Solitons in transitional boundary layers

Two-dimensional evolution equations are derived as applied to flows in the near-wall jet and the Blasius boundary layer on a flat plate on which a mechanism of inviscid--inviscid infraction controls the development of large-sized short-scaled disturbances. The first one is an extension of the Korteweg--de Vries equation. As distinct from the shallow-water wave motion underlying the Kadomtsev--Petviashvili equation, the fluid parameters are not assumed to depend only weakly on the direction transversal to the oncoming stream. The second dynamical system provides a two-dimensional analog of the Benjamin--Davis--Acrivos equation. Simple line-soliton solutions are presented in both cases. A generalized Hirota function allows a pair of crossed solitons to be obtained at some distance from a solid surface in the near-wall jet. An oblique periodic nonlinear wave train pointed out for the Blasius boundary layer comes in place of the Tollmien--Schlichting waves when their amplitude attains sufficiently large values. DOI: 10.2514/1.40761