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Theory-derived law of the wall for parallel flat-plates turbulent flow

Author(s): Joey Duran Ocon | Ludek Jirkovsky | Rizalinda L. de Leon | Amador Muriel

Journal: CFD Letters
ISSN 2180-1363

Volume: 4;
Issue: 3;
Start page: 93;
Date: 2012;
Original page

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-the-wall'). 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 [1]. 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 [2]. We found velocity profiles and velocity time evolution of a turbulent system, through simple numerical simulations, that cannot be reproduced from the classical NSE.
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