Taylor's frozen-flow hypothesis in Burgers turbulence.

By detailed analytical treatment of the shock dynamics in the Burgers turbulence with large scale forcing we calculate the velocity structure functions between pairs of points displaced both in time and space. Our analytical treatment verifies the so-called Taylor's frozen-flow hypothesis without relying on any closure and under very general assumptions. We discuss the limitation of the hypothesis and show that it is valid up to time scales smaller than the correlation time scale of temporal velocity correlation function. We support the analytical calculation by performing numerical simulation of the periodically kicked Burgers equation.

Closure of two-dimensional turbulence: the role of pressure gradients.

Inverse energy cascade regime of two-dimensional turbulence is investigated by means of high resolution numerical simulations. Numerical computations of conditional averages of transverse pressure gradient increments are found to be compatible with a recently proposed self-consistent Gaussian model. An analogous low-order closure model for the longitudinal pressure gradient is proposed and its validity is numerically examined. In this case numerical evidence for the presence of higher-order terms in the closure is found. The fundamental role of conditional statistics between longitudinal and transverse components is highlighted.

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.

Three-dimensional forced Burgers turbulence supplemented with a continuity equation.

We investigate turbulent limit of the forced Burgers equation supplemented with a continuity equation in three dimensions. The scaling exponent of the conditional two-point correlation function of density, i.e., approximately /x1-x2/(-alpha3), is calculated self-consistently in the nonuniversal region from which we obtain alpha3=3. Also we derive an equation governing the evolution of the probability density function (PDF) of longitudinal velocity increments in length scale, from which a possible mechanism for the dependence of the inertial PDF to one-point u(rms) is developed.

Multiscale correlation functions in strong turbulence

Under the framework of Yakhot [Phys. Rev. E 57, 1737 (1998)], we model intermittent structure functions in fully developed turbulence, based on the experimentally supported Markovian nature of turbulence cascades [Friedrich and Peinke, Phys. Rev. Lett, 78, 863 (1997)], and calculate the multiscaling correlation functions. Fusion rules [L'vov and Procaccia, Phys. Rev. Lett. 76, 2898 (1996)], which were experimentally tested [Benzi, Biferale, and Toschi, Phys. Rev. Lett. 80, 3244 (1998)] to be compatible with almost uncorrelated multiplicative process are analytically checked by direct calculations.