Chairing Turbulence Theory at APS Division of Fluid Dynamics – Highlight of the year

All our presenters were present and traveled internationally. DNS is the tool of choice for numerical simulations. Theory emerged from results, and I hope that new relations will guide those making turbulence models today.

High-order inertial range scaling exponents in incompressible turbulence using generalized extended self-similarity
Presenter: Sualeh Khurshid, Massachusetts Institute of Technology, Author: Sualeh Khurshid, Massachusetts Institute of Technology

Temporal large-scale intermittency and its impact on flow statistics
Presenter: Lukas Bentkamp, University of Bayreuth, Germany, Author: Lukas Bentkamp, University of Bayreuth, Germany, Author: Michael Wilczek, University of Bayreuth, Germany

Non-locality and scaling of extreme events in fluid turbulence
Presenter: Alain Pumir, Ecole Normale Superieure de Lyon, Author: Alain J Pumir, Ecole Normale Superieure de Lyon, Author: Dhawal Buaria, New York University (NYU)

Probability density functions of dissipation rate and enstrophy in turbulence
Presenter: Toshiyuki Gotoh, Nagoya Inst of Tech, Author: Toshiyuki Gotoh, Nagoya Inst of Tech, Author: Takeshi Watanabe, Nagoya Institute of Technology, Author: Izumi Saito, Nagoya Institute of Technology

Analyzing energy cascade of filtered vortices using a novel turbulence database framework
Presenter: Hanxun Yao, Johns Hopkins University, Author: Hanxun Yao, Johns Hopkins University, Author: Michael Schnaubelt, Johns Hopkins University, Author: Alex Szalay, Johns Hopkins University, Author: Tamer A Zaki, Johns Hopkins University, Author: Charles Meneveau, Johns Hopkins University

Statistical equilibrium of large scales in three-dimensional hydrodynamic turbulence
Presenter: Eric Falcon, Université Paris Cité, MSC, CNRS, Author: Jean-Baptiste Gorce, Université Paris Cité, MSC, CNRS, Author: Eric Falcon, Université Paris Cité, MSC, CNRS

Detailed kinetic energy dynamics of turbulent fluids
Presenter: Justin Beroz, Massachusetts Institute of Technology MI, Author: Justin Beroz, Massachusetts Institute of Technology MI, Author: Steven G Johnson, Massachusetts Institute of Technology MI, Author: John W Bush, Massachusetts Institute of Technology MI

Lagrangian curvature statistics from Gaussian sub-ensembles in turbulent von-Kármán flow
Presenter: Yasmin Hengster, Univ of Edinburgh, Author: Yasmin Hengster, Univ of Edinburgh, Author: Daniel Schanz, German Aerospace Center, Institute of Aerodynamics and Flow Technology, Department of Experimental Methods, Göttingen, Germany, Author: Florian Huhn, German Aerospace Center, Institute of Aerodynamics and Flow Technology, Department of Experimental Methods, Göttingen, Germany, Author: Daniel Garaboa Paz, Group of Nonlinear Physics, University of Santiago de Compostela, Spain, Author: Eberhard Bodenschatz, Max Planck Institute for Dynamics and Self-Organization, Author: Moritz Linkmann, School of Mathematic, University of Edinburgh

Scaling of Lagrangian acceleration in isotropic turbulence at high Reynolds numbers
Presenter: Katepalli R Sreenivasan, New York University (NYU), Author: Dhawal Buaria, New York University (NYU), Author: Katepalli R Sreenivasan, New York University (NYU)

Dynamic Phase Alignment in Navier-Stokes Turbulence
Presenter: Lucio M Milanese, Massachusetts Institute of Technology MI, Author: Lucio M Milanese, Massachusetts Institute of Technology MI, Author: Nuno F Loureiro, MIT PSFC, Author: Stanislav A Boldyrev, University of Wisconsin – Madison

Characteristics of significant and insignificant regions in isotropic turbulence
Presenter: Miguel P Encinar, Univ Politecnica de Madrid, Author: Miguel P Encinar, Univ Politecnica de Madrid, Author: Javier Jimenez, Universidad Politecnica de Madrid

Isotropy, super-isotropy, and the extension of von Karman-Howarth equation: a Lundgren-equation based probability density function approach and its solution to homogeneous isotropic turbulence
Presenter: Simon Goertz, Technische Universität Darmstadt, Chair of Fluid Dynamics, Otto-Berndt-Str. 2, 64287 Darmstadt, Germany, Author: Dominik Plümacher, Technische Universität Darmstadt, Chair of Fluid Dynamics, Otto-Berndt-Str. 2, 64287 Darmstadt, Germany, Author: Simon Goertz, Technische Universität Darmstadt, Chair of Fluid Dynamics, Otto-Berndt-Str. 2, 64287 Darmstadt, Germany, Author: Martin Oberlack, Technische Universität Darmstadt, Chair of Fluid Dynamics, Otto-Berndt-Str. 2, 64287 Darmstadt, Germany

APS Presentation – Alternative Analytical Solution for Planar Oblique Shock Waves

Abstract: One now famous analytical solution for shock waves was developed by Dr. Theodore Meyer within his Ph.D. dissertation under advisement of Professor Ludwig Prandtl. The original solution relies on analysis via control volume of the equations of motion. This approach has limited future development of analytical solutions for more complex flow-fields. In this presentation, we recover the classic solution of Meyer for the planar oblique shock wave via a new approach. We recast the Navier-Stokes equations in terms of generalized functions and an arbitrary surface that evolves in space and time. A closed-form solution for the density field is found, which depends on the integration of a Green’s function and source. The source is a function of the ambient fluid properties and surface shape. The surface shape is constructed with the use of the product of multiple Heaviside functions. The integral is evaluated for the planar oblique shock wave. The newly derived approach yields exactly the same solution as presented by Meyer. The new method represents a possible avenue to attack unsolved canonical fluid flow problems.

