On the disappearance of the lowest-order instability for steep gravity waves in finite depth

This paper extends to very large steepness the results of the linear stability analysis of two-dimensional periodic gravity waves over a bottom of uniform depth. Both subharmonic and superharmonic instabilities are investigated. For the case considered herein, it is shown how the lowest-order instability (class I) completely disappears at a critical wave steepness. These results also confirm numerically a theorem connected with the appearance of superharmonic instabilities in finite depth. (C) 2003 American Institute of Physics.