Charlie had his guitar.
He played Simon and Garfunkel’s America. 
We visited his childhood home in upstate NY.
We laughed, drank and smoked.
He was my wingman and I his. 
Antioch was our playground.
He was 17
me 18.
We ruled.

Charlie’s Meyers-Briggs score was E S T J. This Meyers-Briggs category is called “the Entrepeneur”. Napoleon and Simon Bolivar were also E S T J's. It means that each time Charlie took on a physics or math question he would launch a proper campaign to get to know it,  get to know its relatives, other members of its family, listen to the question, get comfortable with it, ask it what it wanted, and eventually the question would tell him secrets that it hadn't ever told anyone else. 

For years at Los Alamos, in the CNLS we looked forward to our “August Summer Institute” working with Charlie, John Gibbon, Edriss Titi, Dave Levermore, Ciprian Foias and Peter Constantin. Our “Institute” would always rent a separate house for its August members, all living together. After a whole day interacting closely in mathematics discussions, in the late afternoon, Edriss would barbeque kebabs and Charlie would play the guitar, singing perhaps, sometimes going over to help Edriss supervise the kebabs, while we chatted on about today's possibilities, comfortable under the deep blue New Mexico sky during the best time of the day, when the shadows lengthen and one can see everything clearly. 

In about 1987, Charlie and I visited John Gibbon at Imperial College to continue our work on the CGL. Early each morning we took the 45-minute trip on the London Underground to South Kensington Station on the Piccadilly Line. Then we walked over to nearby Imperial College. Each evening, coming back late on the Underground we’d still be going over the day’s work, sitting together and doing what Charlie called “air board”, which meant writing formulas in the air together and commenting about the terms we were all writing in one of our familiar “air-equations”. Often, fellow passengers would stare at us, some perhaps thinking we were crazy and some perhaps wondering if our gestures were some kind of sign language, or perhaps even that our gestures were leaving something hanging in the air which only we could see.   

As a young man, Charlie Doering’s life was focused on his work. Charlie was a consummate theorist, of great energy and ambition. His mind was churning with energy and ideas each morning when he awoke and it continued throughout the day.  

When Charlie was my postdoctoral colleague at Los Alamos during 1986-1988, his energy astounded me.  He was a dynamo. We once roomed together during a week-long trip. His constant flow of ideas and calculations that week literally wore me out.  Charlie matched his strength and energy against worthy and subtle problems. Charlie didn't attack problems.  Instead, he mounted campaigns against them with strategies and persistence worthy of Napoleon.  One of Charlie's great strengths and something that made him essentially unique was his facile combination of physical intuition and functional analysis.  

This unique combination inspired our work together when he was a postdoc at Los Alamos and we worked on the CGL (Complex Ginzburg Landau) equation. This nonlinear equation is ubiquitous and it has had a wide range of applications from fluids to nonlinear optics. So it was valuable to Charlie to know something about it. By this, I mean he had to know everything about it! 

One summer day in 1986, Charlie reported for his postdoctoral work at the Center for Nonlinear Studies at Los Alamos. On the morning of the day, John Gibbon and I had gotten some preliminary results about the CGL equation.  However, our results were quite incomplete. On that day, we just happened to leave my office as Charlie was walking down the hall to report for duty as a postdoc at the CNLS. John and I excitedly asked Charlie in the hallway whether he knew anything about CGL. Charlie answered, “Gentlemen, CGL is my life. I have just spent two years studying that equation.” 

Needless to say, after Charlie joined us, our CGL project had much more strength and focus.  Charlie would not let us stop until we got everything, including sharp optimal upper bounds on the Lyapunov dimension of the attractor, as well as optimal lower bounds on its dimension.  He kept pushing for improvement until he found a case in which these two bounds have the same power law and differed only by a constant shift. This was a dream result. However, Charlie kept raising the height of our goal higher and higher. Eventually, the bound on the Lyapunov dimension for CGL scaled with the number of NLS solitons that could fit into the domain. When we told that result to Ciprian Foias, Ciprian said, “Oh, congratulations!” That response from Ciprian would have been enough for me! However, Charlie immediately turned to taking the NLS limit and investigating its singularity formation in higher dimensions, or with higher nonlinearity. (By the way, NLS stands here for “nonlinear Schroedinger equation”, not “nonlinear studies”.)

Charlie’s campaign in the NLS project followed Leray's approach for singularity formation in the Navier-Stokes equations for fluid turbulance. Charlie was soon collaborating with the best analysts in the field, including Peter Constantin, Ciprian Foias, Dave Levermore, Edriss Titi, and others.  For example, Charlie and Peter Constantin spent five years on planar Couette flow and eventually obtained maxi-min results on the fractal dimension of its attractor for which the 1969 mini-max results of Howard et al. turned out to be an upper bound. Then Charlie continued his “obsession with convection” as he called it about the scaling laws for unstable Rayleigh-Besnard transport in a porous medium, which applies to the mechanism for carbon sequestration. Again, Charlie mounted a campaign and got to grips with this problem by using what he called, a “mother functional”. For more on this, see Charlie’s lecture video about it at https://www.youtube.com/watch?v=eDBHWU945Y8

Charlie, John, Peter, Dave, Edriss and I have followed each other and stayed in touch all through our careers, always trying to get together again like we did in the good old days of the “August Institute”. This was a meeting Charlie used to organise every year during August at Los Alamos. Eventually, an opportunity came for us to get him back to Los Alamos as the Deputy Director for the Center for Nonlinear Studies.  When Charlie returned to the CNLS, all of us felt the power increase immediately.  Charlie was very successful in attracting the best postdocs in his field from all over the world. Charlie also took over as Editor of the Nonlinear Science section of Physics Letters A.  As Editor of PLA, Charlie held the highest standards and brought great credit to that section of the journal which serves as part of his legacy.

Charlie's other great expertise, besides physics, fluid dynamics and functional analysis, was a particular branch of statistical physics that combines nonlinearity and stochastic processes. This burgeoning field of endeavor is often called ``nonequilibrium statistical mechanics.'' Charlie was a world leader in this field and he wrote some of its fundamental papers.  This work sustained Charlie's investigations into turbulence using stochastic analysis.  Charlie was well versed in this topic. In fact, one aspect of Charlie’s PhD thesis with Cecile De Witt at U Texas in Austin investigated the effects of adding noise to the Burgers equation. Charlie found that additive noise creates new solution behaviour for Burgers equation which was not present when either noise or nonlinearity were absent. This issue is still a hot topic in the theory of stochastic partial differential equations (SPDE). Charlie gave me SPDE lessons when he postdoc-ed with me. However, our CGL work with John absorbed all my attention at that time. Perhaps not surprisingly though, my own work now follows in his footsteps. 

Charlie's lecturing style was lucid and enthusiastic.  He sparked ideas as he spoke and often inspired his audience with his style of making new realizations while answering questions.  Often in answering a question Charlie finished by sketching out how this person's question led to an entire new research direction, for anyone who might care to pursue it. For example, Charlie lectured several times per  year for about five years during his work with Peter Constantin on the planar Couette problem.  Each time, Charlie laid out the program, told what had been known previously and then carried his audience to an appreciation of new, interesting, and substantial progress, finishing by revealing an exciting vista of the plethora of results which lay ahead. 

I am proud to have known Charlie Doering. If you want to know more, then just ask me next time you see me. I can tell you many stories about my personal experiences with the late, great Charlie Doering. Charlie was a great companion -- generous and fun.