Digitisation of this thesis was sponsored by Arcadia Fund, a charitable fund of Lisbet Rausing and Peter Baldwin

Drury, Luke O'Connor

Apollo (Cambridge)

Some fluid dynamical problems in astrophysics

In the first part of my dissertation I consider certain aspects of the cosmic turbulence theory of galaxy formation (as revived by Ozernoi), Using a generalised form of a transformation due to Kurskov and Ozernoi I exhibit a formal equivalence between the problem of turbulence in an expanding universe containing a coupled matter-radiation fluid and in a non-expanding fluid with a time- dependent viscosity. This enables me to extend the Olson-Sachs formula for vorticity generation in cosmic turbulence to matter-radiation fluid and to show that, contrary to the hypothesis of Ozernoi, the turbulence can not have an inertial subrange at the epoch of recombination.

In the second part I consider the linear inviscid stability of axisymmetric flows. Using the projective form of the perturbation equations (rather than the linear fonn) I obtain a simple proof of a generalised Richardson criterion which holds for all boundary conditions which do not actively feed energy to the perturbation. Further analysis shows the unifonn density and presure ,discs with self-similar rotation laws are stable to perturbations which are incompressible in character, but that instability is a generic feature of differentially rotating compressible systems; this result is explained in terms of over-reflection of sound waves from the corotation radius. Two families of self-similar discs in which the perturbation equations can he solved exactly are described and used to estimate the magnitude of this effect.

In the third part I consider the problem of numerically solving boundary value problems of the Orr-Sommerfeld type by shooting methods and describe a unifying geometrical interpretation of the principal methods.

In appendix A I apply the methods of section two to plane parallel flows and derive among other results an extension of Rayleigh's inflection point theorem to compressible isobaric and isentropic flows .

In appendix B I describe a program for locating the zeros of a holomorphic function which is very useful in eigenvalue problems of the type considered in section three and give an example of its use .Scanned and made publicly available by the University of Cambridge

Some fluid dynamical problems in astrophysics

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