788 research outputs found

### 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

### Heat transport and flow structure in rotating Rayleigh-B\'enard convection

Here we summarize the results from our direct numerical simulations (DNS) and
experimental measurements on rotating Rayleigh-B\'enard (RB) convection. Our
experiments and simulations are performed in cylindrical samples with an aspect
ratio \Gamma varying from 1/2 to 2. Here \Gamma=D/L, where D and L are the
diameter and height of the sample, respectively. When the rotation rate is
increased, while a fixed temperature difference between the hot bottom and cold
top plate is maintained, a sharp increase in the heat transfer is observed
before the heat transfer drops drastically at stronger rotation rates. Here we
focus on the question of how the heat transfer enhancement with respect to the
non-rotating case depends on the Rayleigh number Ra, the Prandtl number Pr, and
the rotation rate, indicated by the Rossby number Ro. Special attention will be
given to the influence of the aspect ratio on the rotation rate that is
required to get heat transport enhancement. In addition, we will discuss the
relation between the heat transfer and the large scale flow structures that are
formed in the different regimes of rotating RB convection and how the different
regimes can be identified in experiments and simulations.Comment: 12 pages, 10 figure

### 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

### 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

### 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 $1/\Gamma$ and is consistent with several other measured
or computed system properties.Comment: 4 pages, 4 figure

### The role of Stewartson and Ekman layers in turbulent rotating Rayleigh-B\'enard convection

When the classical Rayleigh-B\'enard (RB) system is rotated about its
vertical axis roughly three regimes can be identified. In regime I (weak
rotation) the large scale circulation (LSC) is the dominant feature of the
flow. In regime II (moderate rotation) the LSC is replaced by vertically
aligned vortices. Regime III (strong rotation) is characterized by suppression
of the vertical velocity fluctuations. Using results from experiments and
direct numerical simulations of RB convection for a cell with a
diameter-to-height aspect ratio equal to one at $Ra \sim 10^8-10^9$ ($Pr=4-6$)
and $0 \lesssim 1/Ro \lesssim 25$ we identified the characteristics of the
azimuthal temperature profiles at the sidewall in the different regimes. In
regime I the azimuthal wall temperature profile shows a cosine shape and a
vertical temperature gradient due to plumes that travel with the LSC close to
the sidewall. In regime II and III this cosine profile disappears, but the
vertical wall temperature gradient is still observed. It turns out that the
vertical wall temperature gradient in regimes II and III has a different origin
than that observed in regime I. It is caused by boundary layer dynamics
characteristic for rotating flows, which drives a secondary flow that
transports hot fluid up the sidewall in the lower part of the container and
cold fluid downwards along the sidewall in the top part.Comment: 21 pages, 12 figure

### Clustering of vertically constrained passive particles in homogeneous, isotropic turbulence

We analyze the dynamics of small particles vertically confined, by means of a
linear restoring force, to move within a horizontal fluid slab in a
three-dimensional (3D) homogeneous isotropic turbulent velocity field. The
model that we introduce and study is possibly the simplest description for the
dynamics of small aquatic organisms that, due to swimming, active regulation of
their buoyancy, or any other mechanism, maintain themselves in a shallow
horizontal layer below the free surface of oceans or lakes. By varying the
strength of the restoring force, we are able to control the thickness of the
fluid slab in which the particles can move. This allows us to analyze the
statistical features of the system over a wide range of conditions going from a
fully 3D incompressible flow (corresponding to the case of no confinement) to
the extremely confined case corresponding to a two-dimensional slice. The
background 3D turbulent velocity field is evolved by means of fully resolved
direct numerical simulations. Whenever some level of vertical confinement is
present, the particle trajectories deviate from that of fluid tracers and the
particles experience an effectively compressible velocity field. Here, we have
quantified the compressibility, the preferential concentration of the
particles, and the correlation dimension by changing the strength of the
restoring force. The main result is that there exists a particular value of the
force constant, corresponding to a mean slab depth approximately equal to a few
times the Kolmogorov length scale, that maximizes the clustering of the
particles

### 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

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