Langmuir-type vortices in wall-bounded flows driven by a criss-cross wavy wall topography
Peer reviewed, Journal article
Accepted version
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https://hdl.handle.net/11250/2674029Utgivelsesdato
2020Metadata
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Sammendrag
We investigate a mechanism to manipulate wall-bounded flows whereby wave-like
undulations of the wall topography drives the creation of bespoke longitudinal vortices.
A resonant interaction between the ambient vorticity of the undisturbed shear flow
and the undulation of streamlines enforced by the wall topography serves to slightly
rotate the spanwise vorticity of the mean flow into the streamwise direction, creating
a swirling motion, in the form of regular streamwise rolls. The process is kinematic
and essentially identical to the ‘direct drive’ CL1 mechanism for Langmuir circulation
(LC) proposed by Craik (J. Fluid Mech., vol. 41, issue 4, 1970, pp. 801–821). Wall
shear is modelled by selecting suitable primary flow profiles. A simple, easily integrable
expression for the cross-plane streamfunction is found in two asymptotic regimes:
the resonant onset of the essentially inviscid instability at early times, and the fully
developed steady-state viscous flow. Linear-order solutions for flow over undulating
boundaries are obtained, fully analytical in the special case of a power-law profile.
These solutions allow us to quickly map out the circulation response to boundary design
parameters. The study is supplemented with direct numerical simulations which verify
the manifestation of boundary induced Langmuir vortices in laminar flows with no-slip
boundaries. Simulations show good qualitative agreement with theory. Quantitatively, the
comparisons rest on a displacement length closure parameter adopted in the perturbation
theory. While wall-driven LC appear to become unstable in turbulent flows, we propose
that the mechanism can promote swirling motion in boundary layers, a flow feature which
has been reported to reduce drag in some situations.