Mathematical Sciences: Investigation of Rayleigh-Taylor Flow

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This proposal concerns the motion of an interface between two fluids of different densities when the heavier fluid initially rests on the lighter fluid (Rayleigh-Taylor flow). A combination of analytical and numerical techniques will be employed to follow the motion of a highly convoluted interface for late times when traditional numerical methods have difficulty because of resolution problems. The method relies on actually following the motion of singularities in the unphysical domain that on their approach to the physical domain correspond to interfacial features such as spikes. By subtracting such singularities from a basis representation in the physical domain, it is proposed to calculate a continually distorting Rayleigh-Taylor interface numerically. Interest in the Rayleigh-Taylor instability stems from its disruptive presence in inertial confinement devices where attempt is made to confine a hot plasma through a magnetic field and achieve controlled nuclear fusion for energy needs. Because an accelerating field and a gravitational field are equivalent, the radial acceleration of a plasma as it turns around makes it susceptible to this instability. It is clear that for plasma confinement to succeed, one should be able to control this instability. A first step is to understand the detailed nature of a Rayleigh-Taylor flow. The method of attack is novel and is an attempt to overcome the shortcomings of some other traditional numerical methods.