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 determine the probability laws that describe the motion of the fluid at subsequent times.

G. K. Batchelor in the Theory of Homogeneous Turbulence

On Nonsense

There is no reason to suppose that Carroll was in the slightest degree evasive in denying that he had intended his poem to mean anything at all. But, as he himself pointed out, words can mean much more than a writer intends. They can express meanings buried so deep in an author’s mind that he himself is not aware of them, and they can acquire meanings entirely by accident. Nonsense writing is a peculiarly rich medium for both types of “unintended” meaning.

Martin Gardner in the Hunting of the Snark

Calculator Museums

http://datamath.org/

There are a few wonderful websites online that show the history of calculators. I am very partial to Casio myself, but the Data Math Museum of Calculators has some very interesting history related to the TI series. Also, for those of you who grew up in the United States, one might remember the Little Professor calculator. This was often used by children for their first calculator. I had one as a kid and they are quite the collectors item today.

http://www.mrmartinweb.com/calculator.html

Another site, which is less TI focused, is Mr. Martin’s Calculator Museum website. Bonus in this site are links to particular slide rule and abacus related material.

Quillbot – A Fast Writing Tool

https://quillbot.com/

Quillbot is a nice free (paid version available) tool to help rephrase or fix grammar issues in writing. Sometimes I encounter tough sentences when preparing papers. A quick copy and paste through Quillbot has helped. I also have referred to some of my students to the site. I do caution that sometimes the meaning of sentences or the technical message can be changed. Sometimes small word changes result in large changes in meaning or what we are trying to convey.

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 simulations usually. CFD for acoustic analysis needs to be high-resolution and have small time steps. This is rather complicated by the fact that these simulations take more time than others. At the end of the day, the program produced some aesthetic images.