In fluid dynamics, Rayleigh problem also known as Stokes first problem is a problem of determining the flow created by a sudden movement of an infinitely long plate from rest, named after Lord Rayleigh and Sir George Stokes.
This is considered as one of the simplest unsteady problems that have an exact solution for the Navier-Stokes equations.
The impulse movement of semi-infinite plate was studied by Keith Stewartson.
[1] Consider an infinitely long plate which is suddenly made to move with constant velocity
in an infinite domain of fluid, which is at rest initially everywhere.
The flow is only due to the motion of the plate, there is no imposed pressure gradient.
Hence a self-similar variable can be introduced[4] Substituting this the partial differential equation, reduces it to ordinary differential equation with boundary conditions The solution to the above problem can be written in terms of complementary error function The force per unit area exerted on the plate is Instead of using a step boundary condition for the wall movement, the velocity of the wall can be prescribed as an arbitrary function of time, i.e.,
Then the solution is given by[5] Consider an infinitely long cylinder of radius
is the modified Bessel function of the second kind.
The force per unit area exerted on the cylinder is where
Exact solution is also available when the cylinder starts to slide in the axial direction with constant velocity