# Why does analytical far field solution not match theoretical solution from savemotion? (Wavepaddles)

Hi,

I have some trouble understanding where the theoretical solution of savemotion in Wavepaddles comes from, and why it does match simulated data better then far field analytical solution (see below).

Wave Parameters are the following:

**Type Paddle: Flap-Regular**

** Depth: 0.6 [m] (VariableDraft: 0 [m])**

** WaveOrder: 1st**

** WaveHeight: 0.0588 [m]**

** WavePeriod: 0.87679 [s]**

** WaveLength: 1.19589 [m]**

** Relative depth (d/L): 0.501716 (Deep water)**

** GainStroke: 1**

"simulated" comes from measuretool at x = 6 m.

"theoretical" means the solution which comes from savemotion

"analytical" is defined from Altomare (2017) as:

My concern is the following:

Why do I observe a slight shift in positive eta-direction of "theoretical" and "simulated" wave displacement, while I don't observe it in the "analytical" solution. Meaning the peaks are at >0.3 and the valleys >-0.3, which means the waves do not oscillate symmetrically around 0. This is something I have observed also in other publications ((Altomare (2017)), (Altomare (2015), Trimulyono(2018)), so it seems to be expected, but still I don't understand why above analytical solution doesn't follow that behavior. As I am measuring at x = 6m with a wavelength of 1.2m, I should already converge towards far field solution, so that should not be the problem here.

Could you please give me a hint on that, and explain where the equations from "theoretical" solution from?

I would be very thankful for that.

## Comments

I did figure out the problem here.

I mixed "elevation_o1" (first order solution) and "elevation_o2" (second order solution) from the wave generator file.

I made the same mistake haha, don't worry! Wish they would have written "order" 🤣

Kind regards

Indeed the difference you were observing is due to the 2nd order wave theory applied, where wave crest is sharper and wave trough is less deep.