162 research outputs found
Stochastic Perturbations in Vortex Tube Dynamics
A dual lattice vortex formulation of homogeneous turbulence is developed,
within the Martin-Siggia-Rose field theoretical approach. It consists of a
generalization of the usual dipole version of the Navier-Stokes equations,
known to hold in the limit of vanishing external forcing. We investigate, as a
straightforward application of our formalism, the dynamics of closed vortex
tubes, randomly stirred at large length scales by gaussian stochastic forces.
We find that besides the usual self-induced propagation, the vortex tube
evolution may be effectively modeled through the introduction of an additional
white-noise correlated velocity field background. The resulting
phenomenological picture is closely related to observations previously reported
from a wavelet decomposition analysis of turbulent flow configurations.Comment: 16 pages + 2 eps figures, REVTeX
Vortex in a relativistic perfect isentropic fluid and Nambu Goto dynamics
By a weak deformation of the cylindrical symmetry of the potential vortex in
a relativistic perfect isentropic fluid, we study the possible dynamics of the
central line of this vortex. In "stiff" material the Nanbu-Goto equations are
obtainedComment: 11 pages, Accepted for publication in Physical Review
Curvature correction to the mobility of fluid membrane inclusions
For the first time, using rigorous low-Reynolds-number hydrodynamic theory on curved surfaces via a Stokeslet-type approach, we provide a general and concise expression for the leading-order curvature correction to the canonical, planar, Saffman-Delbrück value of the diffusion constant for a small inclusion embedded in an arbitrarily (albeit weakly) curved fluid membrane. In order to demonstrate the efficacy and utility of this wholly general result, we apply our theory to the specific case of calculating the diffusion coefficient of a locally curvature inducing membrane inclusion. By including both the effects of inclusion and membrane elasticity, as well as their respective thermal shape fluctuations, excellent agreement is found with recently published experimental data on the surface tension dependent mobility of membrane bound inclusions
The uses of coherent structure (Dryden Lecture)
The concept of coherent structure in turbulent flow is a revolutionary idea which is being developed by evolutionary means. The main objective of this review is to list some solid achievements, showing what can be done by using the concept of coherent structure that cannot be done without it. The nature of structure is described in terms of some related concepts, including celerity,
topology, and the phenomenon of coalescence and splitting of structure. The main emphasis is on the mixing layer, as the one flow whose structure is well enough understood so that technical applications are now being made in problems of mixing and chemistry. An attempt is made to identify some conceptual and experimental obstacles that stand in the way of progress in other technically important flows, particularly the turbulent boundary layer. A few comments are included about the role of structure in numerical simulations and in current work on manipulation and control of turbulent flow. Some recent developments are cited which suggest that the time is nearly right for corresponding advances to occur in turbulence modeling
Vortex Reconnection as the Dissipative Scattering of Dipoles
We propose a phenomenological model of vortex tube reconnection at high
Reynolds numbers. The basic picture is that squeezed vortex lines, formed by
stretching in the region of closest approach between filaments, interact like
dipoles (monopole-antimonopole pairs) of a confining electrostatic theory. The
probability of dipole creation is found from a canonical ensemble spanned by
foldings of the vortex tubes, with temperature parameter estimated from the
typical energy variation taking place in the reconnection process. Vortex line
reshuffling by viscous diffusion is described in terms of directional
transitions of the dipoles. The model is used to fit with reasonable accuracy
experimental data established long ago on the symmetric collision of vortex
rings. We also study along similar lines the asymmetric case, related to the
reconnection of non-parallel vortex tubes.Comment: 8 pages, 3 postscript figure
Parallel flow in Hele-Shaw cells with ferrofluids
Parallel flow in a Hele-Shaw cell occurs when two immiscible liquids flow
with relative velocity parallel to the interface between them. The interface is
unstable due to a Kelvin-Helmholtz type of instability in which fluid flow
couples with inertial effects to cause an initial small perturbation to grow.
Large amplitude disturbances form stable solitons. We consider the effects of
applied magnetic fields when one of the two fluids is a ferrofluid. The
dispersion relation governing mode growth is modified so that the magnetic
field can destabilize the interface even in the absence of inertial effects.
However, the magnetic field does not affect the speed of wave propagation for a
given wavenumber. We note that the magnetic field creates an effective
interaction between the solitons.Comment: 12 pages, Revtex, 2 figures, revised version (minor changes
Fluctuations in viscous fingering
Our experiments on viscous (Saffman-Taylor) fingering in Hele-Shaw channels
reveal finger width fluctuations that were not observed in previous
experiments, which had lower aspect ratios and higher capillary numbers Ca.
These fluctuations intermittently narrow the finger from its expected width.
The magnitude of these fluctuations is described by a power law, Ca^{-0.64},
which holds for all aspect ratios studied up to the onset of tip instabilities.
Further, for large aspect ratios, the mean finger width exhibits a maximum as
Ca is decreased instead of the predicted monotonic increase.Comment: Revised introduction, smoothed transitions in paper body, and added a
few additional minor results. (Figures unchanged.) 4 pages, 3 figures.
Submitted to PRE Rapi
Absence of squirt singularities for the multi-phase Muskat problem
In this paper we study the evolution of multiple fluids with different
constant densities in porous media. This physical scenario is known as the
Muskat and the (multi-phase) Hele-Shaw problems. In this context we prove that
the fluids do not develop squirt singularities.Comment: 16 page
- …