The present work proposes a theory of isotropic and homogeneous turbulence for incompressible fluids, which assumes that the turbulence is due to the bifurcations associated to the velocity field. The theory is formulated using a representation of the fluid motion which is more general than the classical Navier-Stokes equations, where the fluid state variables are expressed in terms of the referential coordinates. The theory is developed according to the following four items: 1) Study of the route toward the turbulence through the bifurcations analysis of the kinematic equations. 2) Referential description of the motion and calculation of the velocity fluctuation using the Lyapunov analysis of the local deformation. 3) Study of the mechanism of the energy cascade from large to small scales through the Lyapunov analysis of the relative kinematics equations of motion. 4) Determination of the statistics of the velocity difference with the Fourier analysis. Each item...
A Statistical Theory of Homogeneous Isotropic Turbulence / DE DIVITIIS, Nicola. - arXiv:0902.1839:(2009), pp. 1-34.
A Statistical Theory of Homogeneous Isotropic Turbulence
DE DIVITIIS, Nicola
2009
Abstract
The present work proposes a theory of isotropic and homogeneous turbulence for incompressible fluids, which assumes that the turbulence is due to the bifurcations associated to the velocity field. The theory is formulated using a representation of the fluid motion which is more general than the classical Navier-Stokes equations, where the fluid state variables are expressed in terms of the referential coordinates. The theory is developed according to the following four items: 1) Study of the route toward the turbulence through the bifurcations analysis of the kinematic equations. 2) Referential description of the motion and calculation of the velocity fluctuation using the Lyapunov analysis of the local deformation. 3) Study of the mechanism of the energy cascade from large to small scales through the Lyapunov analysis of the relative kinematics equations of motion. 4) Determination of the statistics of the velocity difference with the Fourier analysis. Each item...I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.