A new approach to the classic closure problem for turbulent boundary layers is
presented. This involves, first, using the well-known mean-flow scaling laws such as
the log law of the wall and the law of the wake of Coles (1956) together with the
mean continuity and the mean momentum differential and integral equations. The
important parameters governing the flow in the general non-equilibrium case are
identified and are used for establishing a framework for closure. Initially closure
is achieved here empirically and the potential for achieving closure in the future
using the wall-wake attached eddy model of Perry & Marusic (1995) is outlined.
Comparisons are made with experiments covering adverse-pressure-gradient flows in
relaxing and developing states and flows approaching equilibrium sink flow. Mean
velocity profiles, total shear stress and Reynolds stress profiles can be computed for
different streamwise stations, given an initial upstream mean velocity profile and the
streamwise variation of free-stream velocity. The attached eddy model of Perry &
Marusic (1995) can then be utilized, with some refinement, to compute the remaining
unknown quantities such as Reynolds normal stresses and associated spectra and
cross-power spectra in the fully turbulent part of the flow.
Lie group symmetry analysis of transport in porous media with variable transmissivity
