Stochastic Forcing Model for the Generation and Evolution of Infragravity waves by Short Gravity Surface Waves

A stochastic forcing model has been developed to estimate the heights of infragravity waves excited by short gravity surface waves. The model includes a wave equation for infragravity waves with the external force term due to pressure disturbances by short gravity waves. The analytical solution of the wave equation was obtained, and the root-mean-square value of the surface elevation of infragravity waves was estimated. The rms value is proportional to the square root of the spectral moment of -2 order, m-2, of short gravity waves, which is also proportional to the product of the wave height and the peak wave period or the significant wave period of short gravity waves. The estimated rms heights of infragravity waves are compared with the observed data compiled by NOWPHAS and show good agreements with them.