Is the Classic Weakly Nonlinear Theory of Hydrodynamic Stability Good Enough and How It Can Be Improved

Summary

In acknowledging that the classic, weakly nonlinear theory should be seen as a milestone in the developement of the theory of hydrodynamic stability, it has been re—examined. It was shown that its equillibrium solution must be divergent. Also, it was pointed out that the original formulation did not fit an arbitrary initial condition, and there was another time scale R other than the two time scales usually thought to exist. Ways for its improvement were suggested, and the results were in agreement with those obtained by numerical simulations, as long as the amplitude of the fundamental wave was not too large.