Prof. John (J. D.) Gibbon, Mathematics Department
Despite its longevity, the phenomenon of incompressible fluid turbulence remains one of the great problems of modern classical science and engineering. Various approaches have been attempted by many parties who have differing interests across a wide spectrum of science and engineering: 1) Navier-Stokes analysis; 2) multifractal physics; 3) large-scale CFD; 4) turbulence modelling; 5) oceanographic and atmospheric flows; 6) active turbulence (flocking of birds and the shoaling of fish and bacteria). My own interests lie in the first two approaches and also in the 6th. The open problem of the regularity of solutions of the 3D Navier-Stokes equations (see Doering & Gibbon "Applied Analysis of the Navier-Stokes equations" CUP '95) leaves us with only with Leray's theory of weak solutions. The 4th paper below shows how this theory can be reconciled with the multifractal physics approach. My most recent work is on helicity in the compressible Euleer/MHD equations. It shows how the barotropic condition on the pressure can be removed and discusses the consequencees of this removal.
A selection of preprints and papers
