淺水波譜形狀特性之研究

Abstract

當波浪自深水進入淺水時，波浪各種機構均變得比較複雜，對於波譜形狀 也不像深水波一樣是一個固定形狀。本文擬以實驗室利用不規則造波機， 以不同水深、不同造波條件，進行不規則造波試驗以決定淺水波譜的形狀 經驗表示式。對於形狀的決定，是以 Pierson-Moskowitz通用型標準波譜 改變其中的波譜形狀參數以適合實驗值來代表實驗波譜的形狀。由實驗結 果證明波譜形狀參數只與相對水深有關，所得的經驗式可提供做一參考。 同時由底床坡度1:30與1:50的試驗得知，底床坡度(緩坡)並不會影響到此 經驗式的適用性。相對水深界於0.3 至0.05之間，由二階係數可知主頻處 應為線性波；非線性波應出現在二倍主頻處，其非線性量約佔線性量的15 ﹪以內，但由於此處能量很小，故非線性的影響應是可以忽略的。相對水 深小於0.05時，波譜形狀分裂成雙峰型，由二階係數可知分裂時在高頻處 所產生第二尖峰的成分波仍是線性波。且隨著波浪的進行，波譜會漸漸地 變成單一波峰型波譜，但主頻略往高頻處移動，非線性量會逐漸的減少。 由本次實驗結果可知，底床摩擦、非線性效應並不是造成波譜形狀變緩的 原因，其原因仍有待研究。 Spectral analysis is a useful method for describing the random waves. Due to the complexity of wave mechanism, it is likely to lack of standard form for shallow water wave. In this study, we use the laboratory wave data obtained in different wave conditions to determine a generalized power spectral form of shallow water waves. From the experimental results, we find the parameter m used in Pierson-Moskowitz is only the function of relative water depth so that we have a empirical formula to determine the spectral form.For the bottom slope,our experiments take the bed slope 1:30 and 1:50.We find that the bottom slope has not obvious effect on the empirical formula. By using of bispectrum theory to judge nonlinear quantities, we find that the nonlinear component energy occupied the total energy about 15﹪when relative water depth between 0.3 and 0.05. When the relative water depth is less than 0.05, the spectral shape will become double peak types. From the results, the shape of the power spectral form becomes milder in shallow water. It is concluded that the milder shape of shallow water wave spectrum can not be completely attributed to nonlinear interaction and bottom friction.