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Oscillatory solution in rotating flow of a Johnson-Segalman fluid. (English) Zbl 1071.76063
Summary: A study is made of the flow engendered in a Johnson-Segalman, incompressible, rotating fluid bounded by a plate. Both the plate and the fluid are in a state of solid body rotation, and additionally a non-torsional oscillation of given frequency is superimposed on the plate for the generation of flow in the rotating system. The governing equations of motion for rotating flow of a Johnson-Segalman fluid are constructed. Periodic solutions are obtained for small Weissenberg number, and we find that a Stokes-Ekman layer is formed on the plate for all frequencies except for the resonant frequency, which is twice the angular velocity of rotation. In the later case there is no oscillatory solution which satisfies the boundary conditions. The structure of the associated boundary layers for non-resonant case is determined.

MSC:
76U05 General theory of rotating fluids
76A10 Viscoelastic fluids
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
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References:
[1] Greenspan, J. Fluid Mech. 17 pp 385– (1963)
[2] Debnath, Acta Mech. 18 pp 333– (1973)
[3] Debnath, Z. Angew. Math. Mech. 55 pp 431– (1975)
[4] Mukherjee, Z. Angew. Math. Mech. 57 pp 188– (1974)
[5] Gupta, Phys. Fluids 15 pp 930– (1972)
[6] Thornley, Quart. J. Mech. Appl. Math. 21 pp 451– (1968)
[7] Soundalgekar, Z. Angew. Math. Mech. 58 pp 718– (1973)
[8] Singh, Z. Angew. Math. Mech. 80 pp 429– (2000)
[9] Mazumder, Trans. ASME, J. Appl. Mech. 58 pp 1104– (1991)
[10] Ganapathy, Trans. ASME, J. Appl. Mech. 61 pp 208– (1994)
[11] Rajagopal, J. Non-Newton. Fluid Mech. 48 pp 239– (1984)
[12] Erdogan, Acta Mech. 108 pp 179– (1995)
[13] Garg, Acta Mech. 88 pp 113– (1991)
[14] Rajagopal, Int. J. Non-Linear Mech. 17 pp 369– (1982)
[15] and 18, 313-320 (1983).
[16] Hayat, Acta Mech. 131 pp 169– (1998)
[17] Hayat, Int. J. Eng. Sci. 38 pp 337– (2000)
[18] Hayat, Int. J. Non-Linear Mech. 36 pp 901– (2001)
[19] Puri, Appl. Anal. (UK) 4 pp 131– (1974)
[20] Puri, Z. Angew. Math. Mech. 54 pp 743– (1974)
[21] Johnson Jr., J. Non-Newton. Fluid Mech. 2 pp 255– (1977)
[22] Migler, Phys. Rev. Lett. 70 pp 287– (1990)
[23] Migler, J. Phys., Condens. Matter. 6 (1994)
[24] Ramamurthy, J. Rheol. 25 pp 337– (1986)
[25] Kraynik, J. Rheol. 25 pp 95– (1981)
[26] Lim, J. Rheol. 33 pp 1359– (1989)
[27] Kalika, J. Rheol. 31 pp 815– (1987)
[28] Rao, Acta Mech. 132 pp 209– (1999)
[29] Rao, Int. J. Non-Linear Mech. 34 pp 63– (1999)
[30] Beard, Proc. Camb. Philos. Soc. pp 60– (1964)
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