This chapter presents the application of the notion of kinematical symmetry to nonlinear equations, namely, to the Navier鈥揝tokes (NS) equation of hydrodynamics. The chapter also explains the determination of the largest kinematical symmetry group of the NS equation up to a stage where a decision has to be taken on t...
First, scaling symmetries of space and time, both tracing back to the NavierStokes equations in the limit of large Reynolds numbers (or r路), give rise to a temporal power-law decay for the turbulent kinetic energy and at the same time an algebraic growth of the integral length scale at ...
It is not know if solutions of the Navier–Stokes equations are smooth for all t>0, however Lions [18] showed a priori estimate(1.9)∫0T‖D0|tγu(t)‖L2(Rn)dt≤const.(J+J32),J=‖u0‖L2(Rn) where 0≤γ<1/4 and u is a weak solution in L2((0,T);L2(Rn)) associated to...
symmetries are of much more general type, i.e., not limited to MPC or PDF equations emerging from Navier-Stokes, but instead they are admitted by other nonlinear partial differential equations like, for example, the Burgers equation when in conservative form and if the nonlinearity is quadratic...
Bassom, Nonclassical symmetry reductions of the three-dimensional incompressible Navier-Stokes equations, J. Phys. A: Math. Gen. 31 (1998) 7965-7980. [38] S. Martini, N. Ciccoli, M.C. Nucci, Group analysis and heir-equations of a mathematical model for thin liquid films, J. Nonlinear...
It unifies a large set of self-similar solutions for the mean velocity of stationary parallel turbulent shear flows. The theory is derived from the Reynolds averaged Navier-Stokes equations, the fluctuation equations, and the velocity product equations, which are the dyad product of the velocity ...
We briefly derive the infinite set of multi-point correlation equations based on the NavierStokes equations for an incompressible fluid. From this we reconsider the previously derived set of Lie symmetries, i.e. those directly induced by the ones from classical mechanics and also new symmetries. ...
Tempesta, Vortices and invariant surfaces generated by symmetries for the 3D Navier-Stokes equations, Phys. A 286 (2000) 79-108.V. Grassi, R.A. Leo, G. Soliani and P. Tempesta, Vortices and invariant sur- faces generated by symmetries for the 3D Navier-Stokes equations, Physica A 286, ...
The theory is derived from the Reynolds averaged Navier-Stokes equations, the fluctuation equations, and the velocity product equations, which are the dyad product of the velocity fluctuations with the equations for the velocity fluctuations. For the plane case the results include the logarithmic law...
1.Queen Mary University of London Centre for Research in String Theory School of Physics Mile End Road London E1 4NS U.K.Springer Berlin HeidelbergJournal of High Energy PhysicsJ. Berkeley and D. S. Berman, "The Navier-Stokes equation and solution generating symmetries from holography," JHEP ...