On ‘spot’ evolution under an adverse pressure gradient

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.

New Insights into Turbulent Spots

“…The recovery trail of an APG spot is longer and stronger. Readers are also referred to Gostelow et al (1995), Smith & Timoshin (2001), Nolan &Zaki (2013), andYaras (2015).…”

Modelling the calmed region behind a spot

“…The present paper is an attempt to extend the mean flow calculation of Smith & Timoshin (2001), but for a zero pressure gradient, to the three-dimensional triggered spot of Doorly & Smith (1992), since a turbulent spot is certainly threedimensional. The aim is to involve the nonlinearity to the extent that the perturbation to the mean flow may be calculated and the calmed region identified.…”