Canuto, V.M., and M.S. Dubovikov 1999. A dynamical model for turbulence. VII. Complete system of five orthogonal tensors for shear driven flows. Phys. Fluids 11, 659-664.
Canuto, V.M., M.S. Dubovikov, and G. Yu 1999. A dynamical model for turbulence. VIII. IR and UV Reynolds stress spectra for shear-driven flows. Phys. Fluids 11, 665-677.
Canuto, V.M., M.S. Dubovikov, and G. Yu 1999. A dynamical model for turbulence. IX. Reynolds stresses for shear-driven flows. Phys. Fluids 11, 678-691..

http://www.giss.nasa.gov/research/briefs/canuto_01/

Turbulence

By Vittorio M. Canuto and Mikhail S. Dubovikov — June 1998
Fig. 1: Photo of sketch in da Vinci notebook
http://www.giss.nasa.gov/research/briefs/canuto_01/

Most flows nature have the tendency to become turbulent descriptions of the ocean and atmosphere depends on how one describes turbulence.

GISS develops realistic, manageable models of turbulence and in "A dynamical model for turbulence", parts I to VI in the journal Physics of Fluids,the authors proposed, worked out and tested a model for turbulence.

In paper VII they derived the general math for the properties of shear and vorticity deriving simplfied expressions to facilitate a new model.

Paper VIII derives the spectral forms of our new turbulent variables and discusses the match with laboratory data detailing individual eddies with more information of the dynamics of the vortices than the integrated quantities (which only yield the total amount of energy carried by all.)

In IX we work out the general expression for the Reynolds stresses, that correlates fluctuating velocities of the turbulence and drains energy from the larger scales of motion in as ordinary viscosity does.

The turbulence model is used at GISS to improve the description of turbulent mixing in the ocean. Soon these results will be applied to the atmosphere..

Dawlish of course just hasn't the ability required for this sort of thing. So if RV or Dr. Dixon care to stick an oar in?
Someone pass a note to Col to see if he has found out how to wipe his botty, as I am sure he would like another opportunity to show us what he's been eating (by opening his gob.)

This was just the first page of these things:

Turbulence...

http://www.giss.nasa.gov/research/briefs/canuto_01/

There were umpteen pages of them:

Research
Computational models of high-dimensional systems arise in a rich variety of engineering and scientific contexts. For example, computational fluid dynamics (CFD) and finite element (FE) analysis have become indispensable tools for many engineering applications. Unfortunately, high-fidelity simulations are often computationally prohibitive for parametric and time-critical applications such as design, design optimization, control, and virtual testing. Moreover, even when adequate computational resources are available, simulations often provide too little understanding of the solutions they produce. There are significant scientific and engineering benefits in developing and studying low-dimensional representations of high-dimensional systems that retain physical fidelity while substantially reducing the size and cost of the computational model.
My research is focused on developing theoretical and computational tools for low-dimensional and low-rank models of multi-scale and multi-physics problems.

Some of them even written in English:
Vortex stretching
From Wikipedia, the free encyclopedia
Studies of vortices in turbulent fluid motion by Leonardo da Vinci.

In fluid dynamics, vortex stretching is the lengthening of vortices in three-dimensional fluid flow, associated with a corresponding increase of the component of vorticity in the stretching direction—due to the conservation of angular momentum.[1]

Vortex stretching is associated with a particular term in the vorticity equation. For example, vorticity transport in an incompressible inviscid flow is governed by

D ω → D t = ( ω → ⋅ ∇ → ) v → , {\displaystyle {D{\vec {\omega }} \over Dt}=({\vec {\omega }}\cdot {\vec {\nabla }}){\vec {v}},}

where D/Dt is the convective derivative. The source term on the right hand side is the vortex stretching term. It amplifies the vorticity ω → {\displaystyle {\vec {\omega }}} when the velocity is diverging in the direction parallel to ω → {\displaystyle {\vec {\omega }}} ..

