Heaving sphere in irregular waves¶
This comparison corresponds to the simulation of a sphere in heave motion submitted to irregular waves. The model is presented by the International Energy Agency (IEA) Offshore Energy System (OES) Task 10 [OES10] as a benchmark case for model validation and verification regrouping 25 organizations. The goal of this section is to compare the use of a linear and nonlinear approach for the computation of the hydrostatic and FroudeKrylov loads.
Description of the test case¶
The sphere considered in this simulation has a radius of \(5\) \(m\) and a total mass of \(2,618 .10^5\) \(kg\). At equilibrium, the center of the sphere is located on the mean water level and its center of gravity is located \(2\) \(m\) below the water line. Main properties of the sphere are presented in the next table.
Parameters  Values 

Radius  \(5\) \(m\) 
Initial sphere location  (\(0\), \(0\), \(0\)) 
Center of gravity  (\(0\), \(0\), \(2\)) 
Mass  \(261.8\times10^3\) \(kg\) 
Ixx  \(1.690\times10^6\) \(kg.m^2\) 
Iyy  \(1.690\times10^6\) \(kg.m^2\) 
Izz  \(2.606\times10^6\) \(kg.m^2\) 
Water detph  Inf 
Water density  \(1000\) \(kg/m^3\) 
K33  \(7.695\times10^5\) \(N/m\) 
K44  \(5.126\times10^6\) \(N.m\) 
K55  \(5.126\times10^6\) \(N.m\) 
The sphere is submitted to an irregular wave field propagating positive along the xaxis. A Jonswap wave spectrum is considered with a significant wave height (Hs) of \(0.5\) \(m\), a spectral peak period (Tp) of \(4.4\) \(s\) and a gamma factor (\(\gamma\)) of \(1\).
Effects of a nonlinear hydrostatic and FroudeKrylov approach¶
The time series of the floating heaving sphere in irregular waves are now compared. Two models are considered:
 a fully linear model;
 a weakly nonlinear model: the hydrostatic and FroudeKrylov loads are computed with a fully nonlinear approach.
The two time series are plotted in Fig. 40. Due to the small steepness of the waves (\(0.26\) %), the two models match perfectly, which validates their mutual implementation in irregular waves.
References¶
[OES10] 

[Nemoh] 
