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- W2891493746 abstract "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 $exp (-kz)$ and $exp (-Kz)$ , with $z$ the wall distance, $k$ the magnitude of the horizontal wavevector $boldsymbol{k}$ , and where $K(boldsymbol{k},Re)$ is a function of $boldsymbol{k}$ and the Reynolds number $Re$ . Moreover, for $krightarrow infty$ or $k_{1}rightarrow 0$ (with $k_{1}$ the stream-wise wavenumber), $Krightarrow k$ is found, in which case solutions consist of a linear combination of $exp (-kz)$ and $zexp (-kz)$ , and are independent of the Reynolds number. These analytical relations are compared in the limit of $k_{1}=0$ to the rough boundary layer experiments by Vanderwel & Ganapathisubramani ( J. Fluid Mech. , vol. 774, 2015, R2) and are in reasonable agreement for $ell _{k}/unicode[STIX]{x1D6FF}leqslant 0.5$ , with $unicode[STIX]{x1D6FF}$ the boundary-layer thickness and $ell _{k}=2unicode[STIX]{x03C0}/k$ ." @default.
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- W2891493746 date "2019-01-25" @default.
- W2891493746 modified "2023-10-03" @default.
- W2891493746 title "On the decay of dispersive motions in the outer region of rough-wall boundary layers" @default.
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- W2891493746 doi "https://doi.org/10.1017/jfm.2018.1019" @default.
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