The Gibbs ensemble of a vortex filament
نویسندگان
چکیده
Certain investigations of turbulent 3-D fluids seem to indicate that the vorticity field of the fluid is strongly concentrated along thin structures, called vortex filaments. A. Chorin has developed a statistical-mechanics theory of vortex filaments to describe the statistics of turbulent flows, see [4]. In his investigations vortex filaments are modelled by trajectories of self-avoiding walks on a lattice. The kinematic energy H of such filaments is properly defined (due to the lattice cut-off) and Gibbs measures of the form
منابع مشابه
The attraction between a flexible filament and a point vortex
We determine the inviscid dynamics of a point vortex in the vicinity of a flexible filament. For a wide range of filament bending rigidities, the filament is attracted to the point vortex, which generally moves tangentially to it. We find evidence that the point vortex collides with the filament at a critical time, with the separation distance tending to zero like a square root of temporal dist...
متن کاملDynamics of a planar vortex filament under the quantum local induction approximation
The Hasimoto planar vortex filament is one of the rare exact solutions to the classical local induction approximation (LIA). This solution persists in the absence of friction or other disturbances, and it maintains its form over time. As such, the dynamics of such a filament have not been extended to more complicated physical situations. We consider the planar vortex filament under the quantum ...
متن کاملGeometry and Topology of Finite-gap Vortex Filaments
In this talk, I will discuss the vortex filament flow, and its connection with the nonlinear Schrödinger equation (NLS), the geometry of solutions to the filament flow that correspond to finite-gap solutions of NLS, and in particular, the relationship between geometric properties of the filament to features of the Floquet spectrum of a periodic NLS potential. These will be illustrated by the ex...
متن کاملMultiple breathers on a vortex filament
In this paper we investigate the correspondence between the Da Rios-Betchov equation, which appears in the three-dimensional motion of a vortex filament, and the nonlinear Schrödinger equation. Using this correspondence we map a set of solutions corresponding to breathers in the nonlinear Schrödinger equation to waves propagating along a vortex filament. The work presented generalizes the recen...
متن کاملMotion of a Vortex Filament in the Local Induction Approximation: Reformulation of the Da Rios-Betchov Equations in the Extrinsic Filament Coordinate Space
In recognition of the highly non-trivial task of computation of the inverse Hasimoto transformation mapping the intrinsic geometric parameter space onto the extrinsic vortex filament coordinate space a reformulation of the Da Rios-Betchov equations in the latter space is given. The nonlinear localized vortex filament structure solution given by the present formulation is in detailed agreement w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008