On 'spot' evolution under an adverse pressure gradient

The unsteady travelling 'spots' or spot-like disturbances are produced, in an otherwise planar boundary layer, by an initial impulse/blip, from wall f orcing or from nearby external forcing. Theory and computations are describ ed for the evolving spot-like structure, yielding initial-value problems fo r inviscid spot-like disturbances, commencing near the onset of an adverse pressure gradient. A transient stage incorporates the initial conditions, f ollowing which adverse pressure gradient effects become significant. Leadin g 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 adver se pressure gradient effects with three-dimensionality, nonlinearity and no n-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 ca se. Nonlinear interactions eventually change the internal structure, partic ularly at the spot-like disturbance leading edge, while pointing to the mea n-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 re gion trailing a spot-like disturbance, in which an attached thinned wall la yer is identified. Non-parallel effects lead to enhanced spot-like disturba nce 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 p osition to the separation position. Links with recent experiments on advers e-gradient spot-like disturbances and with findings on calmed region proper ties are investigated, as well as the unsteady forcing effects from an inci dent relatively thick vortical wake outside the boundary layer.