Shallow water equations: Magic and limitations

D Liang from Cambridge University explains the shallow water equations and their applications to the dam-break and other steep-fronted flow modeling. They assume that the horizontal scale of the flow is much greater than the vertical scale, which means the flow is restricted within a thin layer, thus the vertical momentum is insignificant and the pressure distribution is hydrostatic. The left hand sides of the two momentum equations represent the acceleration of the fluid particle in the horizontal plane. If the fluid acceleration is ignored, then the two momentum equations are simplified into the so-called diffusion wave equations. In contrast to the SWEs approach, it is much less convenient to model floods with the Navier-Stokes equations. In conventional computational fluid dynamics (CFD), cumbersome treatments are needed to accurately capture the shape of the free surface. The SWEs are derived using the assumptions of small vertical velocity component, smooth water surface, gradual variation and hydrostatic pressure distribution.

A three-dimensional tunnel model for calculation of train-induced ground vibration

The frequency range of interest for ground vibration from underground urban railways is approximately 20 to 100 Hz. For typical soils, the wavelengths of ground vibration in this frequency range are of the order of the spacing of train axles, the tunnel diameter and the distance from the tunnel to nearby building foundations. For accurate modelling, the interactions between these entities therefore have to be taken into account. This paper describes an analytical three-dimensional model for the dynamics of a deep underground railway tunnel of circular cross-section. The tunnel is conceptualised as an infinitely long, thin cylindrical shell surrounded by soil of infinite radial extent. The soil is modelled by means of the wave equations for an elastic continuum. The coupled problem is solved in the frequency domain by Fourier decomposition into ring modes circumferentially and a Fourier transform into the wavenumber domain longitudinally. Numerical results for the tunnel and soil responses due to a normal point load applied to the tunnel invert are presented. The tunnel model is suitable for use in combination with track models to calculate the ground vibration due to excitation by running trains and to evaluate different track configurations. © 2006 Elsevier Ltd. All rights reserved.

An efficient frequency-domain algorithm for wave scattering problems with application to jet noise

This paper presents a pseudo-time-step method to calculate a (vector) Green function for the adjoint linearised Euler equations as a scattering problem in the frequency domain, for use as a jet-noise propagation prediction tool. A method of selecting the acoustics-related solution in a truncated spatial domain while suppressing any possible shear-layer-type instability is presented. Numerical tests for 3-D axisymmetrical parallel mean flows against semi-analytical reference solutions indicate that the new iterative algorithm is capable of producing accurate solutions with modest computational requirements.

On a classical problem of acoustic wave scattering by a free vortex: Numerical modelling

The scattering of sound from a point source by a Rankine vortex is investigated numerically by solving the Euler equations with the novel high-resolution CABARET method. For several Mach numbers of the vortex, the time-average amplitudes of the scattered field obtained from the numerical modeling are compared with the theoretical scaling laws' predictions. Copyright © 2009 by Sergey Karabasov.

Wave propagation in a slowly-varying duct with mean vortical swirling flow

The propagation of unsteady disturbances in a slowlyvarying cylindrical duct carrying mean swirling flow is investigated using a multiple-scales technique. This is applicable to turbomachinery flow behind a rotor stage when the swirl and axial velocities are of the same order. The presence of mean vorticity couples acoustic and vorticity equations which produces an eigenvalue problem that is not self-adjoint unlike that for irrotational mean flow. In order to determine the amplitude variation along the duct, an adjoint solution for the coupled system of equations is derived. The solution breaks down where a mode changes from cut on to cut off. In this region the amplitude is governed by a form of Airy's equation, and the effect of swirl is to introduce a small shift in the origin of the Airy function away from the turning-point location. The variation of axial wavenumber and amplitude along the duct is calculated. In hard-walled ducts mean swirl is shown to produce much larger amplitude variation along the duct compared with a nonswirling flow. Mean swirl also has a large effect in ducts with finite-impedance walls which differs depending on whether modes are co-rotating with the swirl or counter rotating. © 2001 by A.J. Cooper, Published by the American Institute of Aeronautics and Astronautics, Inc.

Influence of surfactant solubility on the deformation and breakup of a bubble or capillary jet in a viscous fluid

In a previous study [M. Hameed, J. Fluid Mech. 594, 307 (2008)] the authors investigated the influence of insoluble surfactant on the evolution of a stretched, inviscid bubble surrounded by a viscous fluid via direct numerical simulation of the Navier-Stokes equations, and showed that the presence of surfactant can cause the bubble to contract and form a quasisteady slender thread connecting parent bubbles, instead of proceeding directly toward pinch-off as occurs for a surfactant-free bubble. Insoluble surfactant significantly retards pinch-off and the thread is stabilized by a balance between internal pressure and reduced capillary pressure due to a high concentration of surfactant that develops during the initial stage of contraction. In the present study we investigate the influence of surfactant solubility on thread formation. The adsorption-desorption kinetics for solubility is in the diffusion controlled regime. A long-wave model for the evolution of a capillary jet is also studied in the Stokes flow limit, and shows dynamics that are similar to those of the evolving bubble. With soluble surfactant, depending on parameter values, a slender thread forms but can pinch-off later due to exchange of surfactant between the interface and exterior bulk flow. © 2009 American Institute of Physics.

