Acoustic radiation patterns for a source in a hard-walled unflanged circular duct

Acoustic radiation patterns are measured over a 320 deg arc for a point source in a finite length, hard walled, unflanged circular duct. The measured results are compared with computed results which are based on the Wiener-Hopf solution for radiation from a semi-infinite unflanged duct. Measurements and computations are presented for frequencies slightly below and slightly above each of the first four higher order radial mode cutoff frequencies. It is found that the computed and measured patterns show better agreement below the mode cut-off frequencies than above and that the agreement is better at lower frequencies that at higher frequencies. The computed radiation patterns do not show fine lobes which are caused by diffraction from the back end of the duct

Variational Principles for Lagrangian Averaged Fluid Dynamics

The Lagrangian average (LA) of the ideal fluid equations preserves their transport structure. This transport structure is responsible for the Kelvin circulation theorem of the LA flow and, hence, for its convection of potential vorticity and its conservation of helicity. Lagrangian averaging also preserves the Euler-Poincar\'e (EP) variational framework that implies the LA fluid equations. This is expressed in the Lagrangian-averaged Euler-Poincar\'e (LAEP) theorem proven here and illustrated for the Lagrangian average Euler (LAE) equations.Comment: 23 pages, 3 figure

Two-component {CH} system: Inverse Scattering, Peakons and Geometry

An inverse scattering transform method corresponding to a Riemann-Hilbert problem is formulated for CH2, the two-component generalization of the Camassa-Holm (CH) equation. As an illustration of the method, the multi - soliton solutions corresponding to the reflectionless potentials are constructed in terms of the scattering data for CH2.Comment: 22 pages, 3 figures, draft, please send comment

Resonant Interactions in Rotating Homogeneous Three-dimensional Turbulence

Direct numerical simulations of three-dimensional (3D) homogeneous turbulence under rapid rigid rotation are conducted to examine the predictions of resonant wave theory for both small Rossby number and large Reynolds number. The simulation results reveal that there is a clear inverse energy cascade to the large scales, as predicted by 2D Navier-Stokes equations for resonant interactions of slow modes. As the rotation rate increases, the vertically-averaged horizontal velocity field from 3D Navier-Stokes converges to the velocity field from 2D Navier-Stokes, as measured by the energy in their difference field. Likewise, the vertically-averaged vertical velocity from 3D Navier-Stokes converges to a solution of the 2D passive scalar equation. The energy flux directly into small wave numbers in the $k_z=0$ plane from non-resonant interactions decreases, while fast-mode energy concentrates closer to that plane. The simulations are consistent with an increasingly dominant role of resonant triads for more rapid rotation

Forward velocity effects on fan noise and the influence of inlet aeroacoustic design as measured in the NASA Ames 40 x 80 foot wind tunnel

The inlet radiated noise of a turbofan engine was studied. The principal research objectives were to characterize or suppress such noise with particular regard to its tonal characteristics. The major portion of this research was conducted by using ground-based static testing without simulation of aircraft forward speed or aircraft installation-related aeroacoustic effects

Glasses as sources of condensed phosphates on the early earth

Procedures for the analysis of phosphorus in geological material normally aims for the determination of the total amount of P expressed as orthophosphate [Formula: see text] or the differentiation between inorganic and organic P. This is probably due to analytical difficulties but also to the prevalent opinion that the chemistry of phosphorus in geological environments is almost entirely restricted to the mineral apatite. Because of the low solubility of apatite it is, therefore, commonly argued that little P was around for prebiotic chemistry and that pre-biological processes would essentially have had to do without this indispensable element unless it was provided by alternative sources or mechanisms (such as reduction and activation by lightning or delivery to Earth by celestial bodies). It is a paradox that the potential existence of reactive phosphorus compounds, such as the mineral schreibersite - iron phosphide, in geological material on Earth is seldom considered although we are aware of the existence of such compounds in meteorite material. The content of Al(2)O(3) in rocks appears to be important for the speciation of phosphorus and for how strongly it binds to silicates. In general, low alumina seems to promote the existence of isolated charge-balanced phosphorus complexes

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