From your question it seems like you are familiar with linear Response Amplitude Operators (RAO's) for floating objects, giving vessel responses to unit waves of different periods (1st order wave motions). 

It seems like this paper will describe what you are looking for;  (2nd order wave motions)

“Slow Drift-Oscillations of a Ship in Irregular Waves”

Authors: Odd M. Faltinsen and Arne E. Løken,

Affiliation: NTNU and Det Norske Veritas (DNV) 

http://www.mic-journal.no/ABS/MIC-1980-4-1.asp

The low-frequency responses are the motions caused mainly by second-order wave loads, current, mean wind component, mooring systems and thrusters.

Less obvious and perhaps not immediate focus may be the direction of waves and heading.   Compounding this is the steering system (human and/or machine) aimed at maintaining a heading.  Helms-men/-persons (human control) often differ profoundly in their strategies for maintaining heading, e.g., one may chase a fixed heading as a ship yaws (and occasionally drop off a wave as fixated on the chase); while a second may let the ship move through a yaw cycle with aim to keep vessel on average on assigned heading [when asked heading, may reply at x-heading coming to Y the assigned heading).   Both of these strategies have been programmed into autopilot systems...  These strategies, it is noteworthy, can have profound effects with bow-thrusters that can snap any off heading deviation into that desired.   These control system effects can -- and do lead -- to quite large effects on the human crew and passengers in safety, task performance and motion sickness.  

My late colleague John Guignard and I were particularly concerned with motion sickness:

Bittner, A.C., Jr., & Guignard, J.C. (1988). Shipboard evaluation of motion sickness incidence. In F. Aghazadeh (Ed.), Trends in ergonomics/human factors V (pp. 529-541).  New York: North-Holland.

Bittner, A.C., Jr., & Guignard, J.C. (1985a). Human factors engineering principles for minimization of adverse ship motion effects: Theory and practice. Naval Engineers Journal, 97(4), 205-213.

Bittner, A.C., Jr., & Guignard, J.C. (1985b). Reply by the authors [to comments re: "Human factors engineering principles..."]. Naval Engineers Journal, 97(5), 109-111.

In my point of view, it is the response of the ship or floating structure to the large wave lengths (may linear or non-linear). Please refer to the dispersion relation of the linear wave theory for more details about the wave length and frequency.