passive effect