PhD in Scientific Computing Alum Beth Wingate Charts Unseen Currents in Fluid Dynamics and Applied Mathematics

Article by Wendy Sutton

Office of the Vice President for Research

Beth Wingate, a professor of mathematics at the University of Exeter in the United Kingdom warmly recalls her time at the University of Michigan. Her memories include lunches at Zingerman’s, browsing the poetry section of Borders Bookstore on Friday nights and participating in the annual football games between the atmospheric and oceanic scientists and their space science colleagues. During those foundational years as a PhD student in the Atmospheric, Oceanic and Space Sciences (AOSS) program, Wingate not only cultivated her academic interests but also forged lifelong friendships and memories.


After obtaining her BS in Aerospace, Aeronautical and Astronautical Engineering and MS in Fluid Dynamics, including her first studies of atmospheric dynamics, from The Ohio State University in 1986, Wingate launched her career as an aerospace engineer. At McDonnell Douglas, later acquired by Boeing, she worked on turbulence models for the engine inlets of F-15s and other high-speed military aircraft, but soon realized that aerospace engineering did not align with her interests. Instead, she found that her interests were more in tune with planetary-scale fluid dynamics.


“Just because you can do something,” she explained, “doesn’t mean that is what you want to focus on.” What she wanted to focus on were climate and environmental issues.


On the recommendations of colleagues from NASA Langley, Wingate reached out to John Boyd, Professor Emeritus of Climate and Space Sciences and Engineering at U-M. In 1991, Wingate became Boyd’s fourth PhD student. Not long after her arrival at U-M, she also began studying asymptotic analysis with Professor Stanley Jacobs.


After four years working in industry, Wingate understood the direction she wanted to pursue. The program allowed her to explore her diverse interests in physics and mathematics, providing a unique education that has served her well throughout her career.

A comparison of the solution derived from the averaging method with the “true” solution, showing spatio-temporal oscillations in the height field of the one-dimensional rotating shallow water equations. Top: fast-wave-averaged approximation of the height field. Middle: the transformation of this quantity back into normal space. Bottom: quality of the coarse solution compared to fine solver solution. Source: https://doi.org/10.1137/17M1131611

Wingate studied a number of subjects, including nonlinear fluid dynamics in the ocean. She also studied numerical methods, focusing on the spectral element method which involved studying optimal interpolation points on triangles and developing new basis functions with better computational properties.


As an advisor, John Boyd encouraged Wingate’s intellectual exploration and creativity. Her love of math, which she describes as “of the mind” and requiring no empirical evidence, aligns with this philosophy. Boyd, a Science Fiction writer, also inspired Wingate to cultivate her interests in poetry in addition to her scientific interests.

 

“I was always interested in writing poetry,” Wingate shares, ‘It’s not a one or the other sort of thing. Creativity comes from many sources. If you cut off one, it affects the other.’”


Wingate began to attend poetry reading gatherings at U-M, sometimes attended by well-known poets like Robert Pinsky, a Poet In Residence in the College of Engineering at U-M who gave a reading from some of his favorite poems. “My interest in poetry and philosophy integrates itself into my academic choices,” Wingate explains. “It is really the same thing that interests me in all these things. It’s the balance between cosmos – coherence – and chaos that is so interesting to me mathematically. That’s also the case in poetry.”


As an Advanced Studies Postdoctoral researcher at the National Center for Atmospheric Research (NCAR), Wingate significantly contributed to the field of numerical analysis by developing and applying spectral element methods. Collaborating with Mark Taylor, currently the Chief Computational Scientist at Sandia National Laboratories and the son of her former U-M math professor Al Taylor, she explored near-optimal interpolation techniques on triangular mesh elements.


The following year, Wingate accepted a position as a Center for Nonlinear Studies postdoctoral researcher at Los Alamos National Laboratory, where she later became a staff scientist. There, she was a part of the COSIM ocean modeling project involving theoretical fluid dynamics in

triply periodic boxes, an approach that uses a section of fluid with repeating boundary conditions in all three spatial dimensions to model idealized fluid phenomenon. This work inspired an interest in fast singular limits, which remains a focus of her research today. Wingate also had the opportunity to act as a liaison with the Department of Energy, bridging communication between DOE program managers developing new programs and lawmakers crafting informed policies based on current research.


Wingate credits her background in scientific computing and the power of computational discovery as critical to her research. Her ability to do numerical experiments allows her to test out theories regarding wave frequencies in oscillatory fluid dynamics. “I had a strong foundation in mathematics from my engineering degree,” Wingate said. “But if you want to really be creative with numerical algorithms, you have to understand more fundamental numerical mathematics as well as the application.”


By varying the model’s parameter regimes, she can often gain insight into specific phenomena or test her theoretical models. By applying scientific computing to study low-frequency waves in fluid dynamics, for instance, Wingate runs simulations to observe how nonlinear wave triads can produce persistent oscillations. Her aim is to improve the time-to-solution for higher climate model resolutions.

 

In 2013, after over fifteen years at Los Alamos, Wingate accepted a position as a professor of mathematics at the University of Exeter. The shift from working with postdocs at Los Alamos to undergraduates and PhD students at a university has been both challenging and rewarding, allowing her more opportunities to teach and cultivate curiosity in the next generation.


“Go into things with a sense of adventure,” Wingate advises her students. “Even if things don’t turn out the way you thought they would, if you go into it with a sense of adventure, sometimes things turn out better than you might imagine.” As Wingate herself discovered during her time at U-M, venturing into the unknown with an adventurous spirit can lead to unexpected and lifelong rewards, including lasting friendships and cherished memories.

Beth Wingate lectures at the 14th International Conference on Mathematical and Numerical Aspects of Wave Propagation in 2019 at the Vienna University of Technology (TU Wien), Vienna, Austria. (Photo used with permission)