Kajian Teoritis terhadap Persamaan Gelombang Nonlinier
DOI:
https://doi.org/10.5614/jts.2007.14.3.5Keywords:
Persamaan gelombang linier, Teori gelombang yang diturunkan untuk amplitudo gelombang sangat kecil, Teori gelombang nonlinier, Teori gelombang yang diturunkan untuk amplitudo gelombang yang cukup besar.Abstract
Abstrak. Paper ini menyajikan hasil perumusan persamaan gelombang nonlinier dengan prosedur yang lain. Dimana amplitudo gelombang, persamaan momentum dari Euler dan tekanan hidrodinamis dari Bernoulli sepenuhnya digunakan, tanpa pemotongan atau linierisasi. Potensial kecepatan dan persamaan dispersi yang dihasilkan menjadi persamaan gelombang linier bila digunakan amplitudo sangat kecil. Pada persamaan potensial kecepatan terdapat fenomena breaking, dengan bentuk yang sama dengan kriteria breaking dari Miche. Panjang gelombang yang dihasilkan dari persamaan dispersi adalah lebih kecil dari panjang gelombang dari teori gelombang linier. Peranan amplitudo gelombang pada persamaan dispersi adalah memperpendek panjang gelombang. Semakin besar amplitudo gelombang, semakin panjang gelombang.Abstract. This paper presents derivation of a nonlinear wave equation with different procedure. In which, wave amplitude, momentum Euler's equation and hydrodynamic pressure of Bernoulli are fully used and no linearization. The resulted potential and dispersion equation become equations of linier wave theory when small amplitude inserted to the equations. Velocity potential equation gives breaking phenomena that the same as Miche's breaking criteria. Wave length resulted from the dispersion equation shorter than wave length resulted by linear wave theory. Existences of wave amplitude in dispersion equation make wave length shorter. Larger wave amplitude shorter wave length.
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