Adiabatic invariance for continuum modes in fluids and plasmas

Hirota, Makoto; Tokuda, Shinji

In various theories such as stability, wave-mean field interaction and weak turbulence, the wave action (or wave quantum) is worth studying since it is conserved with good accuracy in weakly nonlinear phenomena. In this work, without invoking the short wavelength limit, we have developed a technique for evaluating the wave action not only for each single eigenmode, but also for a continuum mode. The adiabatic invariance of the wave action can be discussed for both eigenmodes and continuum modes. It is decisive in determining whether resonant coupling between an eigenmode and a continuum mode leads to either exponential growth or continuum damping (Landau damping).