On the Origin of Turbulence

Abstract

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 (P. Bradshaw, 1978). This Reynolds number depends upon the linear dimension, L, of the system, the coefficient of viscosity μ, the density ρ, and the velocity v in the following manner $R = \frac{\rho vL}{\mu}$. Following (S. Chandrasekhar (1949), ApJ 110, 329) 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.