A WALL-WAKE MODEL FOR THE TURBULENCE STRUCTURE OF BOUNDARY-LAYERS .1.EXTENSION OF THE ATTACHED EDDY HYPOTHESIS

The attached eddy hypothesis developed for zero pressure gradient boun dary layers and for pipe flow is extended here to boundary layers with arbitrary streamwise pressure gradients, both favourable and adverse. It is found that in order to obtain the correct quantitative results for all components of the Reynolds stresses, two basic types of eddy s tructure geometries are required. The first type, called type-A, is in terpreted to give a 'wall structure' and the second, referred to as ty pe-B, gives a 'wake structure'. This is in analogy with the convention al mean velocity formulation of Coles where the velocity is decomposed into a law of the wall and a law of the wake. If the above mean veloc ity formulation is accepted, then in principle, once the eddy geometri es are fixed for the two eddy types, all Reynolds stresses and associa ted spectra contributed from the attached eddies can be computed witho ut any further empirical constants. This is done by using the momentum equation and certain convolution integrals developed here based on th e attached eddy hypothesis. The theory is developed using data from eq uilibrium and quasi-equilibrium flows. In Part 2 the authors' non-equi librium data are used.