Statistical properties of freely decaying two-dimensional hydrodynamic turbulence

Abstract

Statistical characteristics of freely decaying two-dimensional hydrodynamic turbulence at high Reynolds numbers are numerically studied. In particular, numerical experiments (with resolution up to 8192 × 8192) provide a Kraichnan-type turbulence spectrum E k ∼ k −3 . By means of spatial filtration, it is found that the main contribution to the spectrum comes from the sharp vorticity gradients in the form of quasi-shocks. Such quasi-singularities are responsible for a strong angular dependence of the spectrum owing to well-localized (in terms of the angle) jets with minor and/or large overlapping. In each jet, the spectrum decreases as k −3 . The behavior of the third-order structure function accurately agrees with Kraichnan direct cascade concept corresponding to a constant enstrophy flux. It is shown that the power law exponents ζn for higher structure functions grow more slowly than the linear dependence of n, which testifies to turbulence intermittency.

Nonlinear Spin Waves in Graphene Structures

“…(31), separated by the distance 2a large enough compared to the width of the kink, interact with each other, their own shape remaining unchanged. As shown below, negative values of a in model A correspond to the re°ection from a repulsive barrier, in accordance with the potential model, 23 due to the violation of kink/antikink topological charge conservation law, implied by model B. 17,18 Thus, we can formally consider the¯eld function (31) in model B …”

Kink-antikink collisions for twin models

“…Usually one can use collective coordinates to obtain the KK attractive interaction potential U KK as a function of the separation of the pair kink-antikink [10,11]. The potential U KK can be intuitively understood as the energy of the static field configuration consisting of a kink at +Z and an antikink at −Z [12].…”

Hadron Amplitudes in Composite Superconformal String Model

“…For composite superstring model we consider the set of states and of superconformal generators for the i-th section between theV i−1,i vertex andV i,i+1 vertex in (8). (See Fig.…”

“…Just this reason led to superstring models for non-hadrons: for massless gluons (open strings) on the trajectory J = 1 + α ′ P M 2 and for massless gravitons (closed strings) on the trajectory J = 2 + 1/2α ′ P M 2 . A generalization of classical multi-reggeon (multi-string) vertices [7] was suggested by one of authors in 1993 [8] as a new solution of duality equations for many-string vertices in [7]. These string amplitudes have been used for description of many π-mesons interaction [8].…”

“…A generalization of classical multi-reggeon (multi-string) vertices [7] was suggested by one of authors in 1993 [8] as a new solution of duality equations for many-string vertices in [7]. These string amplitudes have been used for description of many π-mesons interaction [8]. New string vertices [9] give a new geometric picture for string interaction which has a natural description in terms of three two-dimensional surfaces (composite string) for moving open string instead of usual one surface.…”