9704546 Childress This research deals with several problems in fluid dynamics and magnetohydrodynamics (MHD). Continuing work on the MHD dynamo problem will focus on the dynamical fate of intense small-scale magnetic structure creating duing the kinematic phase of fast dynamo action. This question is important since observations of galactic magnetic fields indicate that the equilibrated fields have no dominant small-scale structure. A second project deals with separation in the corner region of Prandtl-Batchelor flows within a domain (such as a rectangle), where the Euler limit has boundary stagnation points. The breakdown of boundary layer theory due to the presence of boundary stagnation points can be investigated in the limit of large Reynolds number R by imposing wall data which is within close to that of the Euler limit with core vorticity 1. A third con- tinuing study deals with an experiment in non-Boussinesq convec- tion at high Rayleigh and Prandtl numbers and an analysis of the large-scale motion which occurs in this flow. In a new research initiative, we will study analytical and numerical modeling of high-lift mechanisms in flapping insect flight, with particular emphasis on hovering. We will study by simulation the shedding of vortices from a sharp edge in time-dependent 2D Navier-Stokes flows at Reynolds numbers of several thousand. We shall analyze the significance and implication of the Kutta condition, the optimal use of shed vortices in the production of lift, and applications within conical symmetry to 3D flapping motions. The Universe is pervaded by magnetic fields, threading through galaxies, and surrounding stars and planets. However, the origin of these fields is not well understood. In particular the galactic fields pose many unanswered questions. This reseapch concerns the dynamo theory of this magnetism. This unifying theory proposes that all fields originate from amplification of a seed magnetic field developed during the big bang. The process of amplification, dynamo action, resembles the laboratory dynamo effect but is more complicated because it occurs in free fluid motion, usually turbulent motion. Our research is attempting to understand the processes underlying this amplification and the structure of the fields which result, especially how this structure is developed by the natural processes available in turbulence. Other parts of our research program deal with aspects of classical fluid dynamics of importance in the convective flows within planets and stars. It is flows of these kinds which are often responsible for the dynamo effect. For example, convection within the Earth's fluid core is believed to drive the Earth's dipolar magnetic field. A new initiative in our research program will deal with the fluid mechanics of insect hovering flight. Our ilterest is in utilizing lifting mechanisms of flapping insect hoverers in the design of small unmanned airborne vehicles. These mechanisms utilize vortices which are shed into the fluid near the flyer, and interact with it so as to augment the lift. We shall study the basic process of shedding of vorticity from surfaces, the optimization of the resulting lift, and the numerical simulation of the flows in two dimensions. Important three-dimensional effects will be modeled using conical symmetry of the flow field.
