Laminar boundary layer on an impulsively started rotating sphere

The problem of determining the development with time of the flow of a viscous incompressible fluid outside a rotating sphere is considered. The sphere is started impulsively from rest to rotate with constant angular velocity about a diameter. The motion is governed by a coupled set of three nonlinear time‐dependent partial differential equations which are solved by first employing the semi‐analytical method of series truncation to reduce the number of independent variables by one and then solving numerically a finite set of partial differential equations in one space variable and the time. The calculations have been carried out on the assumption that the Reynolds number is very large. The physical properties of the flow are calculated as functions of the time and compared with existing solutions for large and small times. A radial jet is found to develop with time near the equator of the sphere as a consequence of the collision of the boundary layers.

[1]  F. Smith,et al.  SEPARATION OF JETS OR THERMAL BOUNDARY LAYERS FROM A WALL , 1977 .

[2]  S. Nigam.  Note on the boundary layer on a rotating sphere , 1954 .

[3]  K. Stewartson.  On rotating laminar boundary layers , 1958 .

[4]  S. Dennis,et al.  Flow past an impulsively started circular cylinder , 1973, Journal of Fluid Mechanics.

[5]  L. Howarth.  CXXIX. Note on the boundary layer on a rotating sphere , 1951 .

[6]  W. E. Milne.  Numerical Solution of Differential Equations , 1953 .

[7]  S. Dennis,et al.  Calculation of the flow between two rotating spheres by the method of series truncation , 1978 .

[8]  K. S. Rangasami,et al.  Growth of boundary layer on a rotating sphere , 1953 .

[9]  The circle at low Reynolds number as a test of the method of series truncation , 1966 .

[10]  K. E. Barrett.  On the impulsively started rotating sphere , 1967, Journal of Fluid Mechanics.

[11]  W. Banks.  The laminar boundary layer on a rotating sphere , 1976 .

[12]  D. Joseph,et al.  Viscous incompressible flow between concentric rotating spheres. Part 1. Basic flow , 1971, Journal of Fluid Mechanics.

[13]  D. Greenspan.  Numerical studies of steady, viscous, incompressible flow between two rotating spheres , 1975 .

[14]  W. Banks.  THE BOUNDARY LAYER ON A ROTATING SPHERE , 1965 .

[15]  E. R. Benton.  Laminar boundary layer on an impulsively started rotating sphere , 1965, Journal of Fluid Mechanics.

[16]  C. Pearson.  A numerical study of the time-dependent viscous flow between two rotating spheres , 1967, Journal of Fluid Mechanics.

[17]  R. Manohar,et al.  The boundary layer on a rotating sphere , 1967 .

[18]  F. P. Bowden,et al.  The aerodynamic resistance to a sphere rotating at high speed , 1963, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[19]  C. R. Illingworth.  I. Boundary Layer growth on a spinning body , 1954 .