Large-scale lognormality in turbulence modeled by Ornstein-Uhlenbeck process

Lognormality was found experimentally for coarse-grained squared turbulence velocity and velocity increment when the coarsening scale is comparable to the correlation scale of the velocity (Mouri et al. Phys. Fluids 21, 065107, 2009). We investigate this large-scale lognormality by using a simple stochastic process with correlation, the Ornstein-Uhlenbeck (OU) process. It is shown that the OU process has a similar large-scale lognormality, which is studied numerically and analytically.Comment: 7 pages, 5 figures, PRE in pres

A class of steady solutions to two-dimensional free convection

We obtained steady solutions to the two-dimensional Boussinesq approximation equations without mean temperature gradient. This system is referred to as free convection in this paper. Under an external flow described by the stream function \mPsi = - Ayf(x), two types of steady solutions are found depending on the boundary conditions. One is kept steady by the balance between the strain of \mPsi and the diffusion. The solution is similar to the Burgers vortex layer solution. The other is done by the balance between vorticity induced by the buoyancy and vorticity flux caused by the external flow. Detailed argument on these two balances is presented for $f(x) = x$. Then two examples other than $f(x) = x$ are shown to have either of the two balancing mechanism. We discuss the relation between these solutions and long-lived fine scale coherent structures observed in direct numerical simulations of two-dimensional free convection turbulence.Comment: REVTeX4, 9 pages, 10 figures, submitted to Phys.Rev.

Numerical simulation of Faraday waves oscillated by two-frequency forcing

We perform a numerical simulation of Faraday waves forced with two-frequency oscillations using a level-set method with Lagrangian-particle corrections (particle level-set method). After validating the simulation with the linear stability analysis, we show that square, hexagonal and rhomboidal patterns are reproduced in agreement with the laboratory experiments [Arbell and Fineberg, Phys. Rev. Lett. 84, 654 (2000) and Phys. Rev. Lett. 85, 756 (2000)]. We also show that the particle level-set's high degree of conservation of volume is necessary in the simulations. The numerical results of the rhomboidal states are compared with weakly nonlinear analysis. Difficulty in simulating other patterns of the two-frequency forced Faraday waves is discussed.Comment: 20 pages, 12 figure

One-dimensional hydrodynamic model generating a turbulent cascade

As a minimal mathematical model generating cascade analogous to that of the Navier-Stokes turbulence in the inertial range, we propose a one-dimensional partial-differential-equation model that conserves the integral of the squared vorticity analogue (enstrophy) in the inviscid case. With a large-scale forcing and small viscosity, we find numerically that the model exhibits the enstrophy cascade, the broad energy spectrum with a sizable correction to the dimensional-analysis prediction, peculiar intermittency and self-similarity in the dynamical system structure.Comment: 5 pages, 4 figure