Study On Rational Fraction Spectrum Of Random Waves In Waters Near Islands And Reefs

Wave spectrum is the main mathematical tool to describe random waves.For deep water wave spectrum,P-M spectrum,ITTC spectrum,JONSWAP spectrum and other forms have been developed.Because the shallow water wave is obviously affected by topography,the correlation between the shallow water wave spectrum and the sea area is high,and most of the measured results are relatively few.At present,a common method for shallow water random wave spectrum analysis is to add a correction function considering water depth on the basis of deep water wave spectrum.This method does not consider the deformation and nonlinear effects of shallow water waves,especially the energy distribution at high and low frequencies.The sea floor topography of the South China Sea varies dramatically,with a large number of reefs distributed near the shore,and it is located in the open area of the Western Pacific Ocean,which is easily affected directly or indirectly by typhoons.Neither deep water spectrum nor shallow water spectrum can perfectly describe the wave characteristics in the near reef area.Therefore,it is necessary to carry out further research on the waves near the islands and reefs.Taking the South China Sea as the background,this paper conducts the following studies on random waves in the near-reef waters:(1)By carrying out field survey research to analyze the wave characteristics near the islands and reefs.Since 2014,with the support of the national 973 major project and the Ministry of Industry and Information Industry,the project team has continuously observed on an island in the Xisha area of the South China Sea and obtained detailed wave observation data.Based on the measured data and statistical methods,the random wave process in the coastal area under the influence of typhoon and non-typhoon weather is studied.The results show that the waves in non-typhoon weather can be described by a smooth narrowband Gaussian random process within 30 minutes to 3 hours.Waves in typhoon weather can be described by a smooth narrowband Gaussian random process in 30 minutes to 1 hour.(2)A new form of wave spectrum,rational fraction wave spectrum,is proposed for waves near islands and reefs.Through the analysis of the measured wave spectra near the islands and reefs under the influence of typhoon,it is found that there are three typical wave spectra near the islands and reefs: unimodal spectrum,bimodal spectrum and platykurtic spectrum.The change of the spectrum type is directly related to the action distance of the typhoon.The strong nonlinearity and weak dispersion of island wave make the wave spectrum of Island Reef have more energy distribution at high frequency region,which can not be well described by traditional wave spectrum.Therefore,a new form of rational fractional wave spectrum is proposed.Rational fraction spectrum can also describe bimodal spectrum and platykurtic specrum.Through verification of a large number of measured spectra,the rational fraction spectrum can well describe the characteristics of island reef wave spectra.(3)Three methods for determining parameters in rational fraction spectrum are given.The first method is based on the derivation of rational fraction formula to establish the functional relationship between continuous 4-order spectral moments and rational fraction wave spectrum parameters.In the second method,a method to determine the spectral parameters of rational fractions according to the spectral half-moment is proposed by analyzing the variation law of rational fractions.The method is half empirical and half theoretical.Third,an empirical method is proposed to determine the environmental parameters of rational fraction spectrum parameters according to wave height,wave period and wind speed according to the variation of environmental parameters and spectrum type correlation analysis.