Reply to Comment by S. Saujani and T. G. Shepherd on "Balance and the Slow Quasimanifold: Some Explicit Results"

Rupert Ford (deceased), Michael E. McIntyre, and Warwick A. Norton

Journal of the Atmospheric Sciences, 59, 2878-2882

Here's the reprint, copyright © American Meteorological Society.

The Comment itself is published in

Journal of the Atmospheric Sciences, 59, 2874-2877

The main topic of discussion is Lighthill radiation, the spontaneous-adjustment emission of inertia-gravity waves by unsteady vortical motion (misnamed `geostrophic' adjustment). This subtle process sets limitations on the concepts of balance, slow quasimanifold, and potential-vorticity invertibility.

NB:   A subsequent discovery, the hyperbalance equations, is presented and discussed in a pair of papers by Dr Ali R. Mohebalhojeh and myself (JAS 2007). If you're interested, follow this link for further explanation and reprint downloads (third paragraph). The discovery of the hyperbalance equations implies that some remarks in the above Reply about non-Hamiltonian `velocity splitting' are wrong. What has, on the other hand, stood scrutiny for the most part is the general rule that imbalance and spontaneous-adjustment emission are exponentially small in the limit of small Rossby number, reinforcing Lighthill's arguments. Admittedly, a likely exception to this general rule has now been discovered. But it is somewhat artificial. The latest twists and turns and literature references -- about Lighthill and non-Lighthill radiation -- can be found in a NEWreview under consideration for the J. Atmos. Sci. Special Collection on `Spontaneous Imbalance'. This paper is titled Spontaneous imbalance and hybrid vortex-gravity structures (.pdf, 0.5 Mbyte) and is dedicated to the memory of James Lighthill and Rupert Ford.

Note by MEM: The above Reply may well be Rupert Ford's last scientific publication. It had to be revised in his absence, in response to the final revision of SS, using extensive notes made during our last co-authors' consultation. The revision tried to echo Rupert's wonderful spirit of generosity, engagement, and enthusiasm, and above all tried to be something like what would have emerged had he still been with us --- conveying some sense of his penetrating insight and rigor and of his joy in serious intellectual endeavour, of his joy in trying to bring understanding to a difficult problem area. There are a few more remarks about Rupert's life and about his brief yet brilliant research career, so tragically cut short in March 2001, in the obituary published in the Quarterly Journal of the Royal Meteorological Society, 127, 1489-1490, April 2001 B. The Royal Meteorological Society, in which Rupert was active as Secretary of the Dynamical Problems Specialist Group, now administers a

Rupert Ford Memorial Fund             Rupert Ford at the height of his powers

supporting travel and exchange among young scientists of any nationality and residency. For anyone wishing to contribute to this fund in Rupert's memory, a plain-text copy of the donation form is available here (1.4 kbyte), and the corresponding Word document here (26 kbyte). Further information is available from the Royal Meteorological Society's website, and their postal address is 104 Oxford Road, Reading RG1 7LL, United Kingdom.

Here as a service to the community is a searchable pdf (8.5 Mbyte) of Rupert's PhD thesis:

Ford, R., 1993: Gravity wave generation by vortical flows in a rotating frame, DAMTP, University of Cambridge, 269pp. This has been recovered and archived here with the kind and generous help of Rupert's father, Professor E. David Ford. There is one page missing, page 198, containing a figure showing shear instability and rollup in a case labelled `simulation Aii.' Pages 145 and 246 are significantly damaged at the right margin, the former quite badly and the latter mainly insofar as the phrase "Hi-iv (solid lines)" is missing from the right-hand edge of the figure caption. Here is a separate scan of pages 145 and 198.

Back to my home page ---- back to Atmospheric Dynamics home page

Michael McIntyre (mem at, DAMTP, University of Cambridge, Silver Street, Cambridge CB3 9EW

Last updated 9 Oct 2012
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