1. 烟圈

4. Mount Etna

7. Extract from the Gallery of Fluid Motion, Physics of Fluids A, Vol
Extract from the Gallery of Fluid Motion, Physics of Fluids A, Vol. 5, September Contribution by Hiroshi Higuchi (Syracuse University).

9. This picture was taken for the Cessna Company by Mr. Paul Bowen
This picture was taken for the Cessna Company by Mr. Paul Bowen. As the trailing vortices descended over the fog layer due to the downwash, the flow field in the wake was made visible by the distortion of the fog layer. For details on the flight, see Cessna.

11. Picture courtesy of DANTEC Measurement Technology.

12. James E. Hobbs, from Lockheed Aircraft service Co
James E. Hobbs, from Lockheed Aircraft service Co., Ontario, California

13. Hurricane Laura Sept

15. vortex

16. 北半球 大型自由涡

17. Chapter 14 flow with moderate Re

18. Flow around a cylinder

19. Integral analysis, mass conservation

20. Integral analysis, momentum

22. Reynolds Number Dependency
Transition to turbulence
300 < Rd < 3*105
3*105 < Rd < 3.5*106
3.5*106 < Rd

28. Classic VIV Catastrophe
If ignored, these vibrations can prove catastrophic to structures, as they did in the case of the Tacoma Narrows Bridge in 1940.

29. Shear layer instability causes vortex roll-up
Flow speed outside wake is much higher than inside
Vorticity gathers at downcrossing points in upper layer
Vorticity gathers at upcrossings in lower layer
Induced velocities (due to vortices) causes this perturbation to amplify

30. Wake Instability

31. Classical Vortex Shedding
Von Karman Vortex Street
Alternately shed opposite signed vortices

32. Additional VIV Parameters
Reynolds Number
subcritical (Re<105) (laminar boundary)
Reduced Velocity
Vortex Shedding Frequency
S0.2 for subcritical flow

33. Strouhal Number vs. Reynolds Number

34. Vortex Shedding Generates forces on CylinderUo
Both Lift and Drag forces persist on a cylinder in cross flow. Lift is perpendicular to the inflow velocity and drag is parallel.
FL(t)
FD(t)
Due to the alternating vortex wake (“Karman street”) the oscillations in lift force occur at the vortex shedding frequency and oscillations in drag force occur at twice the vortex shedding frequency.

35. Vortex Induced Forces
Due to unsteady flow, forces, X(t) and Y(t), vary with time.
Force coefficients:
D(t)
1/2 r U2 d
L(t)
1/2 r U2 d
Cx =
Cy =

37. VIV in the Ocean
Non-uniform currents effect the spanwise vortex shedding on a cable or riser.
The frequency of shedding can be different along length.
This leads to “cells” of vortex shedding with some length, lc.

38. VIV Suppression Helical strake Shroud Axial slats Streamlined fairing
Splitter plate
Ribboned cable
Pivoted guiding vane
Spoiler plates

39. VIV Suppression by Helical Strakes
Helical strakes are a
common VIV suppresion
device.