Eigenvalue confinement in the problem of linear baroclinic instability for oceanic zonal flows

Summary The classical problem of baroclinic instability is examined from the point of view of eigenvalue confinement in the complex plane. The analysis is performed for a baroclinic zonal flow perturbed by a monochromatic plane wave, harmonic in the latitude. The main results, obtained from thea priori properties of the eigenvalue equation, yield estimates of the phase velocity and the growth rate of the perturbation. As a consequence, the spectrum results to be confined within a bounded region of the complex plane, which depends upon the zonal flux only through its extreme values and the maximum of the shear. The larger is the wave number of the meridional structure of the perturbation, the narrower is the obtained confinement: in the case of higher harmonics the present estimates sharpen the results known from the literature.

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Riassunto Si riesamina il problema classico dell'instabilità baroclinica lineare dal punto di vista della localizzazione dei relativi autovalori nel piano complesso. L'analisi è eseguita per un generico flusso zonale baroclinico perturbato da un'onda piana monocromatica, armonica nella latitudine. I risultati principali, ottenuti esaminando le proprietàa priori dell'equazione agli autovalori, forniscono stime sulla velocità di fase e il tasso di accrescimento della perturbazione. Ne consegue la localizzazione dello spettro in una regione limitata del piano complesso che risulta dipendere dal flusso zonale solo tramite i suoi valori estremi ed il massimo dello shear. Il confinamento ottenuto risulta tanto piú stretto quanto maggiore è il numero d'onda della struttura meridionale della perturbazione: nel caso delle armoniche superiori si migliorano le stime esistenti in letteratura.

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Резюме Исследуется классическая проблема бароклинной неустойчивости с точки зрения ограничения собственных значений в комплексной плоскости. Проводится анализ бароклинного зонного течения, возмущенного монохроматической плоской волной, гармонической по широте. Основные результаты, полученные из свойств уравнения для собственных значений, дают оценки для фазовой скорости и интенсивности роста возмущения. Воледствии этого, полученный спектр заключен внутри ограниченной области комплексной области, которая зависит от зонного потока только через его экстремальные значения и максимум сдвига. В случае высших гармоник полученные оценки позволяют улучшить результаты, имеющиеся в литературе.

     

Water injection effects on hot supersonic jet noiseEffets de la température sur le rayonnement acoustique des jets supersoniques en présence d'injection d'eau

The effects of temperature both on supersonic jet noise with water injection (used for noise reduction) and on the efficiency of the method are investigated. The location of injection varies from 1.5D to 15D while the other parameters remain fixed to their optimum values. One notices better overall noise level reductions by injecting close to the nozzle exit. Moreover spectral analysis emphasizes that attenuation in high and low frequencies depends on the location of injection. Finally, the jet temperature does not greatly affect the efficiency of this method as the measured attenuation is similar to that encountered with supersonic jets with ambiant temperature. To cite this article: Y. Marchesse et al., C. R. Mecanique 330 (2002) 1–8     

Sound scattering by a resistive and axially symmetric object in a two-layer ocean

An acoustically resistive and axially symmetric object is placed in a two-layer ocean very far from a point source of acoustic waves. The object is either floating in the water layer or buried in the sediment layer. Both layers are homogenous. The size of the object is small when compared to the depth of the water channel. The free surface of the sea is assumed to be soft and the bottom is assumed to be hard. Between the two layers the classical diffraction boundary conditions are taken. An extension of the Deep Water Approximation method [Ergatis P. Radiation, propagation and scattering of acoustic waves in an underwater environment. PhD thesis, University of Patras; 1997 (in Greek)] is being provided to cover the case of resistive scatterers [Colton, D., Kress, R. Integral equation methods in scattering theory. New York: Wiley; 1983].     

我国建筑声学的20年回顾与展望

我国建筑学声在近20年间，无论在科研、设计、声学材料（结构）的研制、生产和应用方面均有较大的发展。在厅堂音质设计的个别领域还取得了突破性的进展。本文就上述几方面作概要的介绍。     

Study of the uncertainty of façade sound insulation measurements: Analysis of the ISO 12999-1 uncertainty proposal

The result of a measurement is an approximation of the true value of the measurand and is complete when it is accompanied by its uncertainty. Building acoustics requires an assessment of the uncertainties that is understandable and corresponds closely to reality. The new standard ISO 12999-1 gives general uncertainty values for typical sound insulation measurements. The objective of this work is to determine the most accurate method for evaluating the uncertainty of in situ façade sound insulation measurements for both the D_ls,2m,nT values in one-third octave bands and the global magnitude D_ls,2m,nT,w. We establish a comparative analysis between the uncertainty values proposed by the standard ISO 12999-1, the uncertainty values deduced from interlaboratory activities and the average uncertainties deduced from individual calculations for each in situ measurement. The comparison is based on uncertainty calculations for around 1000 in situ façade sound insulation measurements made by our laboratory. The uncertainties given by the standard ISO 12999-1 for D_ls,2m,nT in one-third octave bands are, at low and high frequencies, higher than the values deduced from individual calculations and smaller than the calculated values at mid frequencies. We believe that for D_ls,2m,nT, it is advisable wherever possible to make individual uncertainty calculations for each in situ façade measurement. Nevertheless, the comparison with ISO 12999-1 points to the suitability of including some uncertainty components in the calculation, such as the related to the measurement procedure or source directivity, which are not normally considered in the uncertainty evaluation. Although we have clearly endorsed the use of individual calculations to determine the uncertainty of the sound insulation magnitude in one-third octave bands, we believe the uncertainty proposed by standard ISO 12999-1 could be a more realistic and reasonable approximation for the global magnitude D_ls,2m,nT,w. Therefore if an individual calculation of the uncertainty of the global magnitude is required the Monte Carlo simulation has been shown to be a good method.     