A simple example of vortex stretching in a viscous flow is provided by the Burgers vortex.

Vortex stretching is at the core of the description of the turbulence energy cascade from the large scales to the small scales in turbulence. In general, in turbulence fluid elements are more lengthened than squeezed, on average. In the end, this results in more vortex stretching than vortex squeezing. For incompressible flow—due to volume conservation of fluid elements—the lengthening implies thinning of the fluid elements in the directions perpendicular to the stretching direction. This reduces the radial length scale of the associated vorticity. Finally, at the small scales of the order of the Kolmogorov microscales, the turbulence kinetic energy is dissipated into heat through the action of molecular viscosity.[2][3]

https://en.wikipedia.org/wiki/Vortex_stretching

(Almost.)

Pages and pages and all of it wrong...

When I meet God, I am going to ask him two questions: why relativity? And why turbulence? I really believe he will have an answer for the first.�- Werner Heisenberg, Physicist.

Turbulence simply is...

First we let the others grab the glittering prize, since god has already shown us the answer ... to both, there is no need for me to jump the gun. In fact I shall leave you all to get on with it while I take a siesta. Have hwyl.

On Sunday, 5 June 2016 20:56:34 UTC+1, Weatherlawyer wrote:
This was just the first page of these things:

Turbulence...

http://www.giss.nasa.gov/research/briefs/canuto_01/

There were umpteen pages of them:

Research
Computational models of high-dimensional systems arise in a rich variety of engineering and scientific contexts. For example, computational fluid dynamics (CFD) and finite element (FE) analysis have become indispensable tools for many engineering applications. Unfortunately, high-fidelity simulations are often computationally prohibitive for parametric and time-critical applications such as design, design optimization, control, and virtual testing. Moreover, even when adequate computational resources are available, simulations often provide too little understanding of the solutions they produce. There are significant scientific and engineering benefits in developing and studying low-dimensional representations of high-dimensional systems that retain physical fidelity while substantially reducing the size and cost of the computational model.
My research is focused on developing theoretical and computational tools for low-dimensional and low-rank models of multi-scale and multi-physics problems.

Some of them even written in English:
Vortex stretching
From Wikipedia, the free encyclopedia
Studies of vortices in turbulent fluid motion by Leonardo da Vinci.

In fluid dynamics, vortex stretching is the lengthening of vortices in three-dimensional fluid flow, associated with a corresponding increase of the component of vorticity in the stretching direction—due to the conservation of angular momentum.[1]

Vortex stretching is associated with a particular term in the vorticity equation. For example, vorticity transport in an incompressible inviscid flow is governed by

D ω → D t = ( ω → ⋅ ∇ → ) v → , {\displaystyle {D{\vec {\omega }} \over Dt}=({\vec {\omega }}\cdot {\vec {\nabla }}){\vec {v}},}

where D/Dt is the convective derivative. The source term on the right hand side is the vortex stretching term. It amplifies the vorticity ω → {\displaystyle {\vec {\omega }}} when the velocity is diverging in the direction parallel to ω → {\displaystyle {\vec {\omega }}} ..

A simple example of vortex stretching in a viscous flow is provided by the Burgers vortex.

Vortex stretching is at the core of the description of the turbulence energy cascade from the large scales to the small scales in turbulence. In general, in turbulence fluid elements are more lengthened than squeezed, on average. In the end, this results in more vortex stretching than vortex squeezing. For incompressible flow—due to volume conservation of fluid elements—the lengthening implies thinning of the fluid elements in the directions perpendicular to the stretching direction. This reduces the radial length scale of the associated vorticity. Finally, at the small scales of the order of the Kolmogorov microscales, the turbulence kinetic energy is dissipated into heat through the action of molecular viscosity.[2][3]

https://en.wikipedia.org/wiki/Vortex_stretching

(Almost.)

Pages and pages and all of it wrong...

