Generation of Irregular Disturbances and Solitarylike Waves in Transitional Boundary Layers

The interrelation between erratic signals and large-sized coherent structures excited in boundary layers transitioning to turbulence is investigated. To shed light on the issue of fundamental importance, a new dynamical system has been put forward recently on the basis of simple physical arguments assuming the Reynolds number to tend to infinity. Wave dispersion in the system is defined by the Laplacian of the self-induced pressure resulting from inviscid-inviscid interaction of the intermediate (adjustment) sublayer with the outer oncoming stream. This regime supersedes the triple-deck velocity pattern when the pulsation size attains sufficiently large magnitudes. In the present paper, asymptotic equations governing a three-dimensional disturbance field are expanded into a power series of a small parameter proportional to the magnitude of excess pressure. However, the final closed-form result does not depend on this parameter. The birth of erratic signals typical of transitional boundary-layer flow is demonstrated by computing the two-dimensional disturbance field downstream of a steady obstacle. In accordance with experimental findings, solitarylike coherent structures emerge amid the foam of erratic oscillations surviving the random buffeting by the surrounding fluid. The phase speed of solitarylike waves exceeds the speed of weaker pulsations; therefore, the large-sized waves leave behind the small-sized signals.