ON SPIKES AND SPOTS - STRONGLY NONLINEAR-THEORY AND EXPERIMENTAL COMPARISONS

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.