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On properties of spots in jets and channel flows

Dodia, Bharat Thakarshi; (1995) On properties of spots in jets and channel flows. Doctoral thesis (Ph.D), UCL (University College London). Green open access

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Abstract

This thesis examines theoretically the structure of unsteady three- dimensional disturbances mainly in wall-jet flows and partly in channel flows, these disturbances having a spot-like character sufficiently far downstream of the initial disturbance. A start is made by using an approach similar to that in recent work by Doorly and Smith (1992), Smith (1992). The inviscid initial-value formulation taken, involving the three-dimensional unsteady Euler equations for an incompressible fluid, allows considerable analytical progress on the nonlinear side, as well as being suggested by some of the experimental evidence on turbulent spots and by previous related theory. The behaviour at large scaled times and large scaled distances is associated with two major length scales, proportional to (timey)1/3 and to (time), in the evolving spot. Within both scales it is found that nonlinear effects first enter the reckoning in the edge-layer(s) or caustic region(s) of the spot disturbance. The amplitude acquires the form of a nonlinearly distorted Airy function in this edge-layer, decaying exponentially outside the wing-tip region but approximately sinusoidally inside. As the typical amplitudes increase the nonlinear effects move towards the middle of the spot. Numerical solutions for the governing nonlinear amplitude equations in the (time)1/3 region are shown for two different amplitude levels. The computational results and accompanying analysis confirm that the positions of maximum amplitude gradually move towards the middle of the spot's trailing edge. As the amplitudes are increased further the governing equations for the wall-jet spot become analogous with those for the boundary-layer spot, and comparisons are made. The edge-layer properties further downstream are also examined.

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: On properties of spots in jets and channel flows
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: Thesis digitised by ProQuest.
Keywords: Pure sciences; Channel flows
URI: https://discovery.ucl.ac.uk/id/eprint/10102120
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