ON GLOBAL AND INTERNAL DYNAMICS OF SPOTS - A THEORETICAL APPROACH

Nonlinear effects on the free evolution of three-dimensional disturban ces are discussed, these disturbances having a spot-like character suf ficiently far downstream of the initial disturbance. The inviscid init ial-value formulation taken involving the three-dimensional unsteady E uler equations offers hope of considerable analytical progress on the nonlinear side, as well as being suggested by some of the experimental evidence on turbulent spots and by engineering modelling and previous related theory. The large-time large-distance behaviour is associated with the two major length scales, proportional to (time)1/2 and to (t ime), in the evolving spot; within the former scale the Euler flow exh ibits a three-dimensional triple-deck-like structure; within the latte r scale, in contrast, there are additional time-independent scales in operation. As the typical disturbance amplitude increases, nonlinear e ffects first enter the reckoning in edge layers near the spot's wing-t ips. The nonlinearity is mostly due to interplay between the fluctuati ons present and the three-dimensional mean-flow correction which varie s relatively slowly. The resulting amplitude interaction points to a s ubsequent flooding of nonlinear effects into the middle of the spot. T here it is suggested that the fluctuation/mean-flow interaction become s strongly nonlinear, substantially altering the mean properties in pa rticular. A new global viscous-inviscid interaction between the short and long scales present, involving Reynolds stresses, is also identifi ed. The additional significance of viscous sublayer bursts is also not ed, along with comments on links with experiments and direct numerical simulations, on channel flows and jets, and on further research.