一维非线性声波传播特性

针对一维非线性声波的传播问题进行了有限元仿真和实验研究. 首先推导了一维非线性声波方程的有限元形式, 含有高阶矩阵的非线性项导致声波具有波形畸变、谐波滋生、基频信号能量向高次谐波传递等非线性特性. 编制有限元程序对一维非线性声波进行了计算并对仿真得到的畸变非线性声波信号进行处理, 分析其传播性质和物理意义. 为验证有限元计算结果, 开展了水中的非线性声波传播的实验研究, 得到了不同输入信号幅度激励下和不同传播距离的畸变非线性声波信号. 然后对基波和二次谐波的传播性质进行详细讨论, 分析了二次谐波幅度与传播距离和输入信号幅度的变化关系及其意义, 拟合出二次谐波幅度随传播距离变化的方程并阐述了拟合方程的物理意义. 结果表明, 数值仿真信号及其频谱均与实验结果有较好的一致性, 证实计算方法和结果的正确性, 并提出了具有一定物理意义的二次谐波随传播距离变化的简单数学关系. 最后还对固体中的非线性声波传播性质进行了初步探讨. 本研究工作可为流体介质中的非线性声传播问题提供理论和实验依据.     

A two-dimensional nonlinear model for the generation of stable cavitation bubbles

Bubbles appear by acoustic cavitation in a liquid when rarefaction pressures attain a specific threshold value in a liquid. Once they are created, the stable cavitation bubbles oscillate nonlinearly and affect the ultrasonic field. Here we present a model developed for the study of bubble generation in a liquid contained in a two-dimensional cavity in which a standing ultrasonic field is established. The model considers dissipation and dispersion due to the bubbles. It also assumes that both the ultrasonic field and the bubble oscillations are nonlinear. The numerical experiments predict where the bubbles are generated from a population of nuclei distributed in the liquid and show how they affect the ultrasonic field.     

Corrected Statistical Energy Analysis Model in a Non-Reverberant Acoustic Space

Statistical Energy Analysis (SEA) is a well-known method to analyze the flow of acoustic and vibration energy in a complex structure. This study investigates the application of the corrected SEA model in a non-reverberant acoustic space where the direct field component from the sound source dominates the total sound field rather than a diffuse field in a reverberant space which the classical SEA model assumption is based on. A corrected SEA model is proposed where the direct field component in the energy is removed and the power injected in the subsystem considers only the remaining power after the loss at first reflection. Measurement was conducted in a box divided into two rooms separated by a partition with an opening where the condition of reverberant and non-reverberant can conveniently be controlled. In the case of a non-reverberant space where acoustic material was installed inside the wall of the experimental box, the signals are corrected by eliminating the direct field component in the measured impulse response. Using the corrected SEA model, comparison of the coupling loss factor (CLF) and damping loss factor (DLF) with the theory shows good agreement.     

Dissipative acoustic solitons under a weakly-nonlinear, Lagrangian-averaged Euler-α model of single-phase lossless fluids

A one-dimensional weakly-nonlinear model equation based on a Lagrangian-averaged Euler-α model of compressible flow in lossless fluids is presented. Traveling wave solutions (TWS)s, in the form of a topological soliton (or kink), admitted by this fourth-order partial differential equation are derived and analyzed. An implicit finite-difference scheme with internal iterations is constructed in order to study soliton collisions. It is shown that, for certain parameters, the TWSs interact as solitons, i.e., they retain their “identity” after a collision. Kink-like solutions with an oscillatory tail are found to emerge in a signaling-type initial-boundary-value problem for the linearized equation of motion. Additionally, connections are drawn to related weakly-nonlinear acoustic models and the Korteweg-de Vries equation from shallow-water wave theory.     

Reflection and transmission of plane acoustic waves in an infinite annular duct with a finite gap on the inner wall

The diffraction of acoustic waves by an infinitely long annular duct having a finite gap on the inner wall is investigated rigorously. The related boundary‐value problem is formulated into a modified Wiener–Hopf equation, which is then reduced to a pair of simultaneous Fredholm integral equations of the second kind. At the end of the analysis, numerical results illustrating the effects of the width of the coaxial cylindrical waveguide and the gap length on the diffraction phenomenon are presented. Copyright © 2010 John Wiley & Sons, Ltd.