# Is that reasonable to use kinetic energy and potential energy of a fluid system to define the laminar, transition and turbulent region?

This is my assumption ( I don't know whether it exists or not ):

I suppose a fluid system always contains two types of energy, i.e., kinetic energy and potential energy. The kinetic energy of a fluid system $$E_k$$ is the energy that tends to disperse the mass of fluid. However, the potential energy $$E_p$$ is the energy that tends to 'gather' the mass of fluid, so that it does not disperse instantaneously.

These energies are constantly changing with respect to time,

$$E_k \propto t$$ and $$E_p \propto \frac{1}{t}$$

When $$t \rightarrow \infty$$,

$$E_k \rightarrow \infty$$ and $$E_p \rightarrow 0$$

If my assumption is correct, then I think there is such an instant time $$T_f$$ that the kinetic energy and potential energy are equal to each other (They balance each other). So that, I can define laminar, transition, and turbulence region as

Laminar region: At time $$(0,T_f)$$, $$E_p > E_k$$

Transition region: At time $$T_f$$, $$E_p = E_k$$

Turbulence region: At time $$(T_f, \infty)$$, $$E_p < E_k$$

My question is

(i) Is my assumption reasonable? If not, then why?

(ii) Has anyone already developed this theory?

(iii) Are the concepts of kinetic energy and potential energy I used in my theory reasonable? If so, can you mathematically derive them?