In chronological order:
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In January I did some small-scale experiments on the heights of water jets fired vertically. The accuracy of the measurement was considerably better than previous measurements, and the design of the experiments as a whole was fairly different from most as I intentionally tried to place the water jets in different “regimes” to get different behavior. For the moment I am holding off on publication of these experiments for various reasons, but I am particularly happy with the results so far. I’m planning to start some new related experiments in about a month.
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During the initial part of the COVID-19 pandemic I was editing this paper in response to reviews. I had a few epiphanies which dramatically improved the paper in my view. I recognized a simple way to model what I call the “turbulent Rayleigh” regime of liquid jets (which works nicely with the limited data available), and I also found a simple way to model the boundary between what I call the “downstream transition” and “laminar Rayleigh” regimes. The latter approach stands in strong contrast to the prevailing approaches to this, which I argue are wrong and can’t account for the observed phenomena. The preprint I linked to unfortunately doesn’t contain these improvements as the journal required me to transfer copyright to submit the article. In about a year I can post an updated copy, however. I doubt most would find these developments particularly exciting, but they’ve opened a lot of research possibilities for me. (Re: turbulent Rayleigh modeling, I recently learned that what I did in this paper was only approximately correct, though a good approximation, and that the truly correct approach would be a lot more work.)
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In August, I successfully defended my PhD after 7 years. Few PhDs are easy, but mine was particularly difficult due largely (in my view) to differences in research philosophy between my advisor and myself.
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For a variety of reasons I wasn’t able to get a postdoc in my field after my PhD. However, I was able to figure out some decent ways to continue doing research on the side while working a full-time (non-research) job. I discuss this a bit more here. I am still improving here and learning about my current job (patent examiner). I will have more to report later, perhaps in February.
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Since starting my current job, I’ve made a few notable research accomplishments for my new project. In a paper I published this year I criticized “stability theory” approaches to calculating the breakup of a turbulent liquid jet into droplets. Yet despite my criticisms, which one reviewer called overly negative as I recall, I’ve started doing my own version of stability theory which addresses my criticisms.
Here’s one thing I’ve figured out so far: On a turbulent liquid jet, when one measures the RMS roughness of the jet as a function of distance from the nozzle, there’s an initially linear increase in the RMS roughness with distance. To my knowledge there was no explanation of this behavior before my work. I have developed a theory derived from the Euler (corrected from Navier-Stokes; I’m not including viscosity) equations which easily explains this behavior, and predicts the slope. My theory shows that this behavior is not universal for turbulent jets, however. (Calculating farther downstream is not trivial.)