Sec. 46.8 



DATA ON SEPARATION, EDDYING, AND VORTEXES 



HI 



as could be estimated by the eye), the highest part of the 

 ridge being certainly over 2 feet above the natural water- 

 level . . ." [Brit. Assn. Rep., 1874 (dated 1875), pp. 

 255-264]. 



Two references on this subject, listed in Sec. 7.2 

 of Volume I, are repeated here for the convenience 

 of the reader. These embody a multitude of 

 photographs taken through the water of a basin, 

 showing the air-filled separation zones abaft towed 

 vertical rods of finite lengths. They were made by 

 A. D. Hay and published in "Flow About Semi- 

 Submerged Cylinders of Finite Length," Bureau 

 of Ships, Navy Department, Contract NObs- 

 34006, dated 1 October 1947. Many other photo- 

 graphs of separation zones abaft box-shaped 

 forms, made by A. D. Hay and J. P. Runyon, are 

 embodied in "Photographs and Resistance Meas- 

 urements of Semi-Submerged Right Parallelepipe- 

 dons," Contract NObs-34006, dated I May 1947. 

 Copies of these reports are in the TMB hbrary. 



46.7 Vortex Streets and Related Phenomena. 

 Large vortexes, in pairs or in echelon, may be 

 and usually are shed from non-faired appendages 

 or blunt-ended objects, such as submarine 

 periscopes or thick propeller-blade sections. 

 Similar vortexes may be shed abaft faired append- 

 ages such as struts which are yawed slightly with 

 respect to the flow. The vortexes in pairs appear 

 at very low speeds and those in echelon at the 

 higher speeds. Schematic diagrams of these vortex 

 groups are given in Figs. 7.M, 14. W, 14.X and 

 23.E of Volume I, and in Figs. 40.A and 41. D of 

 the present volume. 



The mechanism by which, at certain combina- 

 tions of forward speed and appendage diameter 

 or thickness, the alternating circulation associated 

 with the shedding of these eddies produces 

 alternating transverse lift forces of considerable 

 magnitude on the moving body, is explained in 

 Sec. 14.22. 



For other treatments the reader is referred to 

 the following: 



(1) Ahlborn, F., "tjber der Mechanismus des hydro- 



dynamischen Widerstandes (On the Mechanism 

 of Hydrodynamic Resistance)," Hamburg, 1902 



(2) Benard, H., Comptes Rendus (in French), 1908:2, 



Vol. 147, pp. 839-842 and 970-972; 1913, Vol. 156, 

 p. 1225; 1926, Vol. 182, p. 1523; 1926, Vol. 183 



(3) Von Kdrmdn, T., Nachr. Ges. Wiss., Gottingen (in 



German), 1911, p. 509; 1912, p. 547 



(4) Von Kdrm^n, T., and Rubach, H., "tJber den 



Mechanismus des Flussigkeits- und Luftwider- 

 standes (On the Mechanism of Resistance in 

 Liquids and in Air)," Physikalische Zeitschrift, 15 

 Jan 1912. An English translation of this paper, 



with some additional material worked up by 

 T. von KArmdn, is given by G. de Bothezat in 

 NACA Rep. 28, 1918, Note IV, pp. 149-158. 



(5) Relf, E. F., and Simmons, L. F. G., "The Frequency 



of the Eddies Generated by the Motion of Circular 

 Cylinders through a Fluid," ARC, R and M 917, 

 1924 



(6) Zahm, A. F., "Flow and Drag Formulas for Simple 



Quadrics," NACA Rep. 253, 1927 



(7) Lagally, M., "Die reibungslose Stromung in Aussen- 



gebiet zweier Kreise (The Frictionless Flow About 

 Two Circles)," Zeit. fiir Ang. Math, und Mech., 

 Aug 1929 



(8) Rosenhead, L., Proc. Roy. Soc, A, 1930, Vol. 129, 



p. 115ff 



(9) Rosenhead, L., and Schwabe, M., "An Experimental 



Investigation of the Flow Behind Circular Cyl- 

 inders in Channels of Different Depths," Proc. 

 Roy. Soc, 1930 



(10) Biermann, D., and Herrnstein, W. H., Jr., "The 



Interference Between Struts in Various Com- 

 binations," NACA Rep. 468, 1933 



(11) Richards, G. J., "An Experimental Investigation of 



the Wake Behind an Elliptic Cylinder," ARC, 

 R and M 1590, 1934-1935, Vol. I, pp. 387-392 



(12) Prandtl, L., and Tietjens, O. G., AHA, 1934, text on 



pp. 130-136, diagram on p. 132, photos in Pis. 24, 

 25,26 



(13) Tietjens, O. G., and Prandtl, L., HAM, 1944, Vol. I, 



diagram only on p. 225 



(14) Lamb, H., HD, 1945, pp. 680-681 



(15) Rouse, H., EMF, 1946, pp. 239-241 



(16) Wright, E. A., SNAME, 1946, Fig. 3, p. 377 



(17) Rouse, H., EH, 1950, pp. 129-130 



(18) Rouse, H., and Howe, J. W., BMF, 1953, frontis- 



piece and Fig. Ill on p. 187. 



The reader who wishes to delve more deeply 

 into the analytic aspects of this matter is referred 

 to L. Landweber's treatment of this phenomenon 

 on TMB Report 485, dated July 1942. 



46.8 Vortex Streets and Vibrating Bodies. 

 The right-hand diagram of Fig. 46. G, adapted 

 from H. Rouse [EH, 1950, Fig. 93 and pp. 129- 

 130], gives quantitative data concerning the 

 vortex trail generated abaft a stationary 2-diml 

 circular cylinder in a uniform stream of velocity 

 U„ . It indicates that the whole system of alternate 

 vortexes left behind by a moving body in a 

 flowing stream, corresponding to this cylinder, 

 follows it with what may be termed a wake 

 velocity. For the cylinder shown the value of this 

 velocity is about 0.14 of the body speed, so that 

 the absolute downstream velocity of the system 

 of vortexes is about 0.86 1/» . The transverse 

 spacing a between the rows of alternate vortexes, 

 for the case of the cyUnder illustrated, is about 

 1.3D. The longitudinal spacing h between vor- 

 texes in either row is about 4.3D. 



