A unified theory for turbulent wake flows described by eddy viscosity

作者：Hutchinson A J^*

来源：International Journal of Non-Linear Mechanics, 2016, 81: 40-54.

DOI：10.1016/j.ijnonlinmec.2015.12.008

• Conservation laws
• Conserved vectors
• Turbulent classical wake
• Turbulent wake of a self-propelled body
• Eddy viscosity

In this paper, we consider the conservation laws for the far downstream wake equations described by eddy viscosity. A basis of conserved vectors is constructed. The well-known conserved quantities for the turbulent classical wake and the turbulent wake of a self-propelled body are obtained by integrating the corresponding conservation law across the wake and imposing the boundary conditions. For the wake of a self-propelled body the additional condition that the drag on the body is zero and is required to obtain the conserved quantity. A third conservation law, which possibly belongs to another type of wake, is discovered. The Lie point symmetry associated with the conserved vector is used to obtain the invariant solution and a typical velocity profile for this wake is provided. This wake appears to have common properties with the other two well-known wakes. We then analyse the invariant solutions to all three wake problems and prove that a simple mathematical relationship exists between them thus unifying the theory for turbulent wake flows.

• 出版日期2016-5