Monday 29 Jan 2018: Theory of turbulent boundary layer beyond the log law: predictions and validations
Prof. Zhen-Su She - Peking University, China
Turbulent boundary layer (TBL) refers to flow passing a solid wall with dominant mean velocity component parallel to the wall, and its analytic theory is a lasting dream for over a century since Prandtl 1904. We report here a new attempt from dilation symmetry consideration of the averaged Navier-Stokes equation (ANSE), validated by its prediction of the mean velocity and kinetic energy profiles (normal to the wall), and energy spectrum for canonical wall-bounded flows (pipe, channel and flat plate TBL), and by its derived algebraic model for simulating more complex industrial flows such as flows passing airfoil. In this talk, we present the main idea of selecting a family of lengths as key similarity variables which preserve the dilation invariance imposed by the wall, and then possess a multi-layer analytic structure valid across the entire boundary layer. The theory thus generalizes the log law of von Karman, which is universal and hence applicable to a variety of wall flows, ranging from incompressible to hypersonic flows, with smooth or rough wall, without and with (mild) pressure gradient (with no separation). Further extension to Rayleigh-Benard convection, Taylor-Couette flow, and atmospheric surface layer, etc. will be briefly discussed.