1,106 research outputs found

### Temperature spectra in shear flow and thermal convection

We show that the P_u(\om) \propto \om^{-7/3} shear velocity power spectrum
gives rise to a P_\Theta (\om ) \propto \om^{-4/3} power spectrum for a
passively advected scalar, as measured in experiment [K. Sreenivasan, Proc. R.
Soc. London A {\bf 434}, 165 (1991)]. Applying our argument to high Rayleigh
number Rayleigh Benard flow, we can account for the measured scaling exponents
equally well as the Bolgiano Obukhov theory (BO59). Yet, of the two
explanations, only the shear approach might be able to explain why no classical
scaling range is seen in between the shear (or BO59) range and the viscous
subrange of the experimental temperature spectrum [I. Procaccia {\it et al.},
Phys. Rev. A {\bf 44}, 8091 (1991)].Comment: 9 pages, 1 figure, 1 tabl

### On geometry effects in Rayleigh-Benard convection

Various recent experiments hint at a geometry dependence of scaling relations
in Rayleigh-B\'enard convection. Aspect ratio and shape dependences have been
found. In this paper a mechanism is offered which can account for such
dependences. It is based on Prandtl's theory for laminar boundary layers and on
the conservation of volume flux of the large scale wind. The mechanism implies
the possibility of different thicknesses of the kinetic boundary layers at the
sidewalls and the top/bottom plates, just as experimentally found by Qiu and
Xia (Phys. Rev. E58, 486 (1998)), and also different $Ra$-scaling of the wind
measured over the plates and at the sidewalls. In the second part of the paper
a scaling argument for the velocity and temperature fluctuations in the bulk is
developeVarious recent experiments hint at a geometry dependence of scaling
relations in Rayleigh-Benard convection. Aspect ratio and shape dependences
have been found. In this paper a mechanism is offered which can account for
such dependences. It is based on Prandtl's theory for laminar boundary layers
and on the conservation of volume flux of the large scale wind. The mechanism
implies the possibility of different thicknesses of the kinetic boundary layers
at the sidewalls and the top/bottom plates, just as experimentally found by Qiu
and Xia (Phys. Rev. E58, 486 (1998)), and also different $Ra$-scaling of the
wind measured over the plates and at the sidewalls. In the second part of the
paper a scaling argument for the velocity and temperature fluctuations in the
bulk is developeComment: 4 pages, 1 figur

### Scaling in thermal convection: A unifying theory

A systematic theory for the scaling of the Nusselt number $Nu$ and of the
Reynolds number $Re$ in strong Rayleigh-Benard convection is suggested and
shown to be compatible with recent experiments. It assumes a coherent large
scale convection roll (``wind of turbulence'') and is based on the dynamical
equations both in the bulk and in the boundary layers. Several regimes are
identified in the Rayleigh number versus Prandtl number phase space, defined by
whether the boundary layer or the bulk dominates the global kinetic and thermal
dissipation, respectively. The crossover between the regimes is calculated. In
the regime which has most frequently been studied in experiment (Ra smaller
than 10^{11}) the leading terms are $Nu\sim Ra^{1/4}Pr^{1/8}$, $Re \sim
Ra^{1/2} Pr^{-3/4}$ for $Pr < 1$ and $Nu\sim Ra^{1/4}Pr^{-1/12}$, $Re \sim
Ra^{1/2} Pr^{-5/6}$ for $Pr > 1$. In most measurements these laws are modified
by additive corrections from the neighboring regimes so that the impression of
a slightly larger (effective) Nu vs Ra scaling exponent can arise. -- The
presented theory is best summarized in the phase diagram figure 1.Comment: 30 pages, latex, 7 figures, under review at Journal of Fluid Mec

### Scale resolved intermittency in turbulence

The deviations $\delta\zeta_m$ ("intermittency corrections") from classical
("K41") scaling $\zeta_m=m/3$ of the $m^{th}$ moments of the velocity
differences in high Reynolds number turbulence are calculated, extending a
method to approximately solve the Navier-Stokes equation described earlier. We
suggest to introduce the notion of scale resolved intermittency corrections
$\delta\zeta_m(p)$, because we find that these $\delta\zeta_m(p)$ are large in
the viscous subrange, moderate in the nonuniversal stirring subrange but,
surprisingly, extremely small if not zero in the inertial subrange. If ISR
intermittency corrections persisted in experiment up to the large Reynolds
number limit, our calculation would show, that this could be due to the opening
of phase space for larger wave vectors. In the higher order velocity moment
$\langle|u(p)|^m\rangle$ the crossover between inertial and viscous subrange is
$(10\eta m/2)^{-1}$, thus the inertial subrange is {\it smaller} for higher
moments.Comment: 12 pages, Latex, 2 tables, 7 figure

### Why surface nanobubbles live for hours

We present a theoretical model for the experimentally found but
counter-intuitive exceptionally long lifetime of surface nanobubbles. We can
explain why, under normal experimental conditions, surface nanobubbles are
stable for many hours or even up to days rather than the expected microseconds.
The limited gas diffusion through the water in the far field, the cooperative
effect of nanobubble clusters, and the pinned contact line of the nanobubbles
lead to the slow dissolution rate.Comment: 5 pages, 3 figure

### Application of extended self similarity in turbulence

From Navier-Stokes turbulence numerical simulations we show that for the
extended self similarity (ESS) method it is essential to take the third order
structure function taken with the modulus and called $D_3^*(r)$, rather than
the standard third order structure function $D_3(r)$ itself. If done so, we
find ESS towards scales larger than roughly 10 eta, where eta is the Kolmogorov
scale. If $D_3(r)$ is used, there is no ESS. We also analyze ESS within the
Batchelor parametrization of the second and third order longitudinal structure
function and focus on the scaling of the transversal structure function. The
Re-asymptotic inertial range scaling develops only beyond a Taylor-Reynolds
number of about 500.Comment: 12 pages, 7 eps-figures, replaces version from April 11th, 1997;
paper now in press at Phys. Rev.

### Physical mechanisms governing drag reduction in turbulent Taylor-Couette flow with finite-size deformable bubbles

The phenomenon of drag reduction induced by injection of bubbles into a
turbulent carrier fluid has been known for a long time; the governing control
parameters and underlying physics is however not well understood. In this
paper, we use three dimensional numerical simulations to uncover the effect of
deformability of bubbles injected in a turbulent Taylor-Couette flow on the
overall drag experienced by the system. We consider two different Reynolds
numbers for the carrier flow, i.e. $Re_i=5\times 10^3$ and $Re_i=2\times 10^4$;
the deformability of the bubbles is controlled through the Weber number which
is varied in the range $We=0.01 - 2.0$. Our numerical simulations show that
increasing the deformability of bubbles i.e., $We$ leads to an increase in drag
reduction. We look at the different physical effects contributing to drag
reduction and analyse their individual contributions with increasing bubble
deformability. Profiles of local angular velocity flux show that in the
presence of bubbles, turbulence is enhanced near the inner cylinder while
attenuated in the bulk and near the outer cylinder. We connect the increase in
drag reduction to the decrease in dissipation in the wake of highly deformed
bubbles near the inner cylinder

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