2,405 research outputs found
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 . Then two
examples other than 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
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