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On 'spot' evolution under an adverse pressure gradient

Smith, FT; Timoshin, SN; (2001) On 'spot' evolution under an adverse pressure gradient. J FLUID MECH , 430 169 - 207. Green open access

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Abstract

The unsteady travelling 'spots' or spot-like disturbances are produced, in an otherwise planar boundary layer, by an initial impulse/blip, from wall forcing or from nearby external forcing. Theory and computations are described for the evolving spot-like structure, yielding initial-value problems for inviscid spot-like disturbances, commencing near the onset of an adverse pressure gradient. A transient stage incorporates the initial conditions, following which adverse pressure gradient effects become significant. Leading and trailing critical layers then form, which confine and define the spot-like disturbance, and these depart from the wall downstream accompanied by disturbance amplification and mean flow distortion. The interplay of adverse pressure gradient effects with three-dimensionality, nonlinearity and non-parallelism is considered in turn.Three-dimensional effects provoke a universal closed planform of spot-like disturbance, which has a different side behaviour from the zero-gradient case. Nonlinear interactions eventually change the internal structure, particularly at the spot-like disturbance leading edge, while pointing to the mean-flow alteration underhanging the spot-like disturbance and to a pressure-feedback alteration for the region behind the spot-like disturbance. These two alterations offer complementary mechanisms for describing the calmed region trailing a spot-like disturbance, in which an attached thinned wall layer is identified. Non-parallel effects lead to enhanced spot-like disturbance growth and larger-scale/shorter-scale interactive behaviour downstream. The approach to separation is also considered, yielding maximal growth for small spot-like disturbances at 5/6 of the way from the minimum pressure position to the separation position. Links with recent experiments on adverse-gradient spot-like disturbances and with findings on calmed region properties are investigated, as well as the unsteady forcing effects from an incident relatively thick vortical wake outside the boundary layer.

Type: Article
Title: On 'spot' evolution under an adverse pressure gradient
Open access status: An open access version is available from UCL Discovery
Keywords: VISCOUS CRITICAL LAYER, PLANE POISEUILLE FLOW, BOUNDARY-LAYERS, FREE DISTURBANCES, TURBULENT SPOTS, BREAK-UP, TRANSITION, ROUGHNESS, INSTABILITY
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/13864
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