On the decay of dispersive motions in the outer region of rough-wall boundary layers

© 2019 Cambridge University Press. In rough-wall boundary layers, wall-parallel non-homogeneous mean-flow solutions exist that lead to so-called dispersive velocity components and dispersive stresses. They play a significant role in the mean-flow momentum balance near the wall, but typically disappear in the outer layer. A theoretical framework is presented to study the decay of dispersive motions in the outer layer. To this end, the problem is formulated in Fourier space, and a set of governing ordinary differential equations per mode in wavenumber space is derived by linearizing the Reynolds-averaged Navier-Stokes equations around a constant background velocity. With further simplifications, analytically tractable solutions are found consisting of linear combinations of and, with the wall distance, the magnitude of the horizontal wavevector, and where is a function of and the Reynolds number. Moreover, for or (with the stream-wise wavenumber), is found, in which case solutions consist of a linear combination of and, and are independent of the Reynolds number. These analytical relations are compared in the limit of to the rough boundary layer experiments by Vanderwel & Ganapathisubramani (J. Fluid Mech., vol. 774, 2015, R2) and are in reasonable agreement for, with the boundary-layer thickness and.

Jaar van publicatie:2019

BOF-keylabel:ja

IOF-keylabel:ja

BOF-publication weight:2

CSS-citation score:1

Auteurs:International

Authors from:Higher Education

Toegankelijkheid:Open