A New Theory on Transfer and Dissipation of Viscous Energy in Compressible, Viscous Fluid Flow

Abstract To better understand turbulence, it is necessary to re-examine the treatment of viscous energy dissipation by the Navier-Stokes (N-S) equations. In this paper, a local viscous energy in a fluid is defined using the product of the local viscous force and the velocity. The gradient of this viscous energy represents the local change rate of viscous energy, in which the sum of all the positive terms describes the irreversible, viscous energy loss in the motion of a viscous fluid, and can be directly used to establish the thermodynamic energy equation. The remainder of the local change rate of viscous energy includes the velocity components. The parts other than the velocity components represent the viscous force components of the fluid in all directions, which can be added to the Euler equation to establish the momentum equation of viscous fluid. Then, new momentum and thermodynamic energy equations for general, compressible, viscous fluid flows are derived, being different from the traditional N-S equations. The term of divergence of velocity in the N-S momentum equation, which is directly related to the local change of density in the fluid, does not appear in the new equation, indicating a decoupling between the compressibility and the viscosity. The viscous force terms in each direction in the N-S momentum equation includes the partial derivatives of the velocity components in the other two directions, while this is not the case in the new equation.