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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?

I thought about this idea a long time ago. I will be very grateful for any useful answers.

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  • $\begingroup$ Well, the Reynolds number is already a measure of kinetic energy to dissipation through viscous effects (ie. the tendency to "gather" the fluid as you put it). And that already can be used to define boundaries for transition. So even if your description of potential energy were valid, at most you would be re-inventing something that the Reynolds number already does. But -- can you explain why you see potential energy as "gathering" the fluid? Potential energy can also be released to create kinetic energy, so it is not clear why it would have the effect you describe. $\endgroup$ – tpg2114 Mar 8 at 15:13
  • $\begingroup$ The terms kinetic energy and potential energy relate to conservative forms of mechanical energy. However, in fluid flow, the is also present non-conservative viscous dissipation of mechanical energy to internal energy. Viscous dissipation allows for the damping of disturbances to the flow. The balance between inertial and viscous dissipation is captured by the Reynolds number, which determines the transition from laminar to turbulent flow. $\endgroup$ – Chet Miller Mar 8 at 18:43

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