Title: Which direction?
Post by: Jules Ruis on October 21, 2006, 11:50:28 AM
Who can help us with a first article or internet link in the field of Fluid Dynamics, Turbulence & Weather Prediction?
Title: Re: Which direction?
Post by: lkmitch on October 23, 2006, 06:41:25 PM
Here's one I wrote about modelling vortex motions using Ultra Fractal. Turns out the a great many complex motions can be captured relatively simply.
Kerry
http://www.fractalus.com/kerry/articles/vortical_flow1.pdf (http://www.fractalus.com/kerry/articles/vortical_flow1.pdf)
Kerry
http://www.fractalus.com/kerry/articles/vortical_flow1.pdf (http://www.fractalus.com/kerry/articles/vortical_flow1.pdf)
Title: Which direction?
Post by: Jules Ruis on October 23, 2006, 07:01:37 PM
Good start and nice example.
Title: Re: Which direction?
Post by: Charleswehner on November 19, 2006, 05:32:44 PM
This is a very good example.
I have only once refused to do a job for an employer, and it related to fluid flow. The Hagen-Poiseuille equations are not adequate to describe fluid flow properly. There are too many simplifying assumptions.
Later, at the University of Liverpool, I attended a supercomputer exhibition. Rolls-Royce had employed a company to use a transputer supercomputer to analyse the airflow around their carbon-fibre turbine blades. Each transputer dealt with only a tiny square area, using the input-output principle. The airflow into the next blade must match the output from the last, and by symmetry this is the airflow out of that next blade.
The input and output were compared, and the error found. To avoid the model oscillating, this error-feedback was "diluted". This led to a slow convergence on the results.
The entire array of transputers ran for months.
Anything that simplifies such computations is a great service to industry.
By the way, there was no chaos theory, no transputers and no PCs in the sixties. I was right to refuse. I would still be working on it by hand today.
Charles
I have only once refused to do a job for an employer, and it related to fluid flow. The Hagen-Poiseuille equations are not adequate to describe fluid flow properly. There are too many simplifying assumptions.
Later, at the University of Liverpool, I attended a supercomputer exhibition. Rolls-Royce had employed a company to use a transputer supercomputer to analyse the airflow around their carbon-fibre turbine blades. Each transputer dealt with only a tiny square area, using the input-output principle. The airflow into the next blade must match the output from the last, and by symmetry this is the airflow out of that next blade.
The input and output were compared, and the error found. To avoid the model oscillating, this error-feedback was "diluted". This led to a slow convergence on the results.
The entire array of transputers ran for months.
Anything that simplifies such computations is a great service to industry.
By the way, there was no chaos theory, no transputers and no PCs in the sixties. I was right to refuse. I would still be working on it by hand today.
Charles
Title: Re: Which direction?
Post by: jehovajah on August 23, 2008, 11:22:01 AM
I have tried to view the pdf and it has caused my ie to crash. It looks like an interesting article and hopefully the maths is not offputting. Remember its mainly about adding and subtracting!
Title: Re: Which direction?
Post by: jehovajah on August 23, 2008, 04:06:16 PM
I have read the article and found it interesting. The application to turbulence is better described by charles brief reply. Maybe a 16 square grid could be investigated to give some initial experience of modelling fluid turbulence in a stirred cup of tea? Mine black with no sugar and one little drop of milk.
Title: Re: Which direction?
Post by: jehovajah on September 13, 2008, 12:03:17 PM
Further thoughts on the 4 * 4 grid. If we set a twisting motion in the centre such that it has an angular velocity
which affects the surrounding squares such that their angular velocity is )
= )
and the velocity perpendicular to any radius from the centre combined with the velocity of the rotating square at that region is /dt +w*r)
I guess.
So if there is a rigid connection between the squares the 4 * 4 rotates as a whole and we might be able to solve the equations for that case trivially, or maybe not. But what about when the squares are not rigidly linked? What kind of movement do we get then for the 4 * 4 squares?
So if there is a rigid connection between the squares the 4 * 4 rotates as a whole and we might be able to solve the equations for that case trivially, or maybe not. But what about when the squares are not rigidly linked? What kind of movement do we get then for the 4 * 4 squares?
Title: Re: Which direction?
Post by: s243a on September 03, 2009, 09:12:53 PM
Here is an interesting quote:
I found the following paper here:
http://www.me.jhu.edu/~meneveau/pubs-fractals.htm
The mathematics is kind of heavy though.
Quote
1.1. Statement of the problem Many flows of interest in science and engineering display complex spatial and temporal structures (eddies) spanning a wide range of scales. The ratio between the largest (L) and smallest ( \eta ) scale can easily exceed 10^4 in typical engineering applications, and can be as high as 10^6 or higher in geophysical applications. Since the nonlinear interaction between eddies of different sizes eludes even the most sophisticated analytical approaches, one must resort to either extensive experimentation or direct numerical simulation (DNS) of the governing equations. The latter approach has gained strength by the rapid increase in the power of digital computers during the past 20 years. Despite this fact, DNS of flows for which the ratio $latex L/ \eta $ is much larger than 10^2 are still prohibitive
http://www.me.jhu.edu/meneveau/pdf-papers/ScottiMeneveau99.pdfI found the following paper here:
http://www.me.jhu.edu/~meneveau/pubs-fractals.htm
The mathematics is kind of heavy though.
Title: Re: Which direction?
Post by: jehovajah on September 20, 2009, 09:21:23 AM
Thankyou for that post. I will look at it with interest over the next few weeks.
My current thought has to do with modeling condensation by an inward rotating spiral of the energy transfer flux (field lines), and evaporation by the outwardly rotating spiral, in short vortices that have a centripetal or centrifugal action. The question of space time i have not resolved yet but i would formalise it under an iteration scheme for a procedure acting on a planar region initially, before looking at the case of a volumetric region. Maths is about adding or subtracting, the hard bit is what? The symbolic logic in the algorithms is what obscures this answer. The tyranny of the abstract such as point creates unecessary difficulties also.
My current thought has to do with modeling condensation by an inward rotating spiral of the energy transfer flux (field lines), and evaporation by the outwardly rotating spiral, in short vortices that have a centripetal or centrifugal action. The question of space time i have not resolved yet but i would formalise it under an iteration scheme for a procedure acting on a planar region initially, before looking at the case of a volumetric region. Maths is about adding or subtracting, the hard bit is what? The symbolic logic in the algorithms is what obscures this answer. The tyranny of the abstract such as point creates unecessary difficulties also.
Title: Re: Which direction?
Post by: jehovajah on September 22, 2009, 04:23:17 AM
For me this is a better link
http://www.me.jhu.edu/meneveau/ (http://www.me.jhu.edu/meneveau/) .
http://www.me.jhu.edu/meneveau/ (http://www.me.jhu.edu/meneveau/) .