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New Theory on Turbulence Generation and Sustenance in a Boundary Layer

1. Turbulence is still an unsolved scientific problem, which is not only important to science but also to engineering applications in aerospace engineering, mechanical engineering, energy engineering, bio engineering and many others.

2. Dr. Chaoqun Liu presented a new theory on turbulence generation and sustenance recently. The new theory is able to well interpret the physics of turbulence which is currently considered by many people as a topic ˇ°impossible to understand, impossible for ever, or God has no answer.ˇ± Contradicting to most of classical theory and/or currently dominant theories, LiuˇŻs theory may bring a revolution to not only the basic fluid mechanics, but also to flow control for flow transition, turbulence, drag reduction, design optimization, etc. It may also bring a revolution to turbulence modeling.

Highlights of LiuˇŻs Turbulence Theory
The fluid motion can be mainly decomposed as a pure shear part and rotation part ignoring the translation part. The shear part is conditionally unstable and rotational part is stable. The laminar flow is dominated by shear part and the turbulent flow is dominated by rotation. Flow has trend to change the shear part to rotation when away from the wall. Therefore, flow transition from laminar state (unstable) to turbulent flow (stable) is doomed.
The vorticty is large near the wall surface where the shear is dominant. The role of all linear unstable modes is to push the vorticity up from the wall (roll up). The flow trend to change shear to rotation will occur inside the flow field and the spanwise vortex will form due to the trend from shear to rotation. The unstable linear modes are small and cannot form vortex. Therefore, the N-factor which is based on linear analysis is questionable.
The linear unstable modes cannot form vortex and the non-linear stage is not interaction of 2-D modes with 3-D modes, but spanwise vortex with 3-D modes. The analytic linear solution departs from DNS at the beginning. They do not agree with each other even in very early stages.
There is no such a process that the Lambda-vortex self deforms to hairpin vortex. The Lambda-vortex root and ring head are formed separately and ring is not part of Lambda-vortex.
Lambda-vortex is a pair of open rotation cores (never close) and is not a vortex tube.
A momentum deficit zone (low speed zone) is formed above the Lambda-vortex and further generates a Lambda-shaped high shear due to the vortex root ejection. The vortex rings are generated by the high shear layer (K-H type) instability.
Multiple vortex rings are all formed by shear layer instability which is generated by momentum deficit (There are not vortex breakdown and reconnection and multiple ring formation is not governed by Crow theory).
U-shaped vortex is a tertiary vortex with the same sign of vorticity as the prime vortex.
The vortex structure is stable and can travel for long distance. ˇ°Vortex breakdownˇ± never happened and is theoretically incorrect.
No matter how to define "vortex", small vortices (turbulence) cannot be generated by "vortex breakdown". All small vortices are generated by shear layer without exception. In other words, "shear layer instability is the mother of turbulence".
If we define vortex is a rotation core, the rotation core is stable and cannot breakdown. Therefore ˇ°vortex breakdownˇ± cannot happen. The only way is that the vortex can be weakened by dissipation when it travels.
The multiple level shear layers are generated by vortex sweeps and ejections. The sweep brings high speed flow down (positive spike) to the lower boundary layer and the ejection brings the low speed flow up (negative spike) to the upper boundary layer. They form the multiple level shear layers.
These multiple shear layers generate small vortices with different sizes.
The energy transport channel is that the high energy is brought down to the lower boundary layer by multiple level sweeps. Without these sweeps, all small vortices (turbulence) would dissipate quickly.
Large vortex cannot pass energy to smaller vortices through ˇ°vortex breakdownˇ± which was never observed by any experiment or DNS.
The disordering of flow structure is mainly not caused by the background noise or non-symmetric spanwise boundary condition, but internal property of the vortex structure. The non-symmetry starts in the middle of the vortex package.
The classical theory including the RichardsonˇŻs eddy cascade, Kolmogorov universal and isotropic hypothesis on smallest vortices, Kolmogorov small length scales are not confirmed and observed. Their theory should be revisited.
Richardson eddy cascade revisit (There is no such a cascade)
Kolmogorov hypothesis revisit (There is no vortex breakdown and there is no energy passing through vortex breakdown. There is no proof of existence of Kolmogorov small scale.)
The smallest scale should be determined by smallest shear layer which is measured by y+ (1-10)
There is no ˇ°turbulence intermittenceˇ±. The faked term is generated by misunderstanding of turbulence package self motion and relative motion, or by observing fluid particle motion in an Euler system.
There is no ˇ°vortex breakdownˇ± which is caused by faked visualization by using improper lambda2 values.
Flow control ¨C control the shear layer, its formation, shape, and direction
Turbulence modeling ¨C model the turbulence packages and relative motion of packages.

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