914 research outputs found

### Dynamics of automatic stations' descent in planetary atmospheres as means of measurement data control

Automatic stations descent in planetary atmospheres as means of measurement data contro

### Constraints on scalar diffusion anomaly in three-dimensional flows having bounded velocity gradients

This study is concerned with the decay behaviour of a passive scalar $\theta$
in three-dimensional flows having bounded velocity gradients. Given an
initially smooth scalar distribution, the decay rate $d/dt$ of the
scalar variance $$ is found to be bounded in terms of controlled
physical parameters. Furthermore, in the zero diffusivity limit, $\kappa\to0$,
this rate vanishes as $\kappa^{\alpha_0}$ if there exists an $\alpha_0\in(0,1]$
independent of $\kappa$ such that $<\infty$ for
$\alpha\le\alpha_0$. This condition is satisfied if in the limit $\kappa\to0$,
the variance spectrum $\Theta(k)$ remains steeper than $k^{-1}$ for large wave
numbers $k$. When no such positive $\alpha_0$ exists, the scalar field may be
said to become virtually singular. A plausible scenario consistent with
Batchelor's theory is that $\Theta(k)$ becomes increasingly shallower for
smaller $\kappa$, approaching the Batchelor scaling $k^{-1}$ in the limit
$\kappa\to0$. For this classical case, the decay rate also vanishes, albeit
more slowly -- like $(\ln P_r)^{-1}$, where $P_r$ is the Prandtl or Schmidt
number. Hence, diffusion anomaly is ruled out for a broad range of scalar
distribution, including power-law spectra no shallower than $k^{-1}$. The
implication is that in order to have a $\kappa$-independent and non-vanishing
decay rate, the variance at small scales must necessarily be greater than that
allowed by the Batchelor spectrum. These results are discussed in the light of
existing literature on the asymptotic exponential decay $\sim
e^{-\gamma t}$, where $\gamma>0$ is independent of $\kappa$.Comment: 6-7 journal pages, no figures. accepted for publication by Phys.
Fluid

### Comparative experimental study of local mixing of active and passive scalars in turbulent thermal convection

We investigate experimentally the statistical properties of active and
passive scalar fields in turbulent Rayleigh-B\'{e}nard convection in water, at
$Ra\sim10^{10}$. Both the local concentration of fluorescence dye and the local
temperature are measured near the sidewall of a rectangular cell. It is found
that, although they are advected by the same turbulent flow, the two scalars
distribute differently. This difference is twofold, i.e. both the quantities
themselves and their small-scale increments have different distributions. Our
results show that there is a certain buoyant scale based on time domain, i.e.
the Bolgiano time scale $t_B$, above which buoyancy effects are significant.
Above $t_B$, temperature is active and is found to be more intermittent than
concentration, which is passive. This suggests that the active scalar possesses
a higher level of intermittency in turbulent thermal convection. It is further
found that the mixing of both scalar fields are isotropic for scales larger
than $t_B$ even though buoyancy acts on the fluid in the vertical direction.
Below $t_B$, temperature is passive and is found to be more anisotropic than
concentration. But this higher degree of anisotropy is attributed to the higher
diffusivity of temperature over that of concentration. From the simultaneous
measurements of temperature and concentration, it is shown that two scalars
have similar autocorrelation functions and there is a strong and positive
correlation between them.Comment: 13 pages and 12 figure

### Passive Scalar Structures in Supersonic Turbulence

We conduct a systematic numerical study of passive scalar structures in
supersonic turbulent flows. We find that the degree of intermittency in the
scalar structures increases only slightly as the flow changes from transonic to
highly supersonic, while the velocity structures become significantly more
intermittent. This difference is due to the absence of shock-like
discontinuities in the scalar field. The structure functions of the scalar
field are well described by the intermittency model of She and L\'{e}v\^{e}que
[Phys. Rev. Lett. 72, 336 (1994)], and the most intense scalar structures are
found to be sheet-like at all Mach numbers.Comment: 4 pages, 3 figures, to appear in PR

### Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations

We report results on rotating stratified turbulence in the absence of
forcing, with large-scale isotropic initial conditions, using direct numerical
simulations computed on grids of up to 4096^3 points. The Reynolds and Froude
numbers are respectively equal to Re=5.4 x 10^4 and Fr=0.0242. The ratio of the
Brunt-V\"ais\"al\"a to the inertial wave frequency, N/f, is taken to be equal
to 4.95, a choice appropriate to model the dynamics of the southern abyssal
ocean at mid latitudes. This gives a global buoyancy Reynolds number
R_B=ReFr^2=32, a value sufficient for some isotropy to be recovered in the
small scales beyond the Ozmidov scale, but still moderate enough that the
intermediate scales where waves are prevalent are well resolved. We concentrate
on the large-scale dynamics, for which we find a spectrum compatible with the
Bolgiano-Obukhov scaling, and confirm that the Froude number based on a typical
vertical length scale is of order unity, with strong gradients in the vertical.
Two characteristic scales emerge from this computation, and are identified from
sharp variations in the spectral distribution of either total energy or
helicity. A spectral break is also observed at a scale at which the partition
of energy between the kinetic and potential modes changes abruptly, and beyond
which a Kolmogorov-like spectrum recovers. Large slanted layers are ubiquitous
in the flow in the velocity and temperature fields, with local overturning
events indicated by small Richardson numbers, and a small large-scale
enhancement of energy directly attributable to the effect of rotation is also
observed.Comment: 19 pages, 9 figures (including compound figures

### Diffusion of passive scalar in a finite-scale random flow

We consider a solvable model of the decay of scalar variance in a
single-scale random velocity field. We show that if there is a separation
between the flow scale k_flow^{-1} and the box size k_box^{-1}, the decay rate
lambda ~ (k_box/k_flow)^2 is determined by the turbulent diffusion of the
box-scale mode. Exponential decay at the rate lambda is preceded by a transient
powerlike decay (the total scalar variance ~ t^{-5/2} if the Corrsin invariant
is zero, t^{-3/2} otherwise) that lasts a time t~1/\lambda. Spectra are sharply
peaked at k=k_box. The box-scale peak acts as a slowly decaying source to a
secondary peak at the flow scale. The variance spectrum at scales intermediate
between the two peaks (k_box0). The mixing
of the flow-scale modes by the random flow produces, for the case of large
Peclet number, a k^{-1+delta} spectrum at k>>k_flow, where delta ~ lambda is a
small correction. Our solution thus elucidates the spectral make up of the
``strange mode,'' combining small-scale structure and a decay law set by the
largest scales.Comment: revtex4, 8 pages, 4 figures; final published versio

### Kraichnan model of passive scalar advection

A simple model of a passive scalar quantity advected by a Gaussian
non-solenoidal ("compressible") velocity field is considered. Large order
asymptotes of quantum-field expansions are investigated by instanton approach.
The existence of finite convergence radius of the series is proved, a position
and a type of the corresponding singularity of the series in the regularization
parameter are determined. Anomalous exponents of the main contributions to the
structural functions are resummed using new information about the series
convergence and two known orders of the expansion.Comment: 21 page

### Lagrangian statistics in forced two-dimensional turbulence

We report on simulations of two-dimensional turbulence in the inverse energy
cascade regime. Focusing on the statistics of Lagrangian tracer particles,
scaling behavior of the probability density functions of velocity fluctuations
is investigated. The results are compared to the three-dimensional case. In
particular an analysis in terms of compensated cumulants reveals the transition
from a strong non-Gaussian behavior with large tails to Gaussianity. The
reported computation of correlation functions for the acceleration components
sheds light on the underlying dynamics of the tracer particles.Comment: 8 figures, 1 tabl

### From non-Brownian Functionals to a Fractional Schr\"odinger Equation

We derive backward and forward fractional Schr\"odinger type of equations for
the distribution of functionals of the path of a particle undergoing anomalous
diffusion. Fractional substantial derivatives introduced by Friedrich and
co-workers [PRL {\bf 96}, 230601 (2006)] provide the correct fractional
framework for the problem at hand. In the limit of normal diffusion we recover
the Feynman-Kac treatment of Brownian functionals. For applications, we
calculate the distribution of occupation times in half space and show how
statistics of anomalous functionals is related to weak ergodicity breaking.Comment: 5 page

### Fractal dimension crossovers in turbulent passive scalar signals

The fractal dimension $\delta_g^{(1)}$ of turbulent passive scalar signals is
calculated from the fluid dynamical equation. $\delta_g^{(1)}$ depends on the
scale. For small Prandtl (or Schmidt) number $Pr<10^{-2}$ one gets two ranges,
$\delta_g^{(1)}=1$ for small scale r and $\delta_g^{(1)}$=5/3 for large r, both
as expected. But for large $Pr> 1$ one gets a third, intermediate range in
which the signal is extremely wrinkled and has $\delta_g^{(1)}=2$. In that
range the passive scalar structure function $D_\theta(r)$ has a plateau. We
calculate the $Pr$-dependence of the crossovers. Comparison with a numerical
reduced wave vector set calculation gives good agreement with our predictions.Comment: 7 pages, Revtex, 3 figures (postscript file on request

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