43 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
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
Effect of Plumes on Measuring the Large Scale Circulation in Turbulent Rayleigh-B\'enard Convection
We studied the properties of the large-scale circulation (LSC) in turbulent
Rayleigh-B\'enard (RB) convection by using results from direct numerical
simulations in which we placed a large number of numerical probes close to the
sidewall. The LSC orientation is determined by either a cosine or a polynomial
fit to the azimuthal temperature or azimuthal vertical velocity profile
measured with the probes. We study the LSC in \Gamma=D/L=1/2 and \Gamma=1
samples, where D is the diameter and L the height. For Pr=6.4 in an aspect
ratio \Gamma=1 sample at and the obtained LSC
orientation is the same, irrespective of whether the data of only 8 or all 64
probes per horizontal plane are considered. In a \Gamma=1/2 sample with
at the influence of plumes on the azimuthal
temperature and azimuthal vertical velocity profiles is stronger. Due to
passing plumes and/or the corner flow the apparent LSC orientation obtained
using a cosine fit can result in a misinterpretation of the character of the
large-scale flow. We introduce the relative LSC strength, which we define as
the ratio between the energy in the first Fourier mode and the energy in all
modes that can be determined from the azimuthal temperature and azimuthal
vertical velocity profiles, to further quantify the large-scale flow. For
we find that this relative LSC strength is significantly lower
in a \Gamma=1/2 sample than in a \Gamma=1 sample, reflecting that the LSC is
much more pronounced in a \Gamma=1 sample than in a \Gamma=1/2 sample. The
determination of the relative LSC strength can be applied directly to available
experimental data to study high Rayleigh number thermal convection and rotating
RB convection.Comment: 12 pages, 15 figure
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
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 ()
and 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
Breakdown of the large-scale wind in \Gamma=1/2 rotating Rayleigh-B\'enard flow
Experiments and simulations of rotating Rayleigh-B\'enard convection in
cylindrical samples have revealed an increase in heat transport with increasing
rotation rate. This heat transport enhancement is intimately related to a
transition in the turbulent flow structure from a regime dominated by a
large-scale circulation (LSC), consisting of a single convection roll, at no or
weak rotation to a regime dominated by vertically-aligned vortices at strong
rotation. For a sample with an aspect ratio \Gamma = D/L = 1 (D is the sample
diameter and L its height) the transition between the two regimes is indicated
by a strong decrease in the LSC strength. In contrast, for \Gamma = 1/2 Weiss
and Ahlers [J. Fluid Mech. {\bf{688}}, 461 (2011)] revealed the presence of a
LSC-like sidewall temperature signature beyond the critical rotation rate. They
suggested that this might be due to the formation of a two-vortex state, in
which one vortex extends vertically from the bottom into the sample interior
and brings up warm fluid, while another vortex brings down cold fluid from the
top; this flow field would yield a sidewall temperature signature similar to
that of the LSC. Here we show by direct numerical simulations for \Gamma= 1/2
and parameters that allow direct comparison with experiment that the spatial
organization of the vertically-aligned vortical structures in the convection
cell do indeed yield (for the time average) a sinusoidal variation of the
temperature near the sidewall, as found in the experiment. This is also the
essential and non-trivial difference with the \Gamma=1 sample, where the
vertically-aligned vortices are distributed randomly.Comment: 10 pages, 6 figure