why can a fluid not experience turbulence if we want to imply it with the Stokes law?

Question

is it because with turbulence the system gets complicated? if possible, please give some refenrence to your answer.... I am really trying to understand here....

Answer 1

There are several concepts in fluid mechanics related to Stokes name's:

* The Navier - Stokes Equation
* The Stokes Equation (for creeping flow, or very low speed flow)
*The Stokes hypotesis (to relate the thermodynamic pressure with the normal stresses in a fluid)
* The Stokes' Law

The Stokes' Law relates the drag force on a spherical body with the properties of the flow over this sphere. The equation
Fd = 6 * pi * radius * dynamic viscosity * sphere velocity
(see http://en.wikipedia.org/wiki/Stokes_law)
is valid only when the Reynolds number is extremely small, below 1.

The Stokes' Law could be obtained from the Navier-Stokes. The convective term should be dropped from the equation, since its effect its really small, due to the low Reynolds.

The convective term (see http://en.wikipedia.org/wiki/Navier-Stokes_equations) its the one which give the nonlinear behavior to the Navier-Stokes equation. This behavior allows the existence of different solutions, some of them stable and some of them unstable.

The turbulence only arise in the presence of the non-linearity already mentioned. If the convective term its dropped from the governing equations, they become linear in terms of velocity, and turbulence doesn't arise.

You could find more detailed information about the development of Stokes Law and transition to turbulence in these books:

H. Schlichting "Boundary Layer Theory"
G.K. Batchelor "An Introduction to Fluid Dynamics"
I.G. Currie "Fundamental Mechanics of Fluids"

Answer 2

Because stokes law is only for non-turbulent systems.

When systems get turbulent, they have to be described differently because they behave differently than non-turbulent systems.

There is not a lot to understand. Use the formulae that suite the situation.