365 research outputs found

### Disentangle plume-induced anisotropy in the velocity field in buoyancy-driven turbulence

We present a method of disentangling the anisotropies produced by the cliff
structures in turbulent velocity field and test it in the system of turbulent
Rayleigh-B\'{e}nard (RB) convection. It is found that in the RB system the
cliff structures in the velocity field are generated by thermal plumes. These
cliff structures induce asymmetry in the velocity increments, which leads us to
consider the plus and minus velocity structure functions (VSF). The plus
velocity increments exclude cliff structures, while the minus ones include
them. Our results show that the scaling exponents of the plus VSFs are in
excellent agreement with those predicted for homogeneous and isotropic
turbulence (HIT), whereas those of the minus VSFs exhibit significant
deviations from HIT expectations in places where thermal plumes abound. These
results demonstrate that plus and minus VSFs can be used to quantitatively
study the effect of cliff structures in the velocity field and to effectively
disentangle the associated anisotropies caused by these structures.Comment: 10 pages, 5 figure

### Effect of Prandtl number on heat transport enhancement in Rayleigh-B\'enard convection under geometrical confinement

We study, using direct numerical simulations, the effect of geometrical
confinement on heat transport and flow structure in Rayleigh-B\'enard
convection in fluids with different Prandtl numbers. Our simulations span over
two decades of Prandtl number $Pr$, $0.1 \leq Pr \leq 40$, with the Rayleigh
number $Ra$ fixed at $10^8$. The width-to-height aspect ratio $\Gamma$ spans
between $0.025$ and $0.25$ while the length-to-height aspect ratio is fixed at
one. We first find that for $Pr \geq 0.5$, geometrical confinement can lead to
a significant enhancement in heat transport as characterized by the Nusselt
number $Nu$. For those cases, $Nu$ is maximal at a certain $\Gamma =
\Gamma_{opt}$. It is found that $\Gamma_{opt}$ exhibits a power-law relation
with $Pr$ as $\Gamma_{opt}=0.11Pr^{-0.06}$, and the maximal relative
enhancement generally increases with $Pr$ over the explored parameter range. As
opposed to the situation of $Pr \geq 0.5$, confinement-induced enhancement in
$Nu$ is not realized for smaller values of $Pr$, such as $0.1$ and $0.2$. The
$Pr$ dependence of the heat transport enhancement can be understood in its
relation to the coverage area of the thermal plumes over the thermal boundary
layer (BL) where larger coverage is observed for larger $Pr$ due to a smaller
thermal diffusivity. We further show that $\Gamma_{opt}$ is closely related to
the crossing of thermal and momentum BLs, and find that $Nu$ declines sharply
when the thickness ratio of the thermal and momentum BLs exceeds a certain
value of about one. In addition, through examining the temporally averaged flow
fields and 2D mode decomposition, it is found that for smaller $Pr$ the
large-scale circulation is robust against the geometrical confinement of the
convection cell.Comment: 25 pages, 11 figures, and 1 table in main tex

### Measured Instantaneous Viscous Boundary Layer in Turbulent Rayleigh-B\'{e}nard Convection

We report measurements of the instantaneous viscous boundary layer (BL)
thickness $\delta_v(t)$ in turbulent Rayleigh-B\'{e}nard convection. It is
found that $\delta_v(t)$ obtained from the measured instantaneous
two-dimensional velocity field exhibits intermittent fluctuations. For small
values, $\delta_v(t)$ obeys a lognormal distribution, whereas for large values
the distribution of $\delta_v(t)$ exhibits an exponential tail. The variation
of $\delta_v(t)$ with time is found to be driven by the fluctuations of the
large-scale mean flow velocity and the local horizontal velocities close to the
plate can be used as an instant measure of this variation. It is further found
that in the present parameter range of the experiment the mean velocity profile
measured in the laboratory frame can be brought into coincidence with the
theoretical Prandtl-Blasius laminar BL profile, if it is resampled relative to
the time-dependent frame of $\delta_v(t)$.Comment: 5 pages, 5 figures, Accepted for publication in Phys. Rev. Let

### Horizontal Structures of Velocity and Temperature Boundary Layers in 2D Numerical Turbulent Rayleigh-B\'{e}nard Convection

We investigate the structures of the near-plate velocity and temperature
profiles at different horizontal positions along the conducting bottom (and
top) plate of a Rayleigh-B\'{e}nard convection cell, using two-dimensional (2D)
numerical data obtained at the Rayleigh number Ra=10^8 and the Prandtl number
Pr=4.4 of an Oberbeck-Boussinesq flow with constant material parameters. The
results show that most of the time, and for both velocity and temperature, the
instantaneous profiles scaled by the dynamical frame method [Q. Zhou and K.-Q.
Xia, Phys. Rev. Lett. 104, 104301 (2010) agree well with the classical
Prandtl-Blasius laminar boundary layer (BL) profiles. Therefore, when averaging
in the dynamical reference frames, which fluctuate with the respective
instantaneous kinematic and thermal BL thicknesses, the obtained mean velocity
and temperature profiles are also of Prandtl-Blasius type for nearly all
horizontal positions. We further show that in certain situations the
traditional definitions based on the time-averaged profiles can lead to
unphysical BL thicknesses, while the dynamical method also in such cases can
provide a well-defined BL thickness for both the kinematic and the thermal BLs.Comment: 16 pages, 16 figure

### Effects of polymer additives in the bulk of turbulent thermal convection

We present experimental evidence that a minute amount of polymer additives
can significantly enhance heat transport in the bulk region of turbulent
thermal convection. The effects of polymer additives are found to be the
\textit{suppression} of turbulent background fluctuations that give rise to
incoherent heat fluxes that make no net contribution to heat transport, and at
the same time to \textit{increase} the coherency of temperature and velocity
fields. The suppression of small-scale turbulent fluctuations leads to more
coherent thermal plumes that result in the heat transport enhancement. The fact
that polymer additives can increase the coherency of thermal plumes is
supported by the measurements of a number of local quantities, such as the
extracted plume amplitude and width, the velocity autocorrelation functions and
the velocity-temperature cross-correlation coefficient. The results from local
measurements also suggest the existence of a threshold value for the polymer
concentration, only above which can significant modification of the plume
coherent properties and enhancement of the local heat flux be observed.
Estimation of the plume emission rate suggests that the second effect of
polymer additives is to stabilize the thermal boundary layers.Comment: 8 figures, 11 page

### Prandtl-Blasius temperature and velocity boundary layer profiles in turbulent Rayleigh-B\'{e}nard convection

The shape of velocity and temperature profiles near the horizontal conducting
plates in turbulent Rayleigh-B\'{e}nard convection are studied numerically and
experimentally over the Rayleigh number range $10^8\lesssim
Ra\lesssim3\times10^{11}$ and the Prandtl number range $0.7\lesssim
Pr\lesssim5.4$. The results show that both the temperature and velocity
profiles well agree with the classical Prandtl-Blasius laminar boundary-layer
profiles, if they are re-sampled in the respective dynamical reference frames
that fluctuate with the instantaneous thermal and velocity boundary-layer
thicknesses.Comment: 10 pages, 6 figure

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