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Development of the flow field of a point force in an infinite fluid

Published online by Cambridge University Press:  19 April 2006

C. Sozou
C. Sozou
Affiliation:
Department of Applied Mathematics and Computing Science, University of Sheffield, England
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Abstract

By means of similarity principles an analytical solution is constructed for the development of the linear flow field due to the instantaneous application of a constant point force in an infinite liquid. If the force is applied at the origin O and if ν denotes distance from O, ν denotes the coefficient of kinematic viscosity of the fluid and t the time from the application of the force, the solution constructed exhibits the following features. Initially the flow field set up has a dipole structure with centre at O and axis along the direction of the impressed force. At a station r this dipole structure persists so long as 4νt [Lt ] r2. In an axial cross-section the field lines form two sets of closed loops about two stagnation points in the equatorial plane. The stagnation points occur at r = 1.76(νt)½ and thus propagate to infinity with speed 0.88(ν/t)½. The steady state is reached algebraically.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 91 , Issue 3 , 11 April 1979 , pp. 541 - 546
Copyright
© 1979 Cambridge University Press

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References

Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
Lighthill, M. J. 1976 SIAM Rev. 18, 161.
Lighthill, M. J. 1978 Waves in Fluids. Cambridge University Press.
Sozou, C. & Pickering, W. M. 1977 J. Fluid Mech. 80, 673.