Acknowledgements: Research was sponsored by the Defense Advance Research Project Agency (DARPA) and the Army Research Office and was accomplished under Grant Number W911NF-21-1-0342. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.

Miller, S. A. E., “Alternative Analytical Solution for Planar Oblique Shock Waves,” 75th Annual Meeting of the American Physical Society Division of Fluid Dynamics, Indianapolis, IN, Nov. 20-22, 2022. [Abstract PDF]

APS Presentation – A New Course: Modeling Inhomogeneous Turbulence with a Historic Perspective

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 energy, Reynolds stress transport equation, boundary layer equations, two-dimensional laminar flows, mixing length concepts, Baldwin-Lomax, Cebeci-Smith, one-half equations, one-equations, Prandtl’s model, Spalart-Allmarus, k-omega, k-epsilon, Boussinesq, nonlinear relations, stress transport models, closure, Morkovin hypothesis, and studies in particular flows. These topics are related to turbulent flows that are observed in our daily lives and within various fields of engineering. Student assessment is conducted via analysis assignments, term papers, and a presentation on a topic of their choice. A four part programming project involves creating a parabolic boundary layer marching code with an algebraic closure. Feedback from students and progress on making the course publicly available are presented. Portions of the course appear on online. Course notes and assignments are available freely within a 351 page handout.

Miller, S. A. E., “A New Course: Modeling Inhomogeneous Turbulence with a Historic Perspective,” 75th Annual Meeting of the American Physical Society Division of Fluid Dynamics, Indianapolis, IN, Nov. 20-22, 2022. [Abstract PDF][Presentation PDF]

On Living In An Atomic Age, Lewis

In one way we think a great deal too much of the atomic bomb. ‘How are we to live in an atomic age?’ I am tempted to reply: ‘Why, as you would have lived in the sixteenth century when the plague visited London almost every year, or as you would have lived in a Viking age when raiders from Scandinavia might land and cut your throat at night; or indeed, as you are already living in an age of cancer, an age of syphilis, an age of paralysis, an age of air raids, an age of railway accidents, an age of motor accidents.

In other words, do not let us begin by exaggerating the novelty of our situation. Believe me, dear sir or madam, you and all whom you love were already sentenced to death before the atomic bomb was invented… It is perfectly ridiculous to go about whimpering and drawing long faces because the scientists have added one more chance of painful and premature death to a world which already bristled with such chances and in which death itself was not a chance at all, but a certainty.

If we are all going to be destroyed by an atomic bomb, let that bomb when it comes find us doing sensible and human things—praying, working, teaching, reading, listening to music, bathing the children, playing tennis, chatting to our friends over a pint and a game of darts—not huddled together like frightened sheep and thinking about bombs. They may break our bodies (a microbe can do that) but they need not dominate our minds.

What the atomic bomb has really done is to remind us forcibly of the sort of world we are living in and which, during the prosperous period before, we were beginning to forget. And this reminder is, so far as it goes, a good thing. We have been waked from a pretty dream, and now we can begin to talk about realities.

It is our business to live by our own law not by fears: to follow, in private or in public life, the law of love and temperance even when they seem to be suicidal, and not the law of competition and grab, even when they seem to be necessary to our own survival. For it is part of our spiritual law never to put survival first: not even the survival of our species. We must resolutely train ourselves to feel that the survival of Man on this Earth, much more of our own nation or culture or class, is not worth having unless it can be had by honorable and merciful means.

Nothing is more likely to destroy a species or a nation than a determination to survive at all costs. Those who care for something else more than civilization are the only people by whom civilization is at all likely to be preserved. Those who want Heaven most have served Earth best. Those who love man less than God do most for man.

Let the bomb find you doing well.

C. S. Lewis, On Living In An Atomic Age, 1948.

Prandtl and Meyer

It would be difficult to create the right mood under the present circumstances, but perhaps by accident another beautiful differential equation will come along again, as it once did when I worked with you.

Letter from Meyer to Prandtl, May 5, 1918. Ref. no. GOAR:2647, DLR-Gottingen Archives

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 of plasma actuation on the pressure fluctuations from first mode instability waves on the cone surface via theory with flow-fields predicted by computational fluid dynamics. We present predictions for a seven-degree half-angle cone at free-stream Mach 2.0, 3.5, and 5.0 with varying nose radii. Nose radii range from 0.038 to 38.1 mm and represent both sharp and large leading edge bluntness. For non-actuated flows, we observe that very small radii leading edges do not alter the maximum growth rates. Large radii cones have lower growth rates due to a thicker boundary layer. Spatial coherence of the instability waves decreases with increasing frequency. The growth rates are smaller at higher freestream Mach number. The effect of the simulated plasma actuator adds local heating to the flow-field. Increased nose radii lowers the relative temperature difference between the actuated and base flow-fields. The relative temperature differences are higher at higher freestream Mach number. We find that plasma actuation stabilizes the flow-field and spatial coherence becomes smaller.

  • Cheng, J. and Miller, S. A. E., “Cheng, J. and Miller, S. A. E., “The Prediction of Cross-Spectra from First Mode Instability Waves within High-Speed Flow Over Sharp and Blunt Cones with Plasma Actuation,” Aerospace Science and Technology, Vol. 130, No. 107870, 2022. pp. 1-21. DOI: 10.1016/j.ast.2022.107870 [Link via DOI][PDF Preprint]