78 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
Weak and strong wave turbulence spectra for elastic thin plate
Variety of statistically steady energy spectra in elastic wave turbulence
have been reported in numerical simulations, experiments, and theoretical
studies. Focusing on the energy levels of the system, we have performed direct
numerical simulations according to the F\"{o}ppl--von K\'{a}rm\'{a}n equation,
and successfully reproduced the variability of the energy spectra by changing
the magnitude of external force systematically. When the total energies in wave
fields are small, the energy spectra are close to a statistically steady
solution of the kinetic equation in the weak turbulence theory. On the other
hand, in large-energy wave fields, another self-similar spectrum is found.
Coexistence of the weakly nonlinear spectrum in large wavenumbers and the
strongly nonlinear spectrum in small wavenumbers are also found in moderate
energy wave fields.Comment: 5 pages, 3 figure
Single-wavenumber Representation of Nonlinear Energy Spectrum in Elastic-Wave Turbulence of {F}\"oppl-von {K}\'arm\'an Equation: Energy Decomposition Analysis and Energy Budget
A single-wavenumber representation of nonlinear energy spectrum, i.e.,
stretching energy spectrum is found in elastic-wave turbulence governed by the
F\"oppl-von K\'arm\'an (FvK) equation. The representation enables energy
decomposition analysis in the wavenumber space, and analytical expressions of
detailed energy budget in the nonlinear interactions are obtained for the first
time in wave turbulence systems. We numerically solved the FvK equation and
observed the following facts. Kinetic and bending energies are comparable with
each other at large wavenumbers as the weak turbulence theory suggests. On the
other hand, the stretching energy is larger than the bending energy at small
wavenumbers, i.e., the nonlinearity is relatively strong. The strong
correlation between a mode and its companion mode is
observed at the small wavenumbers. Energy transfer shows that the energy is
input into the wave field through stretching-energy transfer at the small
wavenumbers, and dissipated through the quartic part of kinetic-energy transfer
at the large wavenumbers. A total-energy flux consistent with the energy
conservation is calculated directly by using the analytical expression of the
total-energy transfer, and the forward energy cascade is observed clearly.Comment: 11 pages, 4 figure
Identification of Separation Wavenumber between Weak and Strong Turbulence Spectra for Vibrating Plate
A weakly nonlinear spectrum and a strongly nonlinear spectrum coexist in a
statistically steady state of elastic wave turbulence. The analytical
representation of the nonlinear frequency is obtained by evaluating the
extended self-nonlinear interactions. The {\em critical\/} wavenumbers at which
the nonlinear frequencies are comparable with the linear frequencies agree with
the {\em separation\/} wavenumbers between the weak and strong turbulence
spectra. We also confirm the validity of our analytical representation of the
separation wavenumbers through comparison with the results of direct numerical
simulations by changing the material parameters of a vibrating plate
Fluctuations of statistics among subregions of a turbulence velocity field
To study subregions of a turbulence velocity field, a long record of velocity
data of grid turbulence is divided into smaller segments. For each segment, we
calculate statistics such as the mean rate of energy dissipation and the mean
energy at each scale. Their values significantly fluctuate, in lognormal
distributions at least as a good approximation. Each segment is not under
equilibrium between the mean rate of energy dissipation and the mean rate of
energy transfer that determines the mean energy. These two rates still
correlate among segments when their length exceeds the correlation length. Also
between the mean rate of energy dissipation and the mean total energy, there is
a correlation characterized by the Reynolds number for the whole record,
implying that the large-scale flow affects each of the segments.Comment: 7 pages, accepted by Physics of Fluids (see http://pof.aip.org/
On Landau's prediction for large-scale fluctuation of turbulence energy dissipation
Kolmogorov's theory for turbulence in 1941 is based on a hypothesis that
small-scale statistics are uniquely determined by the kinematic viscosity and
the mean rate of energy dissipation. Landau remarked that the local rate of
energy dissipation should fluctuate in space over large scales and hence should
affect small-scale statistics. Experimentally, we confirm the significance of
this large-scale fluctuation, which is comparable to the mean rate of energy
dissipation at the typical scale for energy-containing eddies. The significance
is independent of the Reynolds number and the configuration for turbulence
production. With an increase of scale r above the scale of largest
energy-containing eddies, the fluctuation becomes to have the scaling r^-1/2
and becomes close to Gaussian. We also confirm that the large-scale fluctuation
affects small-scale statistics.Comment: 9 pages, accepted by Physics of Fluids (see http://pof.aip.org
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