Electronic Communications in Probability Surface Stretching for Ornstein Uhlenbeck Velocity Fields
نویسندگان
چکیده
The present note deals with large time properties of the Lagrangian trajectories of a turbulent ow in IR 2 and IR 3. We assume that the ow is driven by an incompressible time-dependent random velocity eld with Gaussian statistics. We also assume that the eld is homogeneous in space and stationary and Markovian in time. Such velocity elds can be viewed as (possibly innnite dimensional) Ornstein-Uhlenbeck processes. In d spatial dimensions we established the (strict) positivity of the sum of the largest d?1 Lyapunov exponents. As a consequences of this result, we prove the exponential stretching of surface areas (when d = 3) and of curve lengths (when d = 2) which connrms conjectures found in the theory of turbulent ows.
منابع مشابه
Surface Stretching for Ornstein Uhlenbeck Velocity Fields
The present note deals with large time properties of the Lagrangian trajectories of a turbulent flow in IR and IR. We assume that the flow is driven by an incompressible time-dependent random velocity field with Gaussian statistics. We also assume that the field is homogeneous in space and stationary and Markovian in time. Such velocity fields can be viewed as (possibly infinite dimensional) Or...
متن کاملConvergence of Passive Scalar Fields in OrnsteinUhlenbeck Flows to Kraichnan's Model
We prove that the passive scalar field in the Ornstein-Uhlenbeck velocity field with wave-number dependent correlation times converges, in the white-noise limit, to that of Kraichnan’s model with higher spatial regularity.
متن کاملConvergence of Passive Scalars in Ornstein-uhlenbeck Flows to Kraichnan’s Model
We prove that the passive scalar field in the Ornstein-Uhlenbeck velocity field with wave-number dependent correlation times converges, in the white-noise limit, to that of Kraichnan’s model with higher spatial regularity.
متن کاملVelocity Fields with Power-Law Spectra for Modeling Turbulent Flows
We consider a generalization of homogeneous and isotropic Çinlar velocity fields to capture power-law spectra. The random velocity field is non-Gaussian with a representation motivated by Lagrangian and Eulerian observations. A wide range of turbulent flows can be generated by varying the stochastic parameters of the model. The velocity field being a functional version of Poisson shot-noise is ...
متن کاملOrnstein-Uhlenbeck limit for the velocity process of an N-particle system interacting stochastically
An N-particle system with stochastic interactions is considered. Interactions are driven by a Brownian noise term and total energy conservation is imposed. The evolution of the system, in velocity space, is a diffusion on a (3N − 1)-dimensional sphere with radius fixed by the total energy. In the N → ∞ limit, a finite number of velocity components are shown to evolve independently and according...
متن کامل