Practical results gained from statistical theories of turbulence usually appear in the form an inertial range energy spectrum $\mathcal{E}(k)\sim k^{-q}$ and a cut-off wave-number $k_{c}$. For example, values $q=5/3$ $\ell k_{c}\sim \mathit{Re}^{3/4}$ are intimately associated with Kolmogorov's 1941 theory. To extract such spectral information Navier-Stokes equations, Doering Gibbon (2002) intr...

The variation in moisture content between subsequent irrigations determines the use of infiltration equations that contain representative physical parameters soil when irrigation begins. This study analyzes reliability hydrodynamic model to simulate advanced phase border irrigation. For solution model, a Lagrangian scheme implicit finite differences is used, while for infiltration, Kostiakov eq...

This paper presents a model which provides a smooth transition between a kinetic and a hydrodynamic domain. The idea is to use a buffer zone, in which both diffusion and kinetic equations will be solved. The solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations. We use an artificial connecting function which makes the equation on each dom...

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved us...

The Boltzmann equation for a gas of smooth, inelastic hard spheres is introduced and its homogeneous solution for an isolated system is discussed. The possibility of hydrodynamic excitations is explored using the linearized Boltzmann equation for small spatial perturbations of the homogeneous state. It is shown that the spectrum of the generator for this linear dynamics contains five points at ...

Mathematically, the typical difference of Discrete Boltzmann Model (DBM) from the traditional hydrodynamic one is that the Navier-Stokes (NS) equations are replaced by a discrete Boltzmann equation. But physically, this replacement has a significant gain: a DBM is roughly equivalent to a hydrodynamic model supplemented by a coarse-grained model of the Thermodynamic Non-Equilibrium (TNE) effects...