Boundary layers are often studied with no pressure gradient
or with an imposed pressure gradient. Either of these assumptions
can lead to difficulty in obtaining solutions. A major advance in fluid
dynamics last century (1969) was the development of a triple deck
formulation for boundary layers where the pressure is not
specified but emerges through an interaction between
boundary layer and the inviscid outer flow. This has given rise to
new computational problems and computations have in turn
fed ideas back into theoretical developments. In this survey talk
based on my new book, I will look at three problems:
flow past a plate, flow separation and flow in channels
and discuss the interaction between theory and computation
in advancing boundary layer theory.