tailieunhanh - BASIC COASTAL ENGINEERING Part 3

Tham khảo tài liệu 'basic coastal engineering part 3', kỹ thuật - công nghệ, kiến trúc - xây dựng phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 58 Basic Coastal Engineering H __sinh3 kd L p cosh kd 2 cosh 2 kd In deep water the steepness value given by Eq. is greater than 1 7 so the limit has no practical meaning. For a relative depth d L as small as the limiting steepness from Eq. is . This puts a significant restriction on the use of the second-order theory as the wave propagates into shallower water. The Stokes second-order equations for particle velocity and acceleration follow pH cosh k d z u r Zu 1 7 cos kx - st T sinh kd 3 pH 2 cosh 2k d z 1 ------- cos 2 kx - st 4TL sinh4 kd w pH z sin kx - st T sinh kd 3 pH 2 sinh 2k d z . z ---- . sin2 kx - st 4TL sinh4 kd ax az 2p2H cosh k d z . . ZuZ sin kx - st T2 sinh kd 3p3H2 cosh 2k d z TL sinh4 kd sin2 kx -st 2p2H sinh k d z 7 7 cos kx - st T2 sinh kd 3p3H2 sinh 2k d z ----Zul 7----cos 2 kx - st T2L sinh kd The second-order terms in Eqs. to also have twice the frequency of the first-order terms leading to asymmetries in the particle velocity and acceleration as a particle completes its orbit. The particle velocity and acceleration are increased under the wave crest and diminished under the wave trough. Again these asymmetries increase as the wave steepness increases. Since the horizontal component of particle velocity is maximum at the wave crest and trough and zero at the still water positions this crest trough asymmetry in velocity causes particle orbits that are not closed and results in a small drift of the water particles in the direction of wave propagation. This mass transport is also evident in the second-order particle displacement equations. Finite-Amplitude Waves 59 Ỉ - H s - d kx - st 2 sinh kd pH2 k 3cosh2k d z . . 1-------- sin 2 kx st 8L sinh2 kd V 2 sinh2 kd J pH2 cosh 2k d z r- ----------------st 4L sinh2 kd H z z c s tx - st 2 sinh kd 3 pH2 sinh 2k d z -----. cos2 kx - st 16L sinh4 kd Note that the last term in Eq. is not periodic but continually increases

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