Solitary waves in Poiseuille flow of a rotating fluid
Author:
Chia-Shun Yih
Journal:
Quart. Appl. Math. 52 (1994), 739-752
MSC:
Primary 76U05; Secondary 76B25
DOI:
https://doi.org/10.1090/qam/1306047
MathSciNet review:
MR1306047
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Abstract: Solutions are obtained for various modes of solitary waves in a strongly rotating fluid in Poiseuille flow. The nonlinear Bragg-Hawthorne equation is the basis of the theory, and the method of solution can be carried to any order of approximation. There are two sequences of modes, each infinite in number. One consists of modes travelling with the flow, called P modes, and the other consists of modes travelling against it, called N modes. Generally, the displacements of streamlines from their asymptotic positions are in opposite directions for two corresponding modes of the two sequences. In particular, the streamlines of the first mode travelling with the flow are displaced radially outward from their asymptotic positions, and those of the first mode travelling against the flow are displaced radially inward. In other words, the first P mode is a bulging wave, whereas the first N mode is a pinching or necking one.
S. L. Bragg and W. R. Hawthorne, Some exact solutions of the flow through annular cascade actuator discs, J. Aeronaut. Sci. 17, 243–249 (1950)
C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, Method for solving the Korteweg-de Vries equation, Phys. Rev. Lett 19, 1095–1097 (1967)
E. Jahnke and F. Emde, Table of Functions, Dover, New York, 1945
S. Leibovich, Weakly nonlinear waves in rotating fluids, J. Fluid Mech. 42, 803–822 (1969)
R. R. Long, Steady motion of a symmetric obstacle moving along the axis of a rotating fluid, J. Meteorology 10, 197 (1953)
C.-S. Yih, Solutions of the hyper-Bessel equation, Quart. Appl. Math. XIII, 462–463 (1956)
S. L. Bragg and W. R. Hawthorne, Some exact solutions of the flow through annular cascade actuator discs, J. Aeronaut. Sci. 17, 243–249 (1950)
C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, Method for solving the Korteweg-de Vries equation, Phys. Rev. Lett 19, 1095–1097 (1967)
E. Jahnke and F. Emde, Table of Functions, Dover, New York, 1945
S. Leibovich, Weakly nonlinear waves in rotating fluids, J. Fluid Mech. 42, 803–822 (1969)
R. R. Long, Steady motion of a symmetric obstacle moving along the axis of a rotating fluid, J. Meteorology 10, 197 (1953)
C.-S. Yih, Solutions of the hyper-Bessel equation, Quart. Appl. Math. XIII, 462–463 (1956)
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Article copyright:
© Copyright 1994
American Mathematical Society