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Sharks, Aeroplanes and the Rotating-Disk Boundary Layer

... And a Wee Bit About Dolphins

The classic belief that surface roughness inevitably increases the skin-friction drag that acts on bodies moving through a fluid has been superseded [1,2]. The right sort of roughness [3] can reduce drag. Evolution discovered this long before Engineers did and equipped sharks with rough skin. The challenge that remains for the Engineer is to establish what type of roughness exactly is energetically beneficial in the context of any particular technological, engineering application and then attempt to exploit this in industry.

I will summarize results of our programme [4-6] investigating the effects of surface roughness on the stability of the boundary-layer flow over a rotating disk. This flow represents a generic example of a general class of boundary layers that share the common characteristic of a cross-flow velocity component. Boundary layers of this type exist, for instance, on highly-swept wings of aircraft. All such boundary layers display similar laminar-turbulent transition characteristics. Our results [4-6] reveal stabilising, that is energetically beneficial, effects on the dominant instability mode responsible for transition in these boundary layers. Our goal is to develop theoretical methods to enable the design of energetically optimal surface roughness for laminar-flow control in the context of new, passive drag-reduction techniques for boundary layers with a cross-flow component.


[1] Sirovich, L. & Karlson, S. 1997 Turbulent drag reduction by passive mechanisms, Nature 388, 753.

[2] Choi, K.-S., 2006 The rough with the smooth, Nature 440, 754.

[3] Carpenter, P.W. 1997 The right sort of roughness, Nature 388, 713.

[4] Cooper, A.J., Harris, J.H., Garrett, S.J., Özkan, M. & Thomas, P.J. 2015 The effects of anisotropic and isotropic roughness on the convective stability of the rotating-disk boundary layer, Phys. Fluids. 27, 014107.

[5] Garrtett, S.J., Cooper, A.J., Harris, J.H., Özkan, M., Segalini, A. & Thomas, P.J. 2016 On the stability of von Kármán rotating-disk boundary layers with radial anisotropic surface roughness, Phys. Fluids. 28, 014104.

[6] Özkan, M., J., Thomas, P.J., Cooper, A.J., Garrett, S.J. 2017 Comparison of the Effects of Surface Roughness and Confinement on Rotor-Stator Cavity Flow, Eng. Appl. Comp. Fluid Mech. 11, 142-158.