Consider a wave that stands 40 meters high in the sea on very deep water. How much energy would approximately be contained in this wave if it was 100 meters wide and had been produced by wind?
Is this question even answerable? I read somewhere that the tsunami that caused massive destruction in South-East Asia a few years ago, was just something like a meter tall in open sea..
We have $40*100*1000=4\times10^6$ cubic meters of water per kilometer, which is $4\times 10^9$ kilograms of water per kilometer, average 20 meters above sea level, which leads to $4\times 10^9 \times 20 \times 10 = 8\times 10^{11} J/km$ in gravitational potential energy. Kinetic energy should be about the same as potential so lets say $1.6\times 10^{12} J/km$ or $0.3$ kilotons per kilometer. For reference the Hiroshima A-bomb was about $10$ kilotons yield.
Erm
The equation for sea wave energy is
Energy = 2,452.5 × wavelength × wave span × amplitude²
Since the minimum wavelength for a stable sea wave is around 12 times the amplitude, the above simplifies to
Energy ≥ 28,853 × span × amplitude³
Therefore for your 40 meter crest to trough wave
Energy ≥ 28,853 × span × 20³
Energy / span ≥ 231MJ/m
Your specified span of 100m is much shorter than the minimum wavelength of 240m, which makes this wave short lived due to diffraction. But anyway, the energy is
Energy ≥ 23,100MJ
