The nonlinear interaction of TollmienSchlichting waves and TaylorGoertler vortices in curved channel flows
Abstract
The development of TollmienSchlichting waves (TSWs) and TaylorGoertler vortices (TGVs) in fully developed viscous curvedchannel flows is investigated analytically, with a focus on their nonlinear interactions. Two types of interactions are identified, depending on the amplitude of the initial disturbances. In the lowamplitude type, two TSWs and one TGV interact, and the scaled amplitudes go to infinity on a finite time scale; in the higheramplitude type, which can also occur in a straight channel, the same singularity occurs if the angle between the TSW wavefront and the TGV is greater than 41.6 deg, but the breakdown is exponential and takes an infinite time if the angle is smaller. The implications of these findings for external flow problems such as the design of laminarflow wings are indicated. It is concluded that longitudinal vortices like those observed in the initial stages of the transition to turbulence can be produced unless the present interaction mechanism is destroyed by boundarylayer growth.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 June 1988
 DOI:
 10.1098/rspa.1988.0060
 Bibcode:
 1988RSPSA.417..255H
 Keywords:

 Channel Flow;
 Flow Geometry;
 Goertler Instability;
 TollmienSchlichting Waves;
 Vorticity;
 Flow Stability;
 Interactional Aerodynamics;
 Laminar Flow;
 Stream Functions (Fluids);
 Viscous Flow;
 Fluid Mechanics and Heat Transfer