The Elder Problem

This paper presents an autobiographical and biographical historical account of the genesis, evolution and resolution of the Elder Problem. It begins with John W. Elder and his autobiographical story leading to his groundbreaking work on natural convection at Cambridge in the 1960’s. His seminal work published in the Journal of Fluid Mechanics in 1967 became the basis for the modern benchmark of variable density flow simulators that we know today as “The Elder Problem”. There have been well known and major challenges with the Elder Problem model benchmark—notably the multiple solutions that were ultimately uncovered using different numerical models. Most recently, it has been shown that the multiple solutions are indeed physically realistic bifurcation solutions to the Elder Problem and not numerically spurious artefacts. The quandary of the Elder Problem has now been solved—a major scientific breakthrough for fluid mechanics and for numerical modelling. This paper—records, reflections, reminiscences, stories and anecdotes—is an historical autobiographical and biographical memoir. It is the personal story of the Elder Problem told by some of the key scientists who established and solved the Elder Problem. 2017 marks the 50 year anniversary of the classical work by John W. Elder published in Journal of Fluid Mechanics in 1967. This set the stage for this scientific story over some five decades. This paper is a celebration and commemoration of the life and times of John W. Elder, the problem named in his honour, and some of the key scientists who worked on, and ultimately solved, it.