A New Way to Calculate Steep Gravity Waves

A simple and efficient way to calculate steep gravity waves is described, which avoids the use of power series expansions or integral equations. The method exploits certain relations between the coefficients in Stokes’s expansion which were discovered by the author in 1978.The method yields naturally the critical wave steepnesses for bifurcation of regular waves into non-uniform steady waves. Moreover, truncation of the series after only two terms yields a simple model for Class 2 bifurcation.The analysis can be used to discuss the stability of steep gravity waves and to derive new integral relations. Particularly relevant to breaking waves are some new relations for the angular momentum. The level of action y_a for a limiting wave can also be expressed in terms of the Fourier coefficients.