When I meet God, I am going to ask him two questions: why relativity? And why turbulence? I really believe he will have an answer for the first.�- Werner Heisenberg, Physicist.

Turbulence simply is...

First we let the others grab the glittering prize, since god has already shown us the answer ... to both, there is no need for me to jump the gun. In fact I shall leave you all to get on with it while I take a siesta. Have hwyl.

You are going to love it when I finally tell you how it's done. But it would be wrong of me to rob you too soon. I shall let you savour it. Let's hope i don't die in my sleep. Or does anyone want a bit more time to prayIi do?

On Sunday, 5 June 2016 23:57:23 UTC+1, Weatherlawyer wrote:
On Sunday, 5 June 2016 20:56:34 UTC+1, Weatherlawyer wrote:
This was just the first page of these things:

Turbulence...

http://www.giss.nasa.gov/research/briefs/canuto_01/

There were umpteen pages of them:

Research
Computational models of high-dimensional systems arise in a rich variety of engineering and scientific contexts. For example, computational fluid dynamics (CFD) and finite element (FE) analysis have become indispensable tools for many engineering applications. Unfortunately, high-fidelity simulations are often computationally prohibitive for parametric and time-critical applications such as design, design optimization, control, and virtual testing. Moreover, even when adequate computational resources are available, simulations often provide too little understanding of the solutions they produce. There are significant scientific and engineering benefits in developing and studying low-dimensional representations of high-dimensional systems that retain physical fidelity while substantially reducing the size and cost of the computational model.
My research is focused on developing theoretical and computational tools for low-dimensional and low-rank models of multi-scale and multi-physics problems.

Some of them even written in English:
Vortex stretching
From Wikipedia, the free encyclopedia
Studies of vortices in turbulent fluid motion by Leonardo da Vinci.

In fluid dynamics, vortex stretching is the lengthening of vortices in three-dimensional fluid flow, associated with a corresponding increase of the component of vorticity in the stretching direction—due to the conservation of angular momentum.[1]

Vortex stretching is associated with a particular term in the vorticity equation. For example, vorticity transport in an incompressible inviscid flow is governed by

D ω → D t = ( ω → ⋅ ∇ → ) v → , {\displaystyle {D{\vec {\omega }} \over Dt}=({\vec {\omega }}\cdot {\vec {\nabla }}){\vec {v}},}

where D/Dt is the convective derivative. The source term on the right hand side is the vortex stretching term. It amplifies the vorticity ω → {\displaystyle {\vec {\omega }}} when the velocity is diverging in the direction parallel to ω → {\displaystyle {\vec {\omega }}} .

A simple example of vortex stretching in a viscous flow is provided by the Burgers vortex.

Vortex stretching is at the core of the description of the turbulence energy cascade from the large scales to the small scales in turbulence. In general, in turbulence fluid elements are more lengthened than squeezed, on average. In the end, this results in more vortex stretching than vortex squeezing. For incompressible flow—due to volume conservation of fluid elements—the lengthening implies thinning of the fluid elements in the directions perpendicular to the stretching direction. This reduces the radial length scale of the associated vorticity. Finally, at the small scales of the order of the Kolmogorov microscales, the turbulence kinetic energy is dissipated into heat through the action of molecular viscosity.[2][3]

https://en.wikipedia.org/wiki/Vortex_stretching

(Almost.)

Pages and pages and all of it wrong...

When I meet God, I am going to ask him two questions: why relativity? And why turbulence? I really believe he will have an answer for the first.�- Werner Heisenberg, Physicist.

Turbulence simply is...

First we let the others grab the glittering prize, since god has already shown us the answer ... to both, there is no need for me to jump the gun. In fact I shall leave you all to get on with it while I take a siesta. Have hwyl.

You are going to love it when I finally tell you how it's done. But it would be wrong of me to rob you too soon. I shall let you savour it. Let's hope i don't die in my sleep. Or does anyone want a bit more time to prayIi do?

https://weatherlawyer.wordpress.com/...iac-papers-ii/