In the late 1950s and early 1960s a small group of mostly work and show its practicality before it was formally exhibited under his name. To our relief that exhibition finally young meteorologists in a few institutions started what later became known as large eddy simulation. Their work occurred in 1966, when Akio published his paper in the new Journal of Computational Physics. As they say, the rest initially grew out of the first successful numerical weather prediction experiments, led by John von Neumann in the is history. Arakawa's methods, together with increasing computing capabilities, rapidly opened the field. It became late 1940s. The group was small partly because numerical simulation of fluid dynamics was looked on with skepti-clear that such schemes could be developed for almost any quantity transported by a variable flow field and with cism, but mostly because only a few computers capable of making a start on the problems existed, nearly all of which almost any gridding scheme. Admittedly there were and still are holdouts for upwind differencing schemes, which were in the United States. The first important published work was by Phillips [2], who generated a model of the are also stable, though damped.
The Science Citation Index helps trace the impact of atmospheric general circulation from nearly biblical foundations-''In the beginning there was darkness and void, this paper. In the first two years after publication 3 and 6 citations were reported. After that the number built up and God sent forth the light.'' An early followup was an attempt to simulate buoyant convection by Malkus and from 14 in 1969 to 26 in 1990, and has generally run between 15 and 20 per year, with a total of about 500 over 30 years. Witt [1]. Both these efforts, though successful to a point, were marred by a mysterious form of computational insta-Examination of the 18 references for one year, 1983, shows that half of them appeared in standard meteorological jour-bility, identified by Phillips [3] as associated with aliased products of variable quantities, one of them usually flow nals, a few in less well known such journals, and about one-third in journals of other fields. The usual gradual velocity. Phillips overcame this ''nonlinear instability'' by Fourier filtering out the high-frequency modes (last oc-decrease in citations for classic papers is apparently countered by the continued increase in numerical simulations tave), thus anticipating, though not quite correctly, the ''2/3 rule'' later used in pseudo-spectral models. Inciden-using Arakawa's methods. However, the citations underestimate the impact, since many recent authors who use the tally, I believe this occurred before the ''fast Fourier transform'' was widely known and applied, although for the methods make primary reference to work of a colleague who has developed them for application to a specific field, low resolutions available at that time it probably would not have mattered much.
or they simply use a generic expression, such as ''variance conserving methods.'' It was generally thought that nonlinear instability was an inherent limitation of centered difference schemes through Although Arakawa's methods eliminated the instability problem, they remain subject to aliasing and to phase er-their wavenumber aliasing. Akio Arakawa realized, however, that if a quadratic variable, like kinetic energy, could rors, often serious for short wavelengths, and they also remain subject to the Courant time step limitation. A large be conserved in a way similar to its conservation in the continuous fluid equations, a degree of stability was as-number of alternative approaches have been developed to try to overcome these problems, including the pseudo-sured. In the early 1960s he began showing, informally and through seminars and conference papers, a possible spectral technique, high-accuracy monotone upwind schemes, semi-Lagrangian schemes, and others. For simple remedy for the problem, using second order numerical approximations to the governing equations which allowed geometries, the spectral or pseudo-spectral methods with the 2/3 rule wavenumber cutoff eliminate aliasing and its conservation of quadratic moments. Akio was cautious and deliberate about going into print with his methods, associated instability and offer higher accuracy. ''Monotonic'' schemes are often applied when it is important not preferring to first develop careful proofs and rather general algorithms, including those using fourth order accuracy to exceed the maximum or minimum value of some transported quantity. Semi-Lagrangian schemes allow, under and curvilinear coordinates. This time delay allowed, or nearly forced, some of us to take advantage of his early certain conditions, a longer time step. The Arakawa tech-101