Study on reverse calculation for unidirectional waves from shallow water

In the coastal region, some wave measurements are usually deployed in shallow water. However, the knowledge of deep-water waves is more required in some cases. Targeting the east coast of Taiwan with a steep slope, we experimentally detect the capability of the linear spectrum theory in reversely estimating unidirectional deep-water waves from the shallow-water waves. Tank experiments of irregular waves show that the nonlinearity of wave-wave interactions significantly contributes to the total energy transfer. The energy of incident waves around peak frequency is transferred to lower and higher frequency domains. Even though waves are travelling through a short distance under a steep slope, the nonlinear wave-wave interactions cannot be neglected. In the application of the linear spectrum theory, the reversely calculated deep-water spectrum is found to be overestimated in frequency over 2Hz and in total energy of spectrum, but underestimated around peak frequency. There is evidence to show that the ratio of H 1/3 /Hs is correlated with the spectral bandwidth and Kurtosis.