2,026 research outputs found
Intersections in genus 3 and the Boussinesq hierarchy
In this note we prove that the enlarged Witten's conjecture is true in the
case of the Boussinesq hierarchy for correlators in genus 3 with descendants
only at one point
The history force on a small particle in a linearly stratified fluid
The hydrodynamic force experienced by a small spherical particle undergoing
an arbitrary time-dependent motion in a density-stratified fluid is
investigated theoretically. The study is carried out under the
Oberbeck-Boussinesq approximation, and in the limit of small Reynolds and small
P\'eclet numbers. The force acting on the particle is obtained by using matched
asymptotic expansions in which the small parameter is given by a/l where a is
the particle radius and l is the stratification length defined by Ardekani &
Stocker (2010), which depends on the Brunt-Vaisala frequency, on the fluid
kinematic viscosity and on the thermal or the concentration diffusivity
(depending on the case considered). The matching procedure used here, which is
based on series expansions of generalized functions, slightly differs from that
generally used in similar problems. In addition to the classical Stokes drag,
it is found the particle experiences a memory force given by two convolution
products, one of which involves, as usual, the particle acceleration and the
other one, the particle velocity. Owing to the stratification, the transient
behaviour of this memory force, in response to an abrupt motion, consists of an
initial fast decrease followed by a damped oscillation with an
angular-frequency corresponding to the Brunt-Vaisala frequency. The
perturbation force eventually tends to a constant which provides us with
correction terms that should be added to the Stokes drag to accurately predict
the settling time of a particle in a diffusive stratified-fluid.Comment: 16 page
Flow organization in non-Oberbeck-Boussinesq Rayleigh-Benard convection in water
Non-Oberbeck-Boussinesq (NOB) effects on the flow organization in
two-dimensional Rayleigh-Benard turbulence are numerically analyzed. The
working fluid is water. We focus on the temperature profiles, the center
temperature, the Nusselt number, and on the analysis of the velocity field.
Several velocity amplitudes (or Reynolds numbers) and several kinetic profiles
are introduced and studied; these together describe the various features of the
rather complex flow organization. The results are presented both as functions
of the Rayleigh number Ra (with Ra up to 10^8) for fixed temperature difference
(Delta) between top and bottom plates and as functions of Delta
("non-Oberbeck-Boussinesqness") for fixed Ra with Delta up to 60 K. All results
are consistent with the available experimental NOB data for the center
temperature Tc and the Nusselt number ratio Nu_{NOB}/Nu_{OB} (the label OB
meaning that the Oberbeck-Boussinesq conditions are valid).
Beyond Ra ~ 10^6 the flow consists of a large diagonal center convection roll
and two smaller rolls in the upper and lower corners. In the NOB case the
center convection roll is still characterized by only one velocity scale.Comment: 31 pages, 22 figure
Local solutions in Sobolev spaces with negative indices for the "good" Boussinesq equation
We study the local well-posedness of the initial-value problem for the
nonlinear "good" Boussinesq equation with data in Sobolev spaces \textit{}
for negative indices of .Comment: Referee comments incorporate
Origin of Lagrangian Intermittency in Drift-Wave Turbulence
The Lagrangian velocity statistics of dissipative drift-wave turbulence are
investigated. For large values of the adiabaticity (or small collisionality),
the probability density function of the Lagrangian acceleration shows
exponential tails, as opposed to the stretched exponential or algebraic tails,
generally observed for the highly intermittent acceleration of Navier-Stokes
turbulence. This exponential distribution is shown to be a robust feature
independent of the Reynolds number. For small adiabaticity, algebraic tails are
observed, suggesting the strong influence of point-vortex-like dynamics on the
acceleration. A causal connection is found between the shape of the probability
density function and the autocorrelation of the norm of the acceleration
A variational framework for flow optimization using semi-norm constraints
When considering a general system of equations describing the space-time
evolution (flow) of one or several variables, the problem of the optimization
over a finite period of time of a measure of the state variable at the final
time is a problem of great interest in many fields. Methods already exist in
order to solve this kind of optimization problem, but sometimes fail when the
constraint bounding the state vector at the initial time is not a norm, meaning
that some part of the state vector remains unbounded and might cause the
optimization procedure to diverge. In order to regularize this problem, we
propose a general method which extends the existing optimization framework in a
self-consistent manner. We first derive this framework extension, and then
apply it to a problem of interest. Our demonstration problem considers the
transient stability properties of a one-dimensional (in space) averaged
turbulent model with a space- and time-dependent model "turbulent viscosity".
We believe this work has a lot of potential applications in the fluid
dynamics domain for problems in which we want to control the influence of
separate components of the state vector in the optimization process.Comment: 30 page
Noise and Inertia-Induced Inhomogeneity in the Distribution of Small Particles in Fluid Flows
The dynamics of small spherical neutrally buoyant particulate impurities
immersed in a two-dimensional fluid flow are known to lead to particle
accumulation in the regions of the flow in which rotation dominates over shear,
provided that the Stokes number of the particles is sufficiently small. If the
flow is viewed as a Hamiltonian dynamical system, it can be seen that the
accumulations occur in the nonchaotic parts of the phase space: the
Kolmogorov--Arnold--Moser tori. This has suggested a generalization of these
dynamics to Hamiltonian maps, dubbed a bailout embedding. In this paper we use
a bailout embedding of the standard map to mimic the dynamics of impurities
subject not only to drag but also to fluctuating forces modelled as white
noise. We find that the generation of inhomogeneities associated with the
separation of particle from fluid trajectories is enhanced by the presence of
noise, so that they appear in much broader ranges of the Stokes number than
those allowing spontaneous separation
- …