Hello,
Regarding your questions :
1) The significant wave height is, by definition, the average of the 1/3 highest individual wave heights in a sea state, obtained from a statistical (or wave-by-wave) analysis from a time series of free surface elevation. It is usually denoted as H1/3. The spectral significant wave height, denoted by Hmo, is computed from the variance spectrum as Hmo = 4 sqrt(mo), where mo is the variance of the sea-state, computed as the integral of the variance spectrum. This spectral significant wave height is obtained from a spectral analysis. In deep and intermediate water depths H1/3 and Hmo can be considered as being (nearly) identical, but this is not true in shallow water and coastal areas ; that is why it is important to mark the difference between these two wave heights. Additional details can be found in textbooks on waves.
=> Note that TOMAWAC, being a spectral model, it can only predict and output the spectral significant wave height Hmo.
2) DMOY is the mean direction of the sea state, i.e. of the waves. It is the average direction (measured clockwise from the North), towards which waves propagate. The definition is given in Appendix 7 of the Tomawac manual, available online.
It has nothing to do with the current direction (if there is an ambiant current field).
3)I am not sure to understand your point. If you create a boundary condition on the significant wave height in the steering file, this boundary condition will be steady during the whole simulation with Tomawac. So it is fully normal that the wave height on the boundary doesn't decrease during the simulation !
If you want that the spectral significant wave height varies in time at the boundary, you have to modify the LIMWAC subroutine and code your desired law for evolution in time of Hmo at the boundary.
I am however not certain that this is what you meant, so do not hesitate to provide additional details regarding this point if I did not answer properly.
Regards,
Michel Benoit