Topology of two-dimensional turbulence

Velocity differences in the direct enstrophy cascade of two-dimensional turbulence are correlated with the underlying flow topology. The statistics of the transverse and longitudinal velocity differences are found to be governed by different structures. The wings of the transverse distribution are dominated by strong vortex centers, whereas the tails of the longitudinal differences are dominated by saddles. Viewed in the framework of earlier theoretical work, this result suggests that the transfer of enstrophy to smaller scales is accomplished in regions of the flow dominated by saddles.     

Fractality feature in incompressible three-dimensional magnetohydrodynamic turbulence

Direct Numerical Simulation (DNS) of decaying isotropic 3D magnetohydrodynamic (MHD) turbulence based on the 10243-modes in a periodic box is used to study the statistical properties of turbulence. In this paper, the presence of intermittency in MHD turbulence is investigated through the analysis of the Probability Distribution Function (PDF) for Elsässer fields and total energy fluctuations. We observe that the PDFs of the Elsässer fields fluctuations display a strong non-Gaussian behavior at small scale, which can be ascribed to multifractality feature, while the PDFs of the total energy fluctuations have the same shape over all observed scales and are monofractal. The PDFs have stretched exponential tail and satisfy the function P(|δX|) ～ exp(?A|δX| ^μ ). Numerically, we extract the exponent μ and find that it is constant for monofractal behavior as the length scale varies. To check the notion of self-similarity in the respective fluctuation, we apply the compensated structure functions.     

Renormalization-group analysis of supersymmetric mass hierarchies

A renormalization-group analysis is performed for supersymmetric models of the O'Raifeartaigh type coupled to a Yang-Mills supermultiplet. For an appropriate range of coupling constants, we find that large mass ratios can be naturally generated by one-loop corrections to the effective potential. The results confirm Witten's recent observation that these models provide a potential solution to the gauge hierarchy problem. The general renormalization-group analysis of symmetry breaking developed in this paper is applicable in contexts other than supersymmetry. We also give a simple argument that the canonical form of the supersymmetric Ward identities can be maintained in the presence of quantum effects.     

Renormalization-group analysis of the Kobayashi-Maskawa matrix

The one-loop renormalization-group equations for the quark mixing (Kobayashi-Maskawa) matrixV are derived, independent of one's weak interaction basis, in the standard model as well as in its two Higgs and supersymmetric extensions, and their numerical solutions are presented. While the mixing angles |V _ub |, |V _cb |, |V _td | and the phase-invariant measure of CP nonconservationJ all vary slowly with momentum, in the standard model they are predicted to increase in clear contrast to the two Higgs and supersymmetric extensions where they decrease with momentum.     

Structure functions in two-dimensional turbulence

The “variable range decomposition” mean field type approximation is applied to the enstrophy and energy balance equations in 2D homogeneous, isotropic turbulence. Enstrophy is seen to be transferred to smaller scales, energy to larger scales. The approximate enstrophy balance equation is supplemented by an exact relation between the velocity structure functionD(r) and the vorticity structure functionD _ω(r) to form a closed set of equations that is used to calculateD andD _ω from scale zero up to the input scale.D _ω is found to depend only on viscosity and the enstrophy dissipation ε_ω and tends to the constant ≈15ε _ω ^2/3 in the enstrophy inertial range.D(r) in addition to the well-knownr ²-law has a second power law term ∝r ^4/3, which is important in the intermediate range between the viscous range and the enstrophy inertial range. All numerical constants are calculated.     

Logarithmic correlation functions in two-dimensional turbulence

We consider the correlation functions of two-dimensional turbulence in the presence and absence of a three-dimensional perturbation, by means of conformal field theory. In the presence of three-dimensional perturbation, we show that in the strong coupling limit of a small scale random force, there is some logarithmic factor in the correlation functions of velocity stream functions. We show that the logarithmic conformal field theory c_8,1 describes the 2D-turbulence both in the absence and in the presence of the perturbation. We obtain the energy spectrum E(k) ∼ k^−5.125 ln(k) for perturbed 2D-turbulence and E(k) ∼ k⁻⁵ ln(k) for unperturbed turbulence. Recent numerical simulation and experimental results confirm our prediction.     

External dissipation in driven two-dimensional turbulence

Turbulence in a freely suspended soap film is created by electromagnetic forcing and measured by particle tracking. The velocity fluctuations are shown to be adequately described by the forced Navier-Stokes equation for an incompressible two-dimensional fluid with a linear drag term to model the frictional coupling to the surrounding air. Using this equation, the energy dissipation rates due to air friction and the film's internal viscosity are measured, as is the rate of energy injection from the electromagnetic forcing. Comparison of these rates demonstrates that the air friction is a significant energy dissipation mechanism in the system.     

Dynamic multiscaling in two-dimensional fluid turbulence

We obtain, by extensive direct numerical simulations, time-dependent and equal-time structure functions for the vorticity, in both quasi-Lagrangian and Eulerian frames, for the direct-cascade regime in two-dimensional fluid turbulence with air-drag-induced friction. We show that different ways of extracting time scales from these time-dependent structure functions lead to different dynamic-multiscaling exponents, which are related to equal-time multiscaling exponents by different classes of bridge relations; for a representative value of the friction we verify that, given our error bars, these bridge relations hold.