Green-Naghdi(G-N)theoryisafullynonlineartheoryforwaterwaves.SomeresearcherscallitafullynonlinearBoussinesqmodel.DifferentdegreesofcomplexityofG-Ntheoryaredistinguishedby"levels"wherethehigherthelevel,themorecomplicatedandpresumablymoreaccuratethetheoryis.IntheresearchpresentedhereacomparisonwasmadebetweentwodifferentlevelsofG-Ntheory,specificallylevelIIandlevelIIIG-Nrestrictedtheories.AlinearanalyticalsolutionforlevelIIIG-Nrestrictedtheorywasgiven.WavesonaplanarbeachandshoalingwaveswerebothsimulatedwiththesetwoG-Ntheories.ItwasshownforthefirsttimethatlevelIIIG-Nrestrictedtheorycanalsobeusedtopredictfluidvelocityinshallowwater.AlevelIIIG-NrestrictedtheoryisrecommendedinsteadofalevelIIG-Nrestrictedtheorywhensimulatingfullynonlinearshallowwaterwaves.
