Critical layer instability as a resonance between a non-singular mode and continuous modes

The interpretation of an unstable made in terms of resonance between neutral waves is extended to a critical layer instability. It is found that the concept of resonance can be applied to the critical layer instability, if continuous modes are taken into account: The instability occurs due to a resonance between a non-singular mode and a superposition of several continuous modes whose phase speeds are close to the Velocity at the critical level. These continuous modes have pseudomomentum with its sign opposite to the gradient of the potential vorticity at the critical level, which is consistent with the interpretation of the instability in terms of resonance between neutral waves. (C) 1999 The Japan Society of Fluid Mechanics and Elsevier Science B.V. All rights reserved.