The transient for Stokes's oscillating plate: a solution in terms of tabulated functions
- 29 January 1968
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 31 (4), 819-825
- https://doi.org/10.1017/s0022112068000509
Abstract
The motion of a semi-infinite incompressible fluid caused by the sinusoidal oscillation of a plane flat plate is termed Stokes's problem. When the plate starts from rest in a still fluid a transient solution must be added to Stokes's well-known steady-state result. This paper presents a closed-form expression for the transient solution. Previous answers have contained a non-standard integral which could not be evaluated. The answer presented herein contains exponentials and error functions of a complex argument. These functions are readily available in newer mathematical tables. Graphs of the transient solution are presented for both sin (T) and – cos (T) boundary conditions. Velocity distributions in the fluid are also plotted and it is found that the transient period is essentially complete in one-half cycle for the cosine oscillation and in a full cycle for the sine wave case.Keywords
This publication has 1 reference indexed in Scilit:
- Formulas for Calculating the Error Function of a Complex VariableMathematical Tables and Other Aids to Computation, 1951