Life of Wry

So, this happened today…

The Cambridge University Press’s prestigious Journal of Fluid Mechanics published eight articles today in its online publication for its Volume 983 – 25 March 2024 issue… and Peter’s was one of them.

I sure don’t know my way around academic journals. For example, of the eight works published today, six are “articles,” one is a “rapid,” and another is a “focus.” Not sure what those distinctions are. If you click on articles, you get 119 pages — approx 20 articles per page (inclusive of rapids and focuses). That’s well over 2000 articles going back to 2011 (not sure how long this journal’s been around). You can search on most cited, and all kinds of other interesting things. They seem to publish every two weeks, but there also look to be several article drops per each issue. Best I can figure.

Well.. all I know is it’s a huge accomplishment to get into this journal and it took the better part of a year of writing, rewriting, review by a 3-judge panel, a rejection, an appeal of that rejection, more rewrites and finally an acceptance. Not to mention the research that produced the findings that became the subject of the article.

This isn’t Peter’s first published article, but it’s his most notable. Suffice to say, he’s over the moon and we’re proud.

The title of his article is Beyond optimal disturbances: a statistical framework for transient growth (by Peter Frame and Aaron Towne, in that order). It’s an understatement to say we hardly understand a word of it, in spite of numerous attempts on Peter’s part to explain the research. Additionally, both Jim and I have read numerous versions of the article — have even proofread for grammar and spelling — but would still be hard pressed to offer a cogent summary. (Again, understatement.)

To wit, here is the abstract:

The theory of transient growth describes how linear mechanisms can cause temporary amplification of disturbances even when the linearized system is asymptotically stable as defined by its eigenvalues. This growth is traditionally quantified by finding the initial disturbance that generates the maximum response at the peak time of its evolution. However, this can vastly overstate the growth of a real disturbance. In this paper, we introduce a statistical perspective on transient growth that models statistics of the energy amplification of the disturbances. We derive a formula for the mean energy amplification and spatial correlation of the growing disturbance in terms of the spatial correlation of the initial disturbance. The eigendecomposition of the correlation provides the most prevalent structures, which are the statistical analogue of the standard left singular vectors of the evolution operator. We also derive accurate confidence bounds on the growth by approximating the probability density function of the energy. Applying our analysis to Poiseuille flow yields a number of observations. First, the mean energy amplification is often drastically smaller than the maximum. In these cases, it is exceedingly unlikely to achieve near-optimal growth due to the exponential behaviour observed in the probability density function. Second, the characteristic length scale of the initial disturbances has a significant impact on the expected growth, with large-scale initial disturbances growing orders of magnitude more than small-scale ones. Finally, while the optimal growth scales quadratically with Reynolds number, the mean energy amplification scales only linearly for certain reasonable choices of the initial correlation.

Here’re two screen shots of what it looks like on the online site:

I just can’t tell you. We’re proud because he’s pleased and it was a lot of work and he learned a ton. It’s a great accomplishment. Eager to see what his next thing is.