684 research outputs found
On the damped oscillations of an elastic quasi-circular membrane in a two-dimensional incompressible fluid
We propose a procedure - partly analytical and partly numerical - to find the
frequency and the damping rate of the small-amplitude oscillations of a
massless elastic capsule immersed in a two-dimensional viscous incompressible
fluid. The unsteady Stokes equations for the stream function are decomposed
onto normal modes for the angular and temporal variables, leading to a
fourth-order linear ordinary differential equation in the radial variable. The
forcing terms are dictated by the properties of the membrane, and result into
jump conditions at the interface between the internal and external media. The
equation can be solved numerically, and an excellent agreement is found with a
fully-computational approach we developed in parallel. Comparisons are also
shown with the results available in the scientific literature for drops, and a
model based on the concept of embarked fluid is presented, which allows for a
good representation of the results and a consistent interpretation of the
underlying physics.Comment: in press on JF
Kazantsev dynamo in turbulent compressible flows
We consider the kinematic fluctuation dynamo problem in a flow that is
random, white-in-time, with both solenoidal and potential components. This
model is a generalization of the well-studied Kazantsev model. If both the
solenoidal and potential parts have the same scaling exponent, then, as the
compressibility of the flow increases, the growth rate decreases but remains
positive. If the scaling exponents for the solenoidal and potential parts
differ, in particular if they correspond to typical Kolmogorov and Burgers
values, we again find that an increase in compressibility slows down the growth
rate but does not turn it off. The slow down is, however, weaker and the
critical magnetic Reynolds number is lower than when both the solenoidal and
potential components display the Kolmogorov scaling. Intriguingly, we find that
there exist cases, when the potential part is smoother than the solenoidal
part, for which an increase in compressibility increases the growth rate. We
also find that the critical value of the scaling exponent above which a dynamo
is seen is unity irrespective of the compressibility. Finally, we realize that
the dimension is special, since for all other values of the
critical exponent is higher and depends on the compressibility.Comment: 12 pages, 6 figure
Optimal transient growth in an incompressible flow past a backward-slanted step
With the aim of providing a first step in the quest for a reduction of the
aerodynamic drag on the rear-end of a car, we study the phenomena of separation
and reattachment of an incompressible flow focusing on a specific aerodynamic
geometry, namely a backward-slanted step at 25 degrees of inclination. The
ensuing recirculation bubble provides the basis for an analytical and numerical
investigation of streamwise-streak generation, lift-up effect, and
turbulent-wake and Kelvin-Helmholtz instabilities. A linear stability analysis
is performed, and an optimal control problem with a steady volumic forcing is
tackled by means of variational formulation, adjoint method, penalization
scheme and orthogonalization algorithm. Dealing with the transient growth of
spanwise-periodic perturbations and inspired by the need of
physically-realizable disturbances, we finally provide a procedure attaining a
kinetic-energy maximal gain of the order of one million with respect to the
power introduced by the external forcing.Comment: 17 figure
Renormalized transport of inertial particles in surface flows
Surface transport of inertial particles is investigated by means of the
perturbative approach, introduced by Maxey (J. Fluid Mech. 174, 441 (1987)),
which is valid in the case the deflections induced on the particle trajectories
by the fluid flow can be considered small. We consider a class of compressible
random velocity fields, in which the effect of recirculations is modelled by an
oscillatory component in the Eulerian time correlation profile. The main issue
we address here is whether fluid velocity fluctuations, in particular the
effect of recirculation, may produce nontrivial corrections to the streaming
particle velocity. Our result is that a small (large) degree of recirculation
is associated with a decrease (increase) of streaming with respect to a
quiescent fluid. The presence of this effect is confirmed numerically, away
from the perturbative limit. Our approach also allows us to calculate the
explicit expression for the eddy diffusivity, and to compare the efficiency of
diffusive and ballistic transport.Comment: 18 pages, 13 figures, submitted to JF
Does multifractal theory of turbulence have logarithms in the scaling relations?
The multifractal theory of turbulence uses a saddle-point evaluation in
determining the power-law behaviour of structure functions. Without suitable
precautions, this could lead to the presence of logarithmic corrections,
thereby violating known exact relations such as the four-fifths law. Using the
theory of large deviations applied to the random multiplicative model of
turbulence and calculating subdominant terms, we explain here why such
corrections cannot be present.Comment: 7 pages, 1 figur
Point-source inertial particle dispersion
The dispersion of inertial particles continuously emitted from a point source
is analytically investigated in the limit of small inertia. Our focus is on the
evolution equation of the particle joint probability density function p(x,v,t),
x and v being the particle position and velocity, respectively. For finite
inertia, position and velocity variables are coupled, with the result that
p(x,v,t) can be determined by solving a partial differential equation in a
2d-dimensional space, d being the physical-space dimensionality. For small
inertia, (x,v)-variables decouple and the determination of p(x,v,t) is reduced
to solve a system of two standard forced advection-diffusion equations in the
space variable x. The latter equations are derived here from first principles,
i.e. from the well-known Lagrangian evolution equations for position and
particle velocity.Comment: 10 pages, submitted to JF
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