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KUNDU Fluid Mechanics 2E Episode 15

Tham khảo tài liệu 'kundu fluid mechanics 2e episode 15', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 604 icophỵHÌcal Fluid Ifyiiamicji time corresponding to a t 0 jr 2 and 7T. It is clear that the horizontal hodographs are clockwise ellipses with the major axis in the direction of propagation X and the axis ratio is f ứ. The same conclusion applies for the lower signs in Eq. 14.110 . The particle orbits in the horizontal plane arc therefore identical to those of Poincare waves Figure 14.16 . However the plane of the motion is no longer horizontal. From the velocity components Eq. 14.108 we note that u m F-r Ftan0 14.111 w k where 0 lan-1 m fc is the angle made by the wavenumber vector K with the horizontal Figure 14.24 . For upward phase propagation Eq. 14.111 gives u w tanớ so that w is negative if is positive as indicated in Figure 14.24. A three-dimensional sketch of the particle orbit is shown in Figure 14.23b. It is easy to show Exercise 6 that the phase velocity vector c is in the direction of K that c and Cg arc perpendicular and that the fluid motion u is parallel to cg these facts are demonstrated in Chapter 7 for internal waves unaffected by Coriolis forces. The velocity vector at any location rotates clockwise with time. Because of the vertical propagation of phase the tips of the instantaneous vectors also turn with depth. Consider the turning of the velocity vectors with depth when the phase velocity is upward so that the deeper currents have a phase lead over the shallower currents Figure 14.25 . Because the currents at all depths rotate clockwise in time whether the vertical component of c is upward or downward it follows that the tips of the instantaneous velocity vectors should fall on a helical spữal that turns clockwise with depth. Only such a turning in depth coupled with a clockwise rotation of the velocity vectors with time can result in a phase lead of the deeper currents. In the opposite Figure 14.24 Vertical section of an internal wave. The three parallel lines arc constant phase lines with the arrows indicating fluid motion along the .