Too shallow for linear wave theory?

"resonably good" is what is at issue here. Yes second order accounts for depth and predicts a maximum, but quicky diverges from truth as the bottom shoals with respect wave length in large seas. For a condition of d/L = 0.1 the Stokes 2nd order errors are 7%, 13%, 24%, 39%, and 50% for H/d of 0.1, 0.2, 0.4, 0.6, and Hmax respectively (see Mechanics of Wave Forces on Offshore Structures by Sarpkaya & Isaacson, Fig 4.5 page 176). Stokes's 5th order gives much better results for waves in shoaling water.

Of course, where you expect to operate really influences which theory you pick, especially in as shallow as 5m with a H1/3 of 0.5m (assuming the 2m mentioned in post #4 is a max, not a H1/3. If it was an h1/3 then we are in surf, not waves). Here in the Pacific Northwest I have a hard time convincing people from the East Coast US that there is always a 1m, 15 sec swell to contend with even in SS 0, and a 2m 23 sec SW pacific storm swell could appear at any time, and they should use an Ochi-Hubble rather than a Bretschneider.

<<shrug>> Pick your expert text, pick your accepted limitations.

 

And then there are the waves in the Great Lakes, which folks from both coasts tend to underestimate. It can be flat but when it blows the waves can be steep and short.

Which wave models are reasonable to use also depends on the use of the results from the wave model.