Abstract: A new graduate class is developed at the University of Florida called Modeling Inhomogeneous Turbulence with a Historical Perspective. The course covers in-depth concepts of the science and mathematics of turbulence modeling. Major topics of the class include statistics for modeling, the Russian school, law of the wall, chaos, compressible Navier-Stokes equations, mean kinetic …
Category Archives: Mathematics
The prediction of cross-spectra from first mode instability waves within high-speed flow over sharp and blunt cones with plasma actuation
Abstract: Leading edge geometries, such as cones, moving at high-speed undergo intense loading due to the growth of instability waves and turbulent transition. These instability waves are highly spatially coherent. Aerodynamic loading related to instability waves and transition cause large-amplitude vibrations within the underlying structure, which may lead to flight-vehicle failure. We examine the effect …
On Challenges in Turbulent Flow Theory and Experiment
Research in macroscopic classical physics, such as fluid dynamics or aspects of condensed matter physics, continues to confront baffling challenges that are by no means less demanding than those at the post-Newtonian frontiers of physics that have been explored since the beginning of this century. This is so even though the basic equations of macroscopic …
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Hugoniot
Hugoniot with classmates from the École Polytechnique, 1870 . Hugoniot is second from left, front row, see insert.
Paul Richard Heinrich Blasius
At Easter 1902 I had sat my final college examination, and was now studying mathematics. This was not simple for me: Although one can see what follows from certain algebraic manipulations, why would this be done? “By mathematics, you are convicted, instead of convinced”, according to the philosopher Schopenhauer. After some time, I realized that, …
The History of the Navier-Stokes Equations
Over the course of a few years I have collected pictures, biographies, and other tidbits about the many famous people who have created, studied, and dedicated their lives to the Navier-Stokes equations. I set it to the music of Carmina Burana of the MIT Choir (Creative Commons). Enjoy!
On Theory and Experiments
Regarding computing as a straightforward routine, some theoreticians still tend to underestimate its intellectual value and challenge, while practitioners often ignore its accuracy and overrate its validity. C. K. Chu, Columbia University, 1978
Foundations of Turbulence
The mathematical formulation of the problem of homogeneous turbulence is this: Given an infinite body of uniform fluid in which motions conform to the equations and, and given that at some initial instant the velocity of the fluid is a random function of position described by certain probability laws which are independent of position, to …
Proof that Any Number Equals Itself from the Hunting of the Snark
$$\frac{(x+7+10)(1000-8)}{992}-17$$
Acoular
http://www.acoular.org/ My students and myself have had some good luck with the open source and free software package Acoular. We used it to try and visualize the acoustic source distribution within a tornado. It worked fairly well, but of course the technique is dependent on the quality of data used. This is generated by CFD …