λ θ = 0 k θ = 2π θ = 4π The wavelength of a plane wave The increase of phase in the direction of the wave vector 2 Figure 1 Figure by MIT OpenCourseWare
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then C(k) = D(k) and C(k)+ D(k) = 2C(k) = ˜ η o Then η(x,t) = 1 2 ˜ η o −∞ +∞ ∫ (k) e i(kx+ωt) + ei(kx−ωt) [ ]dk Now ω = (sign k)(gk) 1/2 to ensure that
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z = −1 R x (negative slope) Energy Energy 0 0 z x - Rz = 0 x - Rz = ct Plane c plane c // k x x x + Rz = 0 z cg cg 1 Figure by MIT OpenCourseWare
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Look for w = wo ei(kx+ly+mz- ωt) we get the dispersion relationship ω2 = f 2 m 2 + N2 (k 2 + l2 ) k 2 + l2 + m2 4 l k m ω Figure by MIT OpenCourseWare
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Let us consider the more general case of a wall inclined to the horizontal z = ax and let us. Figure by MIT OpenCourseWare.
Figure by MIT OpenCourseWare. Page 2. The equations have been linearized and as usual
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we use the summation convention over repeated indices and cgi = ??. ?ki by definition i = 1
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1. ut = -g?x. The pressure gradient along the wall determines the acceleration z y x. Ocean. Figure 13-1. Figure by MIT OpenCourseWare.
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04 Aug 2011 available online from MIT OpenCourseWare at http://ocw.mit.edu (accessed MM DD ... 802 pure b (units of 104 m2/V sec). 1.36 0.30 0.84 5.9.
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