Ft. Smith, ON SPIKES AND SPOTS - STRONGLY NONLINEAR-THEORY AND EXPERIMENTAL COMPARISONS, Philosophical transactions-Royal Society of London. Physical sciences and engineering, 352(1700), 1995, pp. 405-424
Spikes and spats are discussed mostly for incompressible boundary laye
rs, with the emphasis towards strong nonlinearity. The distinction bet
ween forced and free disturbances then becomes blurred, as spikes and
spots reproduce each other. First, the forced case is concentrated on
the start of spikes. The theory used is that of the two- or three-dime
nsional interacting boundary layer, capturing nonlinear Tollmien-Schli
chting waves, for example, or following a vortex-wave interaction. Fin
ite-time breakup produces shortened time and length scales, yielding a
greement with computations and experiments on the first spike in trans
ition, with subsequent spot formation. After the breakup, normal press
ure gradients and vortex wind-up become significant locally. Second, t
he free case concerns initial-value problems for spots containing a wi
de band of three-dimensional nonlinear disturbances. The theory points
to successive nonlinear stages starting at the wing tips near the spo
t trailing edge but gradually entering the middle as the amplitudes in
crease downstream. This effect combined with shortening scales produce
s a spread angle near 11 degrees, very close to the experimental obser
vations. The overall spot structure is described briefly, including al
so the leading edge. Viscosity arises later in two ways; for the case
mentioned above with spikes originating near the surface and also thro
ugh a novel interaction influencing the global spot.