906 research outputs found
Alternative statistical-mechanical descriptions of decaying two-dimensional turbulence in terms of "patches" and "points"
Numerical and analytical studies of decaying, two-dimensional (2D)
Navier-Stokes (NS) turbulence at high Reynolds numbers are reported. The effort
is to determine computable distinctions between two different formulations of
maximum entropy predictions for the decayed, late-time state. Both formulations
define an entropy through a somewhat ad hoc discretization of vorticity to the
"particles" of which statistical mechanical methods are employed to define an
entropy, before passing to a mean-field limit. In one case, the particles are
delta-function parallel "line" vortices ("points" in two dimensions), and in
the other, they are finite-area, mutually-exclusive convected "patches" of
vorticity which in the limit of zero area become "points." We use
time-dependent, spectral-method direct numerical simulation of the
Navier-Stokes equations to see if initial conditions which should relax to
different late-time states under the two formulations actually do so.Comment: 21 pages, 24 figures: submitted to "Physics of Fluids
Optimal Prandtl number for heat transfer in rotating Rayleigh-Benard convection
Numerical data for the heat transfer as a function of the Prandtl (Pr) and
Rossby (Ro) numbers in turbulent rotating Rayleigh-Benard convection are
presented for Rayleigh number Ra = 10^8. When Ro is fixed the heat transfer
enhancement with respect to the non-rotating value shows a maximum as function
of Pr. This maximum is due to the reduced efficiency of Ekman pumping when Pr
becomes too small or too large. When Pr becomes small, i.e. for large thermal
diffusivity, the heat that is carried by the vertical vortices spreads out in
the middle of the cell, and Ekman pumping thus becomes less efficient. For
higher Pr the thermal boundary layers (BLs) are thinner than the kinetic BLs
and therefore the Ekman vortices do not reach the thermal BL. This means that
the fluid that is sucked into the vertical vortices is colder than for lower Pr
which limits the efficiency of the upwards heat transfer.Comment: 5 pages, 6 figure
DSMC-LBM mapping scheme for rarefied and non-rarefied gas flows
We present the formulation of a kinetic mapping scheme between the Direct
Simulation Monte Carlo (DSMC) and the Lattice Boltzmann Method (LBM) which is
at the basis of the hybrid model used to couple the two methods in view of
efficiently and accurately simulate isothermal flows characterized by variable
rarefaction effects. Owing to the kinetic nature of the LBM, the procedure we
propose ensures to accurately couple DSMC and LBM at a larger Kn number than
usually done in traditional hybrid DSMC-Navier-Stokes equation models. We show
the main steps of the mapping algorithm and illustrate details of the
implementation. Good agreement is found between the moments of the single
particle distribution function as obtained from the mapping scheme and from
independent LBM or DSMC simulations at the grid nodes where the coupling is
imposed. We also show results on the application of the hybrid scheme based on
a simpler mapping scheme for plane Poiseuille flow at finite Kn number.
Potential gains in the computational efficiency assured by the application of
the coupling scheme are estimated for the same flow.Comment: Submitted to Journal of Computational Scienc
Pattern formation of spherical particles in an oscillating flow
We study the self-organization of spherical particles in an oscillating flow
through experiments inside an oscillating box. The interactions between the
particles and the time-averaged (steady streaming) flow lead to the formation
of either one-particle-thick chains or multiple-particle-wide bands, depending
on the oscillatory conditions. Both the chains and the bands are oriented
perpendicular to the direction of oscillation with a regular spacing between
them. For all our experiments, this spacing is only a function of the relative
particle-fluid excursion length normalized by the particle diameter, ,
implying that it is an intrinsic quantity that is established only by the
hydrodynamics. In contrast, the width of the bands depends on both and
the confinement, characterized by the particle coverage fraction . Using
the relation for the chain spacing, we accurately predict the transition from
one-particle-thick chains to wider bands as a function of and .
Our experimental results are complemented with numerical simulations in which
the flow around the particles is fully resolved. These simulations show that
the regular chain spacing arises from the balance between long-range attractive
and short-range repulsive hydrodynamic interactions, caused by the vortices in
the steady streaming flow. We further show that these vortices induce an
additional attractive interaction at very short range when ,
which stabilizes the multiple-particle-wide bands. Finally, we give a
comprehensive overview of the parameter space where we illustrate the different
regions using our experimental data.Comment: 20 pages, 16 figures, 1 table, to be submitted to Physical Review
Regime transitions in stratified shear flows: the link between horizontal and inclined ducts
We present an analytical model that provides the transition curves between
different regimes of stratified shear flows in inclined ducts for high Schmidt
number values. These curves are described by constant values of a generalized
Reynolds number multiplied by the aspect ratio of the duct, showing good
agreement with previous experimental results. The generalized Reynolds number
is obtained by extending to inclined ducts the solution of a one-dimensional
model of a stratified shear flow in a horizontal duct within a regime where
advection is neglected in the momentum equation but included in the density
transport equation
Finite-size effects lead to supercritical bifurcations in turbulent rotating Rayleigh-B\'enard convection
In turbulent thermal convection in cylindrical samples of aspect ratio \Gamma
= D/L (D is the diameter and L the height) the Nusselt number Nu is enhanced
when the sample is rotated about its vertical axis, because of the formation of
Ekman vortices that extract additional fluid out of thermal boundary layers at
the top and bottom. We show from experiments and direct numerical simulations
that the enhancement occurs only above a bifurcation point at a critical
inverse Rossby number 1/\Ro_c, with 1/\Ro_c \propto 1/\Gamma. We present a
Ginzburg-Landau like model that explains the existence of a bifurcation at
finite 1/\Ro_c as a finite-size effect. The model yields the proportionality
between 1/\Ro_c and and is consistent with several other measured
or computed system properties.Comment: 4 pages, 4 figure
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