A model supersonic buried-nozzle jet: instability and acoustic wave scattering and the far-field sound

We consider sound source mechanisms involving the acoustic and instability modes of dual-stream isothermal supersonic jets with the inner nozzle buried within an outer shroud-like nozzle. A particular focus is scattering into radiating sound waves at the shroud lip. For such jets, several families of acoustically coupled instability waves exist, beyond the regular vortical Kelvin-Helmholtz mode, with different shapes and propagation characteristics, which can therefore affect the character of the radiated sound. In our model, the coaxial shear layers are vortex sheets while the incident acoustic disturbances are the propagating shroud modes. The Wiener-Hopf method is used to compute their scattering at the sharp shroud edge to obtain the far-field radiation. The resulting far-field directivity quantifies the acoustic efficiency of different mechanisms, which is particularly important in the upstream direction, where the results show that the scattered sound is more intense than that radiated directly by the shear-layer modes.

Towards an exact factorization of the molecular wave function

An exact single-product factorisation of the molecular wave function for the timedependent Schrodinger equation is investigated by using an ansatz involving a phasefactor. By using the Frenkel variational method, we obtain the Schrodinger equations for the electronic and nuclear wave functions. The concept of a potential energy surface (PES) is retained by introducing a modified Hamiltonian as suggested earlier by Cederbaum. The parameter in the phase factor is chosen such that the equations of motion retain the physically appealing Born- Oppenheimer-like form, and is therefore unique.

Wave propagation in a 2D nonlinear structural acoustic waveguide using asymptotic expansions of wavenumbers

Nonlinear acoustic wave propagation in an infinite rectangular waveguide is investigated. The upper boundary of this waveguide is a nonlinear elastic plate, whereas the lower boundary is rigid. The fluid is assumed to be inviscid with zero mean flow. The focus is restricted to non-planar modes having finite amplitudes. The approximate solution to the acoustic velocity potential of an amplitude modulated pulse is found using the method of multiple scales (MMS) involving both space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrodinger equation (NLSE). The first objective here is to study the nonlinear term in the NLSE. The sign of the nonlinear term in the NLSE plays a role in determining the stability of the amplitude modulation. Secondly, at other frequencies, the primary pulse interacts with its higher harmonics, as do two or more primary pulses with their resultant higher harmonics. This happens when the phase speeds of the waves match and the objective is to identify the frequencies of such interactions. For both the objectives, asymptotic coupled wavenumber expansions for the linear dispersion relation are required for an intermediate fluid loading. The novelty of this work lies in obtaining the asymptotic expansions and using them for predicting the sign change of the nonlinear term at various frequencies. It is found that when the coupled wavenumbers approach the uncoupled pressure-release wavenumbers, the amplitude modulation is stable. On the other hand, near the rigid-duct wavenumbers, the amplitude modulation is unstable. Also, as a further contribution, these wavenumber expansions are used to identify the frequencies of the higher harmonic interactions. And lastly, the solution for the amplitude modulation derived through the MMS is validated using these asymptotic expansions. (C) 2015 Elsevier Ltd. All rights reserved.

Weakly nonlinear acoustic wave propagation in a nonlinear orthotropic circular cylindrical waveguide

Nonlinear acoustic wave propagation is considered in an infinite orthotropic thin circular cylindrical waveguide. The modes are non-planar having small but finite amplitude. The fluid is assumed to be ideal and inviscid with no mean flow. The cylindrical waveguide is modeled using the Donnell's nonlinear theory for thin cylindrical shells. The approximate solutions for the acoustic velocity potential are found using the method of multiple scales (MMS) in space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrodinger Equation (NLSE). The first objective is to study the nonlinear term in the NLSE, as the sign of the nonlinear term determines the stability of the amplitude modulation. On the other hand, at other specific frequencies, interactions occur between the primary wave and its higher harmonics. Here, the objective is to identify the frequencies of the higher harmonic interactions. Lastly, the linear terms in the NLSE obtained using the MMS calculations are validated. All three objectives are met using an asymptotic analysis of the dispersion equation. (C) 2015 Acoustical Society of America.

EXACT INTERNAL CONTROLLABILITY FOR THE WAVE EQUATION IN A DOMAIN WITH OSCILLATING BOUNDARY WITH NEUMANN BOUNDARY CONDITION

In this paper, we study the exact controllability of a second order linear evolution equation in a domain with highly oscillating boundary with homogeneous Neumann boundary condition on the oscillating part of boundary. Our aim is to obtain the exact controllability for the homogenized equation. The limit problem with Neumann condition on the oscillating boundary is different and hence we need to study the exact controllability of this new type of problem. In the process of homogenization, we also study the asymptotic analysis of evolution equation in two setups, namely solution by standard weak formulation and solution by transposition method.