S. A. E. Miller, Ph.D.

The NASA Library is amazing and provided me with the original in Russian.

Kolmogorov, A. N., “The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Number,” Dokl. Akad. Nauk. SSSR, Vol. 30, 1941, pp. 299–303.

It is that time of year again where the World War 2 Airshow occurs near Virginia Beach. Myself and some NASA colleauges headed down on the Saturday to watch flights from 1 pm to approximately 4 pm. It was a beautiful and sunny day. The static dispaly was fun also, including the flight line, and I lost some hearing due to the firing of an 88. There were reenactors from all countries involved (Americans dressed up as Russians, Germans, etc. really). My favorite flight was from twin jet engine messerschmitt, that was a welcome change from all the slower and perhaps less noisy props. I also enjoyed examining the Yak 3.

The American Kite Associate visited Virginia Beach recently. They had three areas on the beach fenced off. The first was for open flying. Anyone could go and fly a kite. The second was a static display of many different types of kites. I love octopus – and there were many so that made me very happy. Finally, there was a competition area for two and four string kites. The flyers tried to pair music with their kites to make a routine – think figure skating but in the area.

Suppose a cylindrical wing (constant chord, incidence, etc.) is placed in an airstream at an angle of yaw — i.e., it is swept back. Now, even if the local speed of the air on the upper surface of the wing becomes supersonic, a shock wave cannot form there because it would have to be a sweptback shock — swept at the same angle as the wing — i.e., it would be an oblique shock. Such an oblique shock cannot form until the velocity component normal to it becomes supersonic.

Sonnet to Turbulence
Stanley Corrsin

Shall we compare you to a liminar flow?
You are more lovely and more sinuous.
Rough winter winds shake branches free of snow,
And summer’s plumes churn up in cumulus.
How do we perceive you? Let me count the ways.
A random vortex field with strain entwined.
Fractal? Big and small swirls in the maze
May give us paradigms of flows to find.
Orthonormal forms non-linearly renew
Intricate flows with many free degrees
Or, in the latest fashion, merely few
As strange attractor. In fact, we need Cray 3s.
Experiment and theory, unforgiving;
For serious searcher, fun … and its a living!

I recently gave a talk at the NASA Langley 2015 Technical Working Group. Slides are available on my website under presentations. One interesting slide shows mathematical relationships between acoustic analogy (turbulence as a source of sound) and nonlinear propagation (Burgers’ equation).

The Chrysler Museum of Art features a new exhibit on Henri Matisse. Henri Matisse is a master of color and a leader of French artists experimenting in color. When these paintings emerged in the early 1900’s they were ridiculed by contemporary critics of the time. It did not take too long for the critics to be silenced. These works mark the beginning of Fauvism. In his work, `Open Window, Collioure,’ the Mediterranean sea is captured with characteristic bright colors. Simple objects in the paintings take on a clear presence with the effect of color overwhelming almost everything else. Often the paintings show simple pleasures of life, inner contemplation, or basic contentment. He also created paper collages that filled very large frames. Near the end of this early era of Fauvism, a following grew and the works became more formalized. An interesting quote adorns the wall,

I have always tried to hide my efforts and wished my works to have a light joyousness of springtime which never lets anyone suspect the labor it has cost me.

Perhaps that is a fitting quote for any creative profession.

I have recently published an article in honor of the late NASA Senior Theoretical Aeroacoustician Dr. Fereidoun `Feri’ Farassat.

During the first week I worked at NASA, while I was sending a fax, Dr. Farassat literally screamed from the other end of building 1208, Is this how NASA researchers spend their time?‘ I was surprised and confused at the time, but now this question remains in my mind everyday. The French impressionist painter Camille Pissarro wrote,everyday a line,’ I might write, `everyday an equation.’ Doing so honors those who have come before us at this prestigious organization and allows us to stand on their shoulders, especially so during this 100th Anniversary of NACA!

The article citation is

Miller, S. A. E., “The Scaling of Broadband Shock-Associated Noise with Increasing Temperature,” International Journal of Aeroacoustics, Vol. 14, Num. 1-2, 2015, pp. 305-326. DOI: 10.1260/1475-472X.14.1-2.327 [Link via DOI] [PDF Preprint]

More important than the technical contribution of the article are the lessons we learned from the person the article honors. The article contains a personal introduction,

It is a privilege to contribute an article to this special edition in honor of Dr. Fereidoun ‘Feri’ Farassat. The present article involves the use of an acoustic analogy and a Green’s function for its solution. Dr. Farassat’s career was heavily involved with both of these fundamental methods in aeroacoustics since his Ph.D. [1] work at Cornell (under advisement of Professor William R. Sears) based on the work of J. E. Ffowcs Williams and D. L. Hawkings [2]. His Ph.D. work laid the foundation for the rest of his career at NASA Langley Research Center (LaRC) within the Aeroacoustics Branch. Dr. Farassat’s developments such as Formulation 1 (Farassat [3]), Formulation 1A (Farassat and Succi [4]), the use of generalized functions (Farassat and Myers [5]), and countless others, were extremely important for the field. Some of these contributions are available on the NASA Technical Reports Server, where Dr. Farassat has over 130 publications available to the public on a wide range of topics.

