Project

# Turbulence

Goal: Searching the answers for the ideas which have raised from my own observation in nature related to Turbulence.

Date: 20 August 2012

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## Project log

This picture shows the how the wave's accumulates in Froude = Sqrt 3 The angle is ASIN(sqrt3/3) =35.26439 degrees.
The attached pictures are from book;
Hydraulics of Open Channel Flow
From Hubert Chanson

Searching the answers for the ideas which have raised from my own observation in nature related to Turbulence.

This diagram was missing on my properly written dokument. It's a key part and was already on the hand written version.

The Figure 8 from the research HYD-399 from The US Bureau of Reclamation from year 1955 shows clearly, how the enegy loss of hydraulic Jump is zero At Fr < 1.73. This is clearly against the old equation of Bresse. And Also "impossible" within the present NS-Equations. It's thus the experimental proof for the extened equations and ideas I present in my papers. This study can be found here in full length; https://www.usbr.gov/tsc/techreferences/hydraulics_lab/reportsdb/wrrl_reports_action.cfm search "HYD-399" Also "HYD-380" and "HYD-415" are related.
Navier-Stokes Excistence and smoothness problem doesn't have solution. The physical premises of this mathematical problem is not correctly understood. Turbulence is a "crack" on fluid; Internal surfaces inside the fluid. It's Collision and friction, not viscous forces.
Smooth solution does not always exist. A counter example is given. (Fr>SQRT(3)) As the practical meaning of this answer is already discussed in my previous papers, this paper concentrates to the complete integration process of the Navier-Stokes equation leading to the solution. This path is as follows; N-S Equation -> Bernoulli Eq. -> Energy (intern) -> Energy (extern)/momentum -> Momentum -> Specific Force -> Factoring the degree-three equation to quadratic -> Derivate ->> ANSWER (@ unity)
As explained in my previous paper, Turbulence is a crack in fluid, and therefore the premises of the continuity & smoothness-problem are wrong, which means that there can't be any meaningful solutions, without the scale problem. As a Prove, I showed (previously) how the anomaly on energy loss in Fr<2 in hydraulic jump can be explained better through this new theory. In this paper this is proved mathematically. The previously ignored 2nd and 3rd solutions from momentum and energy equations provide the answer directly, though they seem meaningless alone, they provide the correct answer when used together. Though, also then, the solution seems grazy at first, because it states, that the efficiency is >1 between Fr=1 and Fr = SQRT(3), which is ofcource impossible. But as there are waves, also this is easily possible. A wavetop can occasionally have more energy, as "aloud", this is averaged by the another wave, which has less.