Internal Wave Generation in Uniformly Stratified Fluids. 1 ... - LEGI

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Internal wave generation. 1. Green’s function 58 Figure 9. Points of contact T + and T – of the uppermost and lowermost tangents from a point r to the sphere. Figure 10. Boussinesq internal wave field of a monochromatically pulsating sphere. Waves are confined in regions III and V, bounded by characteristic cones of semi-angle θ 0 = arc cos (ω/N). There, coordinates σ ± describe transverse distances, with which the phase variates. Figure 11. Boussinesq internal wave field of an impulsively pulsating sphere. Out of the characteristic torus of radius Nta gravity waves, whose surfaces of constant phase are conical (cf. figure 2), dominate. Inside the torus they give way to buoyancy oscillations, whose phase is constant. Figure 12. Original integration path (dotted line), and steepest descent contours (heavy lines), for the asymptotic expansion of (D12). The saddle points ω 1 and ω 2 are situated a distance (α/2t) 2/3 from the origin ω 3 = 0 which makes no contribution to the expansion.
TYPE OF WAVE acoustic electromagnetic gravity SMALL SOURCE a « λ a « λ r » Nt a sin θ NEAR ZONE FAR ZONE a « r « λ →incompressible fluid a « λ « r → radiation of acoustic waves a « r « λ →static fields a « λ « r → radiation of electromagnetic waves Table 1 → outside the characteristic torus Nt « 1 and r » a →homogeneous fluid Nt » 1 and r » Nt a sin θ → radiation of gravity waves
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Internal Wave Generation in Uniform
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1. INTRODUCTION Internal gravity wa
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2. BIBLIOGRAPHICAL REVIEW Investiga
Page 7 and 8: 3. STATEMENT OF THE PROBLEM 3.1. In
Page 9 and 10: Internal wave generation. 1. Green
Page 13 and 14: the source, but disappear as soon a
Page 15 and 16: 5. EXACT GREEN’S FUNCTION 5.1. Mo
Page 17 and 18: theorem and the radiation condition
Page 19 and 20: G(r, t) = 1 8π 2 r +∞ - ∞ e i
Page 21 and 22: 6. ASYMPTOTIC GREEN’S FUNCTION 6.
Page 23 and 24: To better exhibit the angular depen
Page 25 and 26: inverse group velocity with horizon
Page 27 and 28: time-dependent internal wave fields
Page 29 and 30: particles move as expected along ra
Page 31 and 32: and for the displacement vector ζ
Page 33 and 34: Thus, buoyancy waves have simultane
Page 35 and 36: and apply Pierce’s (1963) procedu
Page 37 and 38: ω v (r, ω) ~ U(ω) 2 ω2 - N2 1/2
Page 39 and 40: egion III remains integrable, and t
Page 43 and 44: 9. CONCLUSION Internal wave generat
Page 45 and 46: Let us finally emphasize that, howe
Page 47 and 48: P(r, ω) = F0z ω2 4πr 2 ω2 - N2
Page 49 and 50: educes to the Green’s function. N
Page 51 and 52: Appendix D. SOME INVERSE FOURIER TR
Page 57: CAPTIONS Table 1. Compared structur
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Internal Wave Generation in Uniformly Stratified Fluids. 1 ... - LEGI

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