Dr. Farassat, during his mid- to late-career, was undoubtedly the theoretical backbone of the Aeroacoustics Branch at NASA Langley. He had influenced the technical direction of many researchers within both the branch and NASA as a whole, and had a considerable influence throughout the community, all of which are still being felt today.

Dr. Farassat had a long history of imparting his knowledge to new researchers at NASA Langley. Some of my first and most memorable interactions with Dr. Farassat had started with these teachings. I enjoyed many technical discussions in his office and his guidance changed my technical view-point, especially relating to the acoustic analogy. These discussions saved me large amounts of time and helped me avoid many possible technical failures. He also was not afraid to offer advice, technical or personal, and was genuinely interested in the well-being of everyone he interacted with. He was an unwavering advocate within NASA for the importance of research and was extremely supportive of junior researchers.
I am proud to call Dr. Farassat my colleague and friend. Thank you Feri for the time we had together.

Abstract

A physical explanation for the saturation of broadband shock-associated noise (BBSAN) intensity with increasing jet stagnation temperature has eluded investigators. An explanation is proposed for this phenomenon with the use of an acoustic analogy. To isolate the relevant physics, the scaling of BBSAN peak intensity level at the sideline observer location is examined. The equivalent source within the framework of an acoustic analogy for BBSAN is based on local field quantities at shock wave – shear layer interactions. Propagation of sound through the jet shear layer is predicted with an adjoint vector Green’s function solver of the linearized Euler equations. The combination of the equivalent source and adjoint vector Green’s function allows for correct predictions of the saturation of BBSAN with increasing stagnation pressure and stagnation temperature. The sources and vector Green’s function have arguments involving the steady Reynolds-Averaged Navier-Stokes solution of the jet. It is proposed that saturation of BBSAN with increasing jet temperature occurs due to a balance between the amplification of the sound propagation through the shear layer and the source term scaling.

Acknowledgements

The author benefited greatly from discussions with Boeing/A. D. Welliver Professor Philip J. Morris of the Pennsylvania State University. The availability of experimental data from Professor Dennis K. McLaughlin of the Pennsylvania State University, Dr. James Bridges of NASA Glenn Research Center at Lewis Field, and Dr. Viswanathan of the Boeing Company made this work possible. The author is grateful for continuous support from The National Aeronautics and Space Administration Fundamental Aeronautics Program High Speed Project.

Some References

[1] Farassat, F., “The Sound from Rigid Bodies in Arbitrary Motion,” Cornell University Ph.D. Dissertation, January 1973.
[2] Ffowcs Williams, J. E. and Hawkings, D. L., “Sound Generation by Turbulence and Surfaces in Arbitrary Motion,” Phil. Trans. R. Soc. Lond. A, Vol. 264, No. 1151, 1969, pp. 321–342. doi:10.1098/rsta.1969.0031.
[3] Farassat, F., “Linear Acoustic Formulas for Calculation of Rotating Blade Noise,” AIAA Journal, Vol. 19, No. 9, 1981, pp. 1122-1130. doi:10.2514/3.60051.
[4] Farassat, F. and Succi, G. P., “A Review of Propeller Discrete Frequency Noise Prediction Technology with Emphasis on Two Current Methods for Time Domain Calculations,” Journal of Sound and Vibration, Vol. 71, No. 3, 1980, pp. 399–419. doi:10.1016/0022–460X(80)90422-8.
[5] Farassat, F. and Myers, M. K., “Multidimensional Generalized Functions in Aeroacoustics and Fluid Mechanics-Part 1: Basic Concepts and Operations,” International Journal of Aeroacoustics, Vol. 10, No. 2–3, June 2011, pp. 161–200. doi:10.1260/1475–472X.10.2-3.161.

One hundred years ago, March 3rd 2015, the US Congress created the National Advisory Committee for Aeronautics, the predecessor organisation of NASA. Every allied aircraft has been tested in some form or another at NASA Langley. NASA has created a few websites to celebrate,

NACA 100th Celebration and more NASA Langley specific.

It is certainly an exciting time to be a part of the organization. Over the next month there will be multiple events at NASA and within the community to celebrate!

I should also like to mention how fitting it is, that I had the opportunity to work today (and yesterday and tomorrow) at NASA Langley (site of the original NASA/NACA center), and examined one of the most difficult problems in modern physics – turbulence. That is really an honor and quite amazing! Certainly a life worth living.

While browsing the Internet I found an interesting website on abstract mathematics by Professor Charles Wells. The site is organized into subsections like chapters in a book. I’m especially interested in the use of different fonts, sizes, and colors to illustrate important points. Perhaps the important points are emphasized because of the experience of the author as a teacher. The presentation is such that most people can understand it if they have some background in the field. It is fun to review the site and remind oneself of the notation and key base concepts in abstract mathematics. It is very refreshing relative to the traditional mathematics education for engineers and scientists (that I was a part of for the most part). I wish more professional scientists, engineers, and mathematicians (read researchers) maintained personal websites or offered basic notes online. It is a service to society.