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Register a new userInverse velocity statistics in two dimensional turbulence
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We present a numerical study of two-dimensional turbulent flows in the enstrophy cascade regime, with different large-scale forcings and energy sinks. In particular, we study the statistics of more-than-differentiable velocity fluctuations by means of two recently introduced sets of statistical estimators, namely {it inverse statistics} and {it second order differences}. We show that the 2D turbulent velocity field, $bm u$, cannot be simply characterized by its spectrum behavior, $E(k) propto k^{-alpha}$. There exists a whole set of exponents associated to the non-trivial smooth fluctuations of the velocity field at all scales. We also present a numerical investigation of the temporal properties of $bm u$ measured in different spatial locations.
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The problem of inverse statistics (statistics of distances for which the signal fluctuations are larger than a certain threshold) in differentiable signals with power law spectrum, $E(k) sim k^{-alpha}$, $3 le alpha < 5$, is discussed. We show that for these signals, with random phases, exit-distance moments follow a bi-fractal distribution. We also investigate two dimensional turbulent flows in the direct cascade regime, which display a more complex behavior. We give numerical evidences that the inverse statistics of 2d turbulent flows is described by a multi-fractal probability distribution, i.e. the statistics of laminar events is not simply captured by the exponent $alpha$ characterizing the spectrum.
We present a search for conformal invariance in vorticity isolines of two-dimensional compressible turbulence. The vorticity is measured by tracking the motion of particles that float at the surface of a turbulent tank of water. The three-dimensional turbulence in the tank has a Taylor microscale $Re_lambda simeq 160$. The conformal invariance theory being tested here is related to the behavior of equilibrium systems near a critical point. This theory is associated with the work of Lowner, Schramm and others and is usually referred to as Schramm-Lowner Evolution (SLE). The system was exposed to several tests of SLE. The results of these tests suggest that zero-vorticity isolines exhibit noticeable departures from this type of conformal invariance.
The relative dispersion process in two-dimensional free convection turbulence is investigated by direct numerical simulation. In the inertial range, the growth of relative separation, $r$, is expected as $<r^2(t)>propto t^5$ according to the Bolgiano-Obukhov scaling. The result supporting the scaling is obtained with exit-time statistics. Detailed investigation of exit-time PDF shows that the PDF is divided into two regions, the Region-I and -II, reflecting two types of separating processes: persistent expansion and random transitions between expansion and compression of relative separation. This is consistent with the physical picture of the self-similar telegraph model. In addition, a method for estimating the parameters of the model are presented. Comparing two turbulence cases, two-dimensional free convection and inverse cascade turbulence, the relation between the drift term of the model and nature of coherent structures is discussed.
In wave turbulence, it has been believed that statistical properties are well described by the weak turbulence theory, in which nonlinear interactions among wavenumbers are assumed to be small. In the weak turbulence theory, separation of linear and nonlinear time scales derived from the weak nonlinearity is also assumed. However, the separation of the time scales is often violated even in weak turbulent systems where the nonlinear interactions are actually weak. To get rid of this inconsistency, closed equations are derived without assuming the separation of the time scales in accordance with Direct-Interaction Approximation (DIA), which has been successfully applied to Navier--Stokes turbulence. The kinetic equation of the weak turbulence theory is recovered from the DIA equations if the weak nonlinearity is assumed as an additional assumption. It suggests that the DIA equations is a natural extension of the conventional kinetic equation to not-necessarily-weak wave turbulence.
By analyzing trajectories of solid hydrogen tracers, we find that the distributions of velocity in decaying quantum turbulence in superfluid $^4$He are strongly non-Gaussian with $1/v^3$ power-law tails. These features differ from the near-Gaussian statistics of homogenous and isotropic turbulence of classical fluids. We examine the dynamics of many events of reconnection between quantized vortices and show by simple scaling arguments that they produce the observed power-law tails.
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