GSPS photonic analogue to digital conversion system using broadband continuous wave source

An 80 GSPS photonic ADC system is demonstrated, using broadband MLL and dispersive fibre to form a continuous waveform with time-wavelength mapping, and AWG to channelise. Tests are carried out for RF signals up to 10GHz. © 2005 Optical Society of America.

High rate deposition of ta-C:H using an electron cyclotron wave resonance plasma source

A compact electron cyclotron wave resonance (ECWR) source has been developed for the high rate deposition of hydrogenated tetrahedral amorphous carbon (ta-C:H). The ECWR provides growth rates of up to 1.5 nm/s over a 4-inch diameter and an independent control of the deposition rate and ion energy. The ta-C:H was deposited using acetylene as the source gas and was characterized as having an sp3 content of up to 77%, plasmon energy of 27 eV, refractive index of 2.45, hydrogen content of about 30%, optical gap of up to 2.1 eV and RMS surface roughness of 0.04 nm. © 1999 Elsevier Science S.A. All rights reserved.

High rate deposition of Ta-C:H using an electron cyclotron wave resonance plasma source

A compact electron cyclotron wave resonance (ECWR) source has been developed for the high rate deposition of hydrogenated tetrahedral amorphous carbon (ta-C:H). The ECWR provides growth rates of up to 900 angstrom/min and an independent control of the deposition rate and ion energy. The ta-C:H was deposited using acetylene as the source gas and was characterized in terms of its bonding, stress and friction coefficient. The results indicated that the ta-C:H produced using this source fulfills the necessary requirements for applications requiring enhanced tribological performance.

The preparation, characterization and tribological properties of TA-C : H deposited using an electron cyclotron wave resonance plasma beam source

A compact electron cyclotron wave resonance (ECWR) source has been developed for the high rate deposition of hydrogenated tetrahedral amorphous carbon (ta-C:H). The ECWR provides growth rates of up to 900 Å/min over a 4″ diameter and an independent control of the deposition rate and ion energy. The ta-C:H was deposited using acetylene as the source gas and was characterized in terms of its sp3 content, mass density, intrinsic stress, hydrogen content, C-H bonding, Raman spectra, optical gap, surface roughness and friction coefficient. The results obtained indicated that the film properties were maximized at an ion energy of approximately 167 eV, corresponding to an energy per daughter carbon ion of 76 eV. The relationship between the incident ion energy and film densification was also explained in terms of the subsurface implantation of carbon ions into the growing film.

Deposition of carbon nitride films using an electron cyclotron wave resonance plasma source

Hydrogenated amorphous carbon nitride (a-C:N:H) has been synthesized using a high plasma density electron cyclotron wave resonance (ECWR) technique using N2 and C2H2 as source gases, at different ratios and a fixed ion energy (80 eV). The composition, structure and bonding state of the films were investigated and related to their optical and electrical properties. The nitrogen content in the film rises rapidly until the N2/C2H2 gas ratio reaches 2 and then increases more gradually, while the deposition rate decreases steeply, placing an upper limit for the nitrogen incorporation at 30 at%. For nitrogen contents above 20 at%, the band gap and sp3-bonded carbon fraction decrease from 1.7 to 1.1 eV and approximately 65 to 40%, respectively. Films with higher nitrogen content are less dense than the original hydrogenated tetrahedral amorphous carbon (ta-C:H) film but, because they have a relatively high band gap (1.1 eV), high resistivity (109 Ω cm) and moderate sp3-bonded carbon fraction (40%), they should be classed as polymeric in nature.

Properties of a-C:H films deposited from a methane electron cyclotron wave resonant plasma

An electron cyclotron wave resonant methane plasma discharge was used for the high rate deposition of hydrogenated amorphous carbon (a-C:H). Deposition rates of up to ∼400 Å/min were obtained over substrates up to 2.5 in. in diameter with a film thickness uniformity of ∼±10%. The deposited films were characterised in terms of their mass density, sp3 and hydrogen contents, C-H bonding, intrinsic stress, scratch resistance and friction properties. The deposited films possessed an average sp3 content, mass density and refractive index of ∼58%, 1.76 g/cm3 and 2.035 respectively.Mechanical characterisation indicated that the films possessed very low steady-state coefficients of friction (ca. 0.06) and a moderate shear strength of ∼141 MPa. Nano-indentation measurements also indicated a hardness and elastic modulus of ∼16.1 and 160 GPa respectively. The critical loads required to induce coating failure were also observed to increase with ion energy as a consequence of the increase in degree of ion mixing at the interface. Furthermore, coating failure under scratch test conditions was observed to take place via fracture within the silicon substrate itself, rather than either in the coating or at the film/substrate interface. © 2003 Elsevier B.V. All rights reserved.

Methane chemistry involved in a low-pressure electron cyclotron wave resonant plasma discharg

A low-pressure methane plasma generated by electron cyclotron wave resonance was characterized in terms of electron temperature, plasma density and composition. Methane plasmas were commonly used in the deposition of hydrogenated amorphous carbon thin films. Little variation in the plasma chemistry was observed by mass spectrometry measurements of the gas phase with increasing electron temperature. The results show that direct electron-impact reactions exert greater influence on the plasma chemistry than secondary ion-neutral reactions.