Jahanshah Davoudi

Lagrangian tracers on a surface flow: the role of time correlations.

Finite time correlations of the velocity in a surface flow are found to be important for the formation of clusters of Lagrangian tracers. The degree of clustering characterized by the Lyapunov spectrum of the flow is numerically shown to be in qualitative agreement with the predictions for the white-in-time compressible Kraichnan flow, but to deviate quantitatively. For intermediate values of compressibility the clustering is surprisingly weakened by time correlations.

Theoretical Model for the Kramers-Moyal Description of Turbulence Cascades

We derive the Kramers-Moyal equation for the conditional probability density of velocity increments from the theoretical model recently proposed by V.Yakhot [Phys.Rev.E {\bf 57}, 1737 (1998)] in the limit of high Reynolds number limit. We show that the higher order (n>=3) Kramers-Moyal coefficients tends to zero and the velocity increments are evolved by the Fokker-Planck operator. Our result is compatible with the phenomenological descriptions by R.Friedrich and J.Peinke [Phys.Rev.Lett. {\bf 78}, 863 (1997)].

Stretching of polymers around the Kolmogorov scale in a turbulent shear flow

We present numerical studies of stretching of Hookean dumbbells in a turbulent Navier-Stokes flow with a linear mean profile, ⟨ux⟩=Sy. In addition to the turbulence features beyond the viscous Kolmogorov scale η, the dynamics at the equilibrium extension of the dumbbells significantly below η is well resolved. The variation of the constant shear rate S causes a change of the turbulent velocity fluctuations on all scales and thus of the intensity of local stretching rate of the advecting flow. The latter is measured by the maximum Lyapunov exponent λ1 which is found to increase as λ1∼S3∕2, in agreement with a dimensional argument. The ensemble of up to 2×106 passively advected dumbbells is advanced by Brownian dynamics simulations in combination with a pseudospectral integration for the turbulent shear flow. Anisotropy of stretching is quantified by the statistics of the azimuthal angle ϕ which measures the alignment with the mean flow axis in the x-y shear plane, and the polar angle θ which determines the...

Statistical theory for the Kardar-Parisi-Zhang equation in ( 1 + 1 ) dimensions

The Kardar-Parisi-Zhang (KPZ) equation in (1+1) dimensions dynamically develops sharply connected valley structures within which the height derivative is not continuous. We develop a statistical theory for the KPZ equation in (1+1) dimensions driven with a random forcing that is white in time and Gaussian-correlated in space. A master equation is derived for the joint probability density function of height difference and height gradient P(h-h*, partial differential(x)h,t) when the forcing correlation length is much smaller than the system size and much larger than the typical sharp valley width. In the time scales before the creation of the sharp valleys, we find the exact generating function of h-h* and partial differential(x)h. The time scale of the sharp valley formation is expressed in terms of the force characteristics. In the stationary state, when the sharp valleys are fully developed, finite-size corrections to the scaling laws of the structure functions left angle bracket(h-h*)(n)(partial differential(x)h)(m)right angle bracket are also obtained.

Stochastic -theory in the strong coupling limit

The stochastic

Stochastic φ4-theory in the strong coupling limit

\phi^4

Stochastic φ4φ4-theory in the strong coupling limit

-theory in

Stochastic

d-

\phi^4-

dimensions dynamically develops domain wall structures within which the order parameter is not continuous. We develop a statistical theory for the

Theory in the Strong Coupling Limit

\phi^4