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.