# Fractional hydrodynamic equations for fractal media

@article{Tarasov2005FractionalHE, title={Fractional hydrodynamic equations for fractal media}, author={Vasily E. Tarasov}, journal={Annals of Physics}, year={2005}, volume={318}, pages={286-307} }

Abstract We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the “fractional” continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier–Stokes and Euler equations are considered. We derive the equilibrium equation for fractal media. The sound waves in the continuous medium model for…

## 171 Citations

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Abstract.We examine three fundamental equations governing turbulence of an incompressible Newtonian fluid in a fractal porous medium: continuity, linear momentum balance and energy balance. We find…

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The model incorporates the empirically found trends in highly heterogeneous media, regarding the dependence of the dispersivity on the scale and the dispersion coefficient on the velocity, and concludes that the presence of nontrivial fractal parameters produces anomalous dispersion.

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