85 research outputs found
Navier-Stokes-alpha model: LES equations with nonlinear dispersion
We present a framework for discussing LES equations with nonlinear
dispersion. In this framework, we discuss the properties of the nonlinearly
dispersive Navier-Stokes-alpha model of incompressible fluid turbulence ---
also called the viscous Camassa-Holm equations and the LANS equations in the
literature --- in comparison with the corresponding properties of large eddy
simulation (LES) equations obtained via the approximate-inverse approach.
In this comparison, we identify the spatially filtered NS-alpha equations
with a class of generalized LES similarity models. Applying a certain
approximate inverse to this class of LES models restores the Kelvin circulation
theorem for the defiltered velocity and shows that the NS-alpha model describes
the dynamics of the defiltered velocity for this class of generalized LES
similarity models. We also show that the subgrid scale forces in the NS-alpha
model transform covariantly under Galilean transformations and under a change
to a uniformly rotating reference frame. Finally, we discuss in the spectral
formulation how the NS-alpha model retains the local interactions among the
large scales, retains the nonlocal sweeping effects of large scales on small
scales, yet attenuates the local interactions of the small scales amongst
themselves.Comment: 15 pages, no figures, Special LES volume of ERCOFTAC bulletin, to
appear in 200
Energy transfer in isotropic turbulence at low Reynolds numbers
Detailed measurements were made of energy transfer among the scales of motion in incompressible turbulent fields at low Reynolds numbers generated by direct numerical simulation. It was observed that although the transfer resulted from triad interactions that were non-local in k space, the energy always transferred locally. The results are consistent with the notion of non-uniform advection of small weak eddies by larger and stronger ones, similar to transfer processes in the far dissipation range at high Reynolds numbers
Variational Principles for Lagrangian Averaged Fluid Dynamics
The Lagrangian average (LA) of the ideal fluid equations preserves their
transport structure. This transport structure is responsible for the Kelvin
circulation theorem of the LA flow and, hence, for its convection of potential
vorticity and its conservation of helicity.
Lagrangian averaging also preserves the Euler-Poincar\'e (EP) variational
framework that implies the LA fluid equations. This is expressed in the
Lagrangian-averaged Euler-Poincar\'e (LAEP) theorem proven here and illustrated
for the Lagrangian average Euler (LAE) equations.Comment: 23 pages, 3 figure
Incompressible Turbulence as Nonlocal Field Theory
It is well known that incompressible turbulence is nonlocal in real space
because sound speed is infinite in incompressible fluids. The equation in
Fourier space indicates that it is nonlocal in Fourier space as well. Contrast
this with Burgers equation which is local in real space. Note that the sound
speed in Burgers equation is zero. In our presentation we will contrast these
two equations using nonlocal field theory. Energy spectrum and renormalized
parameters will be discussed.Comment: 7 pages; Talk presented in Conference on "Perspectives in Nonlinear
Dynamics (PNLD 2004)" held in Chennai, 200
Large eddy simulation of two-dimensional isotropic turbulence
Large eddy simulation (LES) of forced, homogeneous, isotropic,
two-dimensional (2D) turbulence in the energy transfer subrange is the subject
of this paper. A difficulty specific to this LES and its subgrid scale (SGS)
representation is in that the energy source resides in high wave number modes
excluded in simulations. Therefore, the SGS scheme in this case should assume
the function of the energy source. In addition, the controversial requirements
to ensure direct enstrophy transfer and inverse energy transfer make the
conventional scheme of positive and dissipative eddy viscosity inapplicable to
2D turbulence. It is shown that these requirements can be reconciled by
utilizing a two-parametric viscosity introduced by Kraichnan (1976) that
accounts for the energy and enstrophy exchange between the resolved and subgrid
scale modes in a way consistent with the dynamics of 2D turbulence; it is
negative on large scales, positive on small scales and complies with the basic
conservation laws for energy and enstrophy. Different implementations of the
two-parametric viscosity for LES of 2D turbulence were considered. It was found
that if kept constant, this viscosity results in unstable numerical scheme.
Therefore, another scheme was advanced in which the two-parametric viscosity
depends on the flow field. In addition, to extend simulations beyond the limits
imposed by the finiteness of computational domain, a large scale drag was
introduced. The resulting LES exhibited remarkable and fast convergence to the
solution obtained in the preceding direct numerical simulations (DNS) by
Chekhlov et al. (1994) while the flow parameters were in good agreement with
their DNS counterparts. Also, good agreement with the Kolmogorov theory was
found. This LES could be continued virtually indefinitely. Then, a simplifiedComment: 34 pages plain tex + 18 postscript figures separately, uses auxilary
djnlx.tex fil
Leray and LANS- modeling of turbulent mixing
Mathematical regularisation of the nonlinear terms in the Navier-Stokes
equations provides a systematic approach to deriving subgrid closures for
numerical simulations of turbulent flow. By construction, these subgrid
closures imply existence and uniqueness of strong solutions to the
corresponding modelled system of equations. We will consider the large eddy
interpretation of two such mathematical regularisation principles, i.e., Leray
and LANS regularisation. The Leray principle introduces a {\bfi
smoothed transport velocity} as part of the regularised convective
nonlinearity. The LANS principle extends the Leray formulation in a
natural way in which a {\bfi filtered Kelvin circulation theorem},
incorporating the smoothed transport velocity, is explicitly satisfied. These
regularisation principles give rise to implied subgrid closures which will be
applied in large eddy simulation of turbulent mixing. Comparison with filtered
direct numerical simulation data, and with predictions obtained from popular
dynamic eddy-viscosity modelling, shows that these mathematical regularisation
models are considerably more accurate, at a lower computational cost.Comment: 42 pages, 12 figure
Recommended from our members
Optical measurement of rates of dissipation of temperature variance due to oceanic turbulence
Inhomogeneities in the refractive index induced by temperature fluctuations in turbulent flows have the effect of scattering light in near-forward angles. We have developed a method that extracts the rate of Temperature Variance Dissipation (TVD) and its spectrum from the properties of light scattering and have built an instrument - Optical Turbulence Sensor (OTS) - that implements the method. OTS uses a linear wavefront sensing Hartmann array and allows for nearly instantaneous measurements of temperature variance in turbulent flows. The instrument has been tested in an situ experiment carried out from a drifting vessel at a site off the coast of Newport, Oregon. Here we compare the temperature variance measured by OTS and its spectra with both theoretical predictions and with spectra obtained from a fast thermistor sensor.This paper was published in Optics Express and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/oe/home.cfm. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.Keywords: Wave-front sensing, Turbulenc
Local shell-to-shell energy transfer via nonlocal Interactions in fluid turbulence
In this paper we analytically compute the strength of nonlinear interactions
in a triad, and the energy exchanges between wavenumber shells in
incompressible fluid turbulence. The computation has been done using
first-order perturbative field theory. In three dimension, magnitude of triad
interactions is large for nonlocal triads, and small for local triads. However,
the shell-to-shell energy transfer rate is found to be local and forward. This
result is due to the fact that the nonlocal triads occupy much less Fourier
space volume than the local ones. The analytical results on three-dimensional
shell-to-shell energy transfer match with their numerical counterparts. In
two-dimensional turbulence, the energy transfer rates to the near-by shells are
forward, but to the distant shells are backward; the cumulative effect is an
inverse cascade of energy.Comment: 10 pages, Revtex
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