705 research outputs found
Scaling and the prediction of energy spectra in decaying hydrodynamic turbulence
Few rigorous results are derived for fully developed turbulence. By applying
the scaling properties of the Navier-Stokes equation we have derived a relation
for the energy spectrum valid for unforced or decaying isotropic turbulence. We
find the existence of a scaling function . The energy spectrum can at any
time by a suitable rescaling be mapped onto this function. This indicates that
the initial (primordial) energy spectrum is in principle retained in the energy
spectrum observed at any later time, and the principle of permanence of large
eddies is derived. The result can be seen as a restoration of the determinism
of the Navier-Stokes equation in the mean. We compare our results with a
windtunnel experiment and find good agreement.Comment: 4 pages, 1 figur
Spectral imbalance and the normalized dissipation rate of turbulence
The normalized turbulent dissipation rate is studied in decaying
and forced turbulence by direct numerical simulations, large-eddy simulations,
and closure calculations. A large difference in the values of is
observed for the two types of turbulence. This difference is found at moderate
Reynolds number, and it is shown that it persists at high Reynolds number,
where the value of becomes independent of the Reynolds number, but
is still not unique. This difference can be explained by the influence of the
nonlinear cascade time that introduces a spectral disequilibrium for
statistically nonstationary turbulence. Phenomenological analysis yields simple
analytical models that satisfactorily reproduce the numerical results. These
simple spectral models also reproduce and explain the increase of
at low Reynolds number that is observed in the simulations
Helicity cascades in rotating turbulence
The effect of helicity (velocity-vorticity correlations) is studied in direct
numerical simulations of rotating turbulence down to Rossby numbers of 0.02.
The results suggest that the presence of net helicity plays an important role
in the dynamics of the flow. In particular, at small Rossby number, the energy
cascades to large scales, as expected, but helicity then can dominate the
cascade to small scales. A phenomenological interpretation in terms of a direct
cascade of helicity slowed down by wave-eddy interactions leads to the
prediction of new inertial indices for the small-scale energy and helicity
spectra.Comment: 7 pages, 8 figure
The imprint of large-scale flows on turbulence
We investigate the locality of interactions in hydrodynamic turbulence using
data from a direct numerical simulation on a grid of 1024^3 points; the flow is
forced with the Taylor-Green vortex. An inertial range for the energy is
obtained in which the flux is constant and the spectrum follows an approximate
Kolmogorov law. Nonlinear triadic interactions are dominated by their non-local
components, involving widely separated scales. The resulting nonlinear transfer
itself is local at each scale but the step in the energy cascade is independent
of that scale and directly related to the integral scale of the flow.
Interactions with large scales represent 20% of the total energy flux. Possible
explanations for the deviation from self-similar models, the link between these
findings and intermittency, and their consequences for modeling of turbulent
flows are briefly discussed
Non-local interactions in hydrodynamic turbulence at high Reynolds numbers: the slow emergence of scaling laws
We analyze the data stemming from a forced incompressible hydrodynamic
simulation on a grid of 2048^3 regularly spaced points, with a Taylor Reynolds
number of Re~1300. The forcing is given by the Taylor-Green flow, which shares
similarities with the flow in several laboratory experiments, and the
computation is run for ten turnover times in the turbulent steady state. At
this Reynolds number the anisotropic large scale flow pattern, the inertial
range, the bottleneck, and the dissipative range are clearly visible, thus
providing a good test case for the study of turbulence as it appears in nature.
Triadic interactions, the locality of energy fluxes, and structure functions of
the velocity increments are computed. A comparison with runs at lower Reynolds
numbers is performed, and shows the emergence of scaling laws for the relative
amplitude of local and non-local interactions in spectral space. The scalings
of the Kolmogorov constant, and of skewness and flatness of velocity
increments, performed as well and are consistent with previous experimental
results. Furthermore, the accumulation of energy in the small-scales associated
with the bottleneck seems to occur on a span of wavenumbers that is independent
of the Reynolds number, possibly ruling out an inertial range explanation for
it. Finally, intermittency exponents seem to depart from standard models at
high Re, leaving the interpretation of intermittency an open problem.Comment: 8 pages, 8 figure
Anisotropy and non-universality in scaling laws of the large scale energy spectrum in rotating turbulence
Rapidly rotating turbulent flow is characterized by the emergence of columnar
structures that are representative of quasi-two dimensional behavior of the
flow. It is known that when energy is injected into the fluid at an
intermediate scale , it cascades towards smaller as well as larger scales.
In this paper we analyze the flow in the \textit{inverse cascade} range at a
small but fixed Rossby number, {}. Several
{numerical simulations with} helical and non-helical forcing functions are
considered in periodic boxes with unit aspect ratio. In order to resolve the
inverse cascade range with {reasonably} large Reynolds number, the analysis is
based on large eddy simulations which include the effect of helicity on eddy
viscosity and eddy noise. Thus, we model the small scales and resolve
explicitly the large scales. We show that the large-scale energy spectrum has
at least two solutions: one that is consistent with
Kolmogorov-Kraichnan-Batchelor-Leith phenomenology for the inverse cascade of
energy in two-dimensional (2D) turbulence with a {}
scaling, and the other that corresponds to a steeper {}
spectrum in which the three-dimensional (3D) modes release a substantial
fraction of their energy per unit time to 2D modes. {The spectrum that} emerges
{depends on} the anisotropy of the forcing function{,} the former solution
prevailing for forcings in which more energy is injected into 2D modes while
the latter prevails for isotropic forcing. {In the case of anisotropic forcing,
whence the energy} goes from the 2D to the 3D modes at low wavenumbers,
large-scale shear is created resulting in another time scale ,
associated with shear, {thereby producing} a spectrum for the
{total energy} with the 2D modes still following a {}
scaling
Lagrangian filtered density function for LES-based stochastic modelling of turbulent dispersed flows
The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one
of the most promising and viable numerical tools to study turbulent dispersed
flows when the computational cost of Direct Numerical Simulation (DNS) becomes
too expensive. The applicability of this approach is however limited if the
effects of the Sub-Grid Scales (SGS) of the flow on particle dynamics are
neglected. In this paper, we propose to take these effects into account by
means of a Lagrangian stochastic SGS model for the equations of particle
motion. The model extends to particle-laden flows the velocity-filtered density
function method originally developed for reactive flows. The underlying
filtered density function is simulated through a Lagrangian Monte Carlo
procedure that solves for a set of Stochastic Differential Equations (SDEs)
along individual particle trajectories. The resulting model is tested for the
reference case of turbulent channel flow, using a hybrid algorithm in which the
fluid velocity field is provided by LES and then used to advance the SDEs in
time. The model consistency is assessed in the limit of particles with zero
inertia, when "duplicate fields" are available from both the Eulerian LES and
the Lagrangian tracking. Tests with inertial particles were performed to
examine the capability of the model to capture particle preferential
concentration and near-wall segregation. Upon comparison with DNS-based
statistics, our results show improved accuracy and considerably reduced errors
with respect to the case in which no SGS model is used in the equations of
particle motion
Coriolis force in Geophysics: an elementary introduction and examples
We show how Geophysics may illustrate and thus improve classical Mechanics
lectures concerning the study of Coriolis force effects. We are then interested
in atmospheric as well as oceanic phenomena we are familiar with, and are for
that reason of pedagogical and practical interest. Our aim is to model them in
a very simple way to bring out the physical phenomena that are involved.Comment: Accepted for publication in European Journal of Physic
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