Theory-Derived Law of the Wall for Parallel Flatplates Turbulent Flow
Keywords:post-Navier Stokes equation, law of the wall, analytical solution, numerical simulations, flat-plate system
It is well known that in a turbulent flow between two parallel flat plates, the horizontal mean velocity varies logarithmically with height (the so-called 'logarithmic-law-of-thewall'). The law of the wall is a description of the mean velocity profile in wall bounded flows and has been regarded as one of the underpinning doctrine in the turbulence community for more than half a century. Much of our understanding in wall turbulence has been based from the continuum Navier-Stokes Equation (NSE). More recently, following studies of a modified Navier Stokes Equation, we applied a modified incompressible NSE to the flow of turbulent fluid between two parallel flat plates and solved it analytically . We extended the analysis to the turbulent flow along a single wall and compared the results with the established controversial von Karman logarithmic law of the wall . We found velocity profiles and velocity time evolution of a turbulent system, through simple numerical simulations, that cannot be reproduced from the classical NSE.