Vanishing viscosity limit for an expanding domain in space

We study the limiting behavior of viscous incompressible flows when the fluid domain is allowed to expand as the viscosity vanishes. We describe precise conditions under which the limiting flow satisfies the full space Euler equations. The argument is based on truncation and on energy estimates, following the structure of the proof of Kato's criterion for the vanishing viscosity limit. This work complements previous work by the authors, see [Kelliher, Comm. Math. Phys. 278 (2008), 753-773] and [arXiv:0801.4935v1].Comment: 23 pages, submitted for publicatio

On the flow map for 2D Euler equations with unbounded vorticity

In Part I, we construct a class of examples of initial velocities for which the unique solution to the Euler equations in the plane has an associated flow map that lies in no Holder space of positive exponent for any positive time. In Part II, we explore inverse problems that arise in attempting to construct an example of an initial velocity producing an arbitrarily poor modulus of continuity of the flow map.Comment: http://iopscience.iop.org/0951-7715/24/9/013/ for published versio

Ceramic and coating applications in the hostile environment of a high temperature hypersonic wind tunnel

A Mach 7, blowdown wind tunnel was used to investigate aerothermal structural phenomena on large to full scale high speed vehicle components. The high energy test medium, which provided a true temperature simulation of hypersonic flow at 24 to 40 km altitude, was generated by the combustion of methane with air at high pressures. Since the wind tunnel, as well as the models, must be protected from thermally induced damage, ceramics and coatings were used extensively. Coatings were used both to protect various wind tunnel components and to improve the quality of the test stream. Planned modifications for the wind tunnel included more extensive use of ceramics in order to minimize the number of active cooling systems and thus minimize the inherent operational unreliability and cost that accompanies such systems. Use of nonintrusive data acquisition techniques, such as infrared radiometry, allowed more widespread use of ceramics for models to be tested in high energy wind tunnels

Serfati solutions to the 2D Euler equations on exterior domains

We prove existence and uniqueness of a weak solution to the incompressible 2D Euler equations in the exterior of a bounded smooth obstacle when the initial data is a bounded divergence-free velocity field having bounded scalar curl. This work completes and extends the ideas outlined by P. Serfati for the same problem in the whole-plane case. With non-decaying vorticity, the Biot-Savart integral does not converge, and thus velocity cannot be reconstructed from vorticity in a straightforward way. The key to circumventing this difficulty is the use of the Serfati identity, which is based on the Biot-Savart integral, but holds in more general settings.Comment: 50 page

A New Method for Laminar Boundary Layer Transition Visualization in Flight: Color Changes in Liquid Crystal Coatings

The visualization of laminar to turbulent boundary layer transition plays an important role in flight and wind tunnel aerodynamic testing of aircraft wing and body surfaces. Visualization can help provide a more complete understanding of both transition location as well as transition modes; without visualization, the transition process can be very difficult to understand. In the past, the most valuable transition visualization methods for fight applications included sublimating chemicals and oil flows. Each method has advantages and limitations. In particular, sublimating chemicals are impractical to use in subsonic applications much above 20,000 feet because of the greatly reduced rates of sublimation at lower temperatures (less than -4 degrees Fahrenheit). Both oil flow and sublimating chemicals have the disadvantage of providing only one good data point per flight. Thus, for many important flight conditions, transition visualization has not been readily available. This paper discusses a new method for visualizing transition in fight by the use of liquid crystals. The new method overcomes the limitations of past techniques, and provides transition visualization capability throughout almost the entire altitude and speed ranges of virtually all subsonic aircraft flight envelopes. The method also has wide applicability for supersonic transition visualization in flight and for general use in wind tunnel research over wide subsonic and supersonic speed ranges

An FFAG Transport Line for the PAMELA Project

The PAMELA project to design an accelerator for hadron therapy using non-scaling Fixed Field Alternating Gradient (NS-FFAG) magnets requires a transport line and gantry to take the beam to the patient. The NS-FFAG principle offers the possibility of a gantry much smaller, lighter and cheaper than conventional designs, with the added ability to accept a wide range of fast changing energies. This paper will build on previous work to investigate a transport line which could be used for the PAMELA project. The design is presented along with a study and optimisation of its acceptance

Chemical spray pyrolysis of Tl-Ba-Ca-Cu-O high-T(sub c) superconductors for high-field bitter magnets

The deposition of Tl-Ba-Ca-Cu-O thick films by spray pyrolyzing a Ba-Ca-Cu-O precursor film and diffusing thallium into the film to form the superconducting phase is examined. This approach was taken to reduce exposure to thallium and its health and safety hazards. The Tl-Ba-Ca-Cu-O system was selected because it has very attractive features which make it appealing to device and manufacturing engineering. Tl-Ba-Ca-Cu-O will accommodate a number of superconducting phases. This attribute makes it very forgiving to stoichiometric fluctuations in the bulk and film. It has excellent thermal and chemical stability, and appears to be relatively insensitive to chemical impurities. Oxygen is tightly bound into the systems, consequently there is no orthorhombic (conductor) to tetragonal (insulator) transition which would affect a component's lifetime. More significantly, the thallium based superconductors appear to have harder magnetic properties than the other high-Tc oxide ceramics. Estimates using magnetoresistance measurements indicate that at 77 K Tl2Ba2CaCu2O10 will have an upper critical field, H(sub c2) fo 26 Tesla for applied fields parallel to the c-axis and approximately 1000 Tesla for fields oriented in the a-b plane. Results to date have shown that superconducting films can be reproducibly deposited on 100 oriented MgO substrates. One film had a zero resistance temperature of 111.5 K. Furthermore, x ray diffraction analysis of the films showed preferential c-axis orientation parallel to the plane of the substrate. These results have now made it possible to consider the manufacture of a superconducting tape wire which can be configured into a topology useful for high-field magnet designs. The research which leads to the preparation of these films and plans for further development are reviewed