We are all familiar with the fact that a linear flow of water in a tube can be
obtained only for velocities below a certain critical limit and that, when the
velocity exceeds this limit, laminar flow ceases and a complex, irregular,
and fluctuating motion sets in. More generally than in this context of flow
through a tube, it is known that motions governed by the equations of Stokes
and Navier change into turbulent motion when a certain nondimensional constant
called the Reynolds number exceeds a certain value of the order of 1000. This Reynolds number depends
upon the linear dimension, L, of the system, the coefficient of viscosity, u,
the density, o, and the velocity v in the following manner R=ovL/u.
Following Chandrasekhar we can make us the question: What is the reason
that a phenomenon like turbulence can occur at all?. We describe the turbulence in fluids as a consequence of the inherent
discontinuity of matter. We start with the description of matter density as
a discontinuous Dirichlet integral function, and through the Euler equation
for matter conservation, we obtain a differential equation which implies a
transference of velocity (and then energy) from one eddys to others, i.e.
from one scale to another, which is one of the main observational features
of turbulence.