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

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

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

Ammonia emissions from cattle urine and dung excreted on pasture

Twelve cattle were kept for three days in a circular area of 16 m radius on short pasture and fed with freshly-cut pasture. Ammonia (NH<sub>3</sub>) emissions from the urine and dung excreted by the cattle were measured with a micrometeorological mass-balance method, during the cattle presence and for 10 subsequent days. Daily-integrated emission rates peaked on Day 3 of the experiment (last day of cattle presence) and declined steadily for five days thereafter. Urine patches were the dominant sources for these emissions. On Day 9, a secondary emissions peak occurred, with dung pats likely to be the main sources. This interpretation is based on simultaneous observations of the pH evolution in urine patches and dung pats created next to the circular plot. Feed and dung samples were analysed to estimate the amounts of nitrogen (N) ingested and excreted. Total N volatilised as NH<sub>3</sub> was 19.8 (± 0.9)% of N intake and 22.4 (± 1.3)% of N excreted. The bimodal shape of the emissions time series allowed to infer separate estimates for volatilisation from urine and dung, respectively, with the result that urine accounted for 88.6 (± 2.6)% of the total NH<sub>3</sub> emissions. The emissions from urine represented 25.5 (± 2.0)% of the excreted urine-N, while the emissions from dung amounted to 11.6 (± 2.7)% of the deposited dung-N. Emissions from dung may have continued after Day 13 but were not resolved by the measurement technique. A simple resistance model shows that the magnitude of the emissions from dung is controlled by the resistance of the dung crust

Ammonia emissions from cattle urine and dung excreted on pasture

Twelve cattle were kept for three days in a circular area of 16 m radius on short pasture and fed with freshly-cut pasture. Ammonia (NH₃) emissions from the urine and dung excreted by the cattle were measured with a micrometeorological mass-balance method, during the cattle presence and for 10 subsequent days. Daily-integrated emission rates peaked on Day 3 of the experiment (last day of cattle presence) and declined steadily for five days thereafter. Urine patches were the dominant sources for these emissions. On Day 9, a secondary emissions peak occurred, with dung pats likely to be the main sources. This interpretation is based on simultaneous observations of the pH evolution in urine patches and dung pats created next to the circular plot. Feed and dung samples were analysed to estimate the amounts of nitrogen (N) ingested and excreted. Total N volatilised as NH₃ was 19.8 (± 0.9)% of N intake and 22.4 (± 1.3)% of N excreted. The bimodal shape of the emissions time series allowed to infer separate estimates for volatilisation from urine and dung, respectively, with the result that urine accounted for 88.6 (± 2.6)% of the total NH₃ emissions. The emissions from urine represented 25.5 (± 2.0)% of the excreted urine-N, while the emissions from dung amounted to 11.6 (± 2.7)% of the deposited dung-N. Emissions from dung may have continued after Day 13 but were not resolved by the measurement technique. A simple resistance model shows that the magnitude of the emissions from dung is controlled by the resistance of the dung crust. © Author(s) 2013

A Kato type Theorem for the inviscid limit of the Navier-Stokes equations with a moving rigid body

The issue of the inviscid limit for the incompressible Navier-Stokes equations when a no-slip condition is prescribed on the boundary is a famous open problem. A result by Tosio Kato says that convergence to the Euler equations holds true in the energy space if and only if the energy dissipation rate of the viscous flow in a boundary layer of width proportional to the viscosity vanishes. Of course, if one considers the motion of a solid body in an incompressible fluid, with a no-slip condition at the interface, the issue of the inviscid limit is as least as difficult. However it is not clear if the additional difficulties linked to the body's dynamic make this issue more difficult or not. In this paper we consider the motion of a rigid body in an incompressible fluid occupying the complementary set in the space and we prove that a Kato type condition implies the convergence of the fluid velocity and of the body velocity as well, what seems to indicate that an answer in the case of a fixed boundary could also bring an answer to the case where there is a moving body in the fluid

Offshore monopile in the southern North Sea: Part I, calibrated input sea state

Safe, reliable access is an essential precondition for the successful maintenance of offshore wind farms. Access from vessels to wind turbines depends on the severity of the sea state in the vicinity of the turbine support structure. This paper presents a validation of a numerical boundary condition developed to reproduce the seasonal sea state at Teesside Offshore Wind Farm, off the coast of the UK. The boundary condition, called customSpectrum, was derived from wave energy spectra obtained by analysis of existing field measurements of wave free-surface displacement at the wind farm site and implemented in OpenFoam, the open-source computational fluid dynamics library. OpenFoam was then used to simulate typical spring, summer, autumn and winter sea states as uni-directional waves. Predicted surface elevations and significant wave heights were found to be in agreement with in situ buoy data, thus validating the OpenFoam model. Satisfactory agreement was achieved between analytical and numerically predicted spectral density functions for the horizontal and vertical water particle velocity components. It was found that the wave activity at Teesside is uni-modal in spring and autumn, and bi-modal in summer and winter. Extending the procedure to multi-directional waves in crossing seas is recommended