We represent a conceptual scrutiny for completely organized convective heat transfer ring within the circular pipeline with power law liquids by means of realizing that diffusivity has been temperature gradient. The investigative resolution is availed and behaviour inspected under persistent thermic flux frontier condition. It demonstrated Nu stubbornly relies upon power-law index n value. (Nus...

The Lagrangian statistics of relative dispersion in fully developed turbulence is numerically investigated. A scaling range spanning many decades is achieved by generating a two-dimensional velocity field by means of a stochastic process with prescribed statistics and of a dynamical model (shell model) with fluctuating characteristic times. When the velocity field obeys Kolmogorov similarity, t...

We investigate chaos synchronization of small-scale motions in the three-dimensional turbulent energy cascade, via pseudospectral simulations of the incompressible Navier-Stokes equations. The modes of the turbulent velocity field below about 20 Kolmogorov dissipation lengths are found to be slaved to the chaotic dynamics of larger-scale modes. The dynamics of all dissipation-range modes can be...

We review the Parisi-Frisch [1] MultiFractal formalism for Navier– Stokes turbulence with particular emphasis on the issue of statistical fluctuations of the dissipative scale. We do it for both Eulerian and Lagrangian Turbulence. We also show new results concerning the application of the formalism to the case of Shell Models for turbulence. The latter case will allow us to discuss the issue of...

Kolmogorov's phenomenological theory for the energy spectrum in a turbulent fluid in three dimensions is perhaps the single most successful theoretical attempt to comprehend fully developed turbulence. (1) Nevertheless it fails to account for certain fluctuation effects (" intermittency ") that are seen experimentally in three dimensions3 2) Furthermore, it is formulated in such general terms t...

Emergent extreme events are a key characteristic of complex dynamical systems. The main tool for detailed and deep understanding of their stochastic dynamics is the statistics of time intervals of extreme events. Analyzing extensive experimental data, we demonstrate that for the velocity time series of fully-developed turbulent flows, generated by (i) a regular grid; (ii) a cylinder; (iii) a fr...

The statistical properties of fully developed hydrodynamic turbulence can be successfully described using methods from nonextensive statistical mechanics. The predicted probability densities and scaling exponents precisely coincide with what is measured in various turbulence experiments. As a dynamical basis for nonextensive behaviour we consider nonlinear Langevin equations with fluctuating fr...

Pressure drop of fully developed, laminar, incompressible flow in smooth mini and microchannels of arbitrary cross-section is investigated. A compact approximate model is proposed that predicts the pressure drop for a wide variety of shapes. The model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The proposed model is comp...

We compare mean velocity profiles measured in turbulent pipe flows (and also in boundary layer flows) with the predictions of a recently proposed scaling law; in particular, we examine the results of the Princeton "super-pipe" experiment and assess their range of validity.