On two-dimensional large-scale primitive equations in oceanic dynamics(Ⅰ)

The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered.It is assumed that the depth of the ocean is a positive constant.Firstly,if the initial data are square integrable,then by Fadeo-Galerkin method,the existence of the global weak solutions for the problem is obtained.Secondly, if the initial data and their vertical derivatives axe all square integrable,then by Faedo-Galerkin method and anisotropic inequalities,the existerce and uniqueness of the giobal weakly strong solution for the above initial boundary problem axe obtained.     

Réduction semi-active du battement de volume généré par une cavité profonde soumise à un écoulement aérodynamiqueSemi-active reduction of the sound generated by a deep cavity under an airflow

We present experimental results obtained with a deep cavity, such as a Helmholtz resonator, excited by an airflow. The resonance under the action of the vortices generated in the shear layer is well described and quantified. The mounting of actuators, based on a few piezo-electric elements, allows us to generate a series of two-dimensional vortices forced at a frequency which is different than the natural resonance frequency. The sound level in the cavity is strongly decreased and only the broadband noise of the turbulence remains. To cite this article: X. Amandolese et al., C. R. Mecanique 330 (2002) 101–106.     

Underwater acoustics and cavitating flow of water entry

The fluid mechanics of water entry is studied through investigating the underwater acoustics and the supercavitation. Underwater acoustic signals in water entry are extensively measured at about 30 different positions by using a PVDF needle hydrophone. From the measurements we obtain (1) the primary shock wave caused by the impact of the blunt body on free surface; (2) the vapor pressure inside the cavity; (3) the secondary shock wave caused by pulling away of the cavity from free surface; and so on. The supercavitation induced by the blunt body is observed by using a digital high-speed video camera as well as the single shot photography. The periodic and 3 dimensional motion of the supercavitation is revealed. The experiment is carried out at room temperature. The project supported by the “BaiRen Plan” of Chinese Academy of Sciences     

Microcontact-based theory for acoustics in microdamaged materials

A universal theory describing the wide range of mechanical and acoustic phenomena in solids with internal contacts such as rocks, concrete, ceramics and composites is quite complex to develop. The goal of this paper is to demonstrate the potential to deduce the macroscopic stress-strain constitutive equation for a material as a whole starting from the microscopic hysteretic force-displacement relationship of individual asperities in contact. The material considered in the proposed model contains a large number of isotropic oriented penny-shaped cracks with rough internal surfaces. The stress-strain relationship we obtained for such a material is based on physical principles and laws. Even so, it displays close resemblance to the phenomenological Preisach-Mayergoyz model adopted for mechanical hysteresis and nonlinearity. This constitutive relationship is then used to simulate an experiment with standing acoustic waves in a resonant bar, and to compare model predictions to actual observations. We show that the most important experimentally measurable nonlinear features of these materials, such as the typical classical and nonclassical shifting behavior of the resonant frequency, the dependencies of the amplitudes of the generated harmonics, the softening due to intensive straining, and the subsequent relaxation effect (slow dynamics) can be attributed and explained in terms of the mechanics and the statistics of the internal contacts. The present model bridges the gap between three scales: macroscopic (material as a whole), mesoscopic (structure of intergranular contacts and cracks) and microscopic scale (contacts of individual asperities).     

Large eddy simulation of compressible round jets with coflow

Large eddy simulations of subsonic round jets are carried out using high order compact finite difference scheme and an explicit filtering based approximate deconvolution method. The jets have a Mach number of 0.9 and Reynolds number of $4.5\times {10}^5$ based on jet diameter and centerline velocity at inflow. Results obtained for the mean flow and turbulence intensities agree well with those in existing literature. We also study the effects of co-flow velocity ratio on the flow physics. Increase in potential core length and decrease in spreading rate of jet is observed in the presence of co-flow. The effects of co-flow velocity ratio on the axial Reynolds stress and turbulent kinetic energy budgets are also presented. It is observed that increasing co-flow velocity ratio leads to reduction in the turbulence intensities and near-field sound levels.     

Reproducible time-of-flight measurements with a piezoelectric transducer for acoustoelastic stress evaluation

The acoustic coupling of a piezoelectric transducer to the specimen by means of a viscous couplant proves to be a weak link in performing acoustoelastic experiments. Measurements reveal that an increased coupling layer thickness potentially leads to a more reproducible time-of-flight determination. To assess the consequences of this approach, a model is developed for the pulse-echo configuration. Diffraction in the specimen is taken into account and a viscoelastic model is used to describe wave propagation in shear wave couplant. The results clearly show the advantages of an increased coupling layer thickness. Paper was presented at the 1994 SEM Spring Conference on Experimental Mechanics held in Baltimore, MD on June 8–10.     

应用电磁超声技术实验分析自由表平面凹坑上P—SV波的转换

本文对正入射条件下自由表平面半球形凹坑上Ｐ－ＳＶ波的转换进行了实验分析，实验中使用了电磁超声技术，确保在各个方向上等声程接收散射ＳＶ波和良好的测量重复性．实验结果表明，随着凹坑直径（Ｄ）与入射波波长（λ）之比的改变，转型ＳＶ波的指向特征有显著改变；当Ｄ／λ＝１时，ＳＶ波则集中于近表平面，并与散射Ｐ波耦合为强烈的瑞利波．本文为自由表平面半球形凹坑上弹性波的散射方向提供了一些实验解，并为应用波型转换方法检测金属孔蚀提供了实验基础．     

Numerical analysis for transverse microbead trapping using 30 MHz focused ultrasound in ray acoustics regime

We have recently devised a remote acoustic manipulation method with high frequency focused ultrasonic beam of 30–200 MHz, and experimentally realized it by the intensity gradient near the beam’s focus. A two-dimensional (or transverse) acoustic trapping was demonstrated by directly applying the acoustic radiation force on lipid spheres and leukemia cells that were individually moved towards the focus. Only longitudinal waves were then considered because both target and propagation media involved were fluid e.g., water or phosphate buffer saline.     

Improving the air coupling of bulk piezoelectric transducers with wedges of power-law profiles: A numerical study

An air-coupled ultrasonic transducer is created by bonding a bulk piezoelectric element onto the surface of a thick plate with a wedge of power-law profile. The wedge is used to improve the ultrasonic radiation efficiency. The power-law profile provides a smooth, impedance-matching transition for the mechanical energy to be transferred from the thick plate to the air, through the large-amplitude flexural waves observed in the thinnest region of the wedge. The performance of the proposed transducer is examined numerically and compared to that of a design where the piezoelectric element is isolated and where it is affixed to a thin plate of uniform thickness. The numerical analysis is first focused on the free-field radiation of the transducers. Then, time-reversal experiments are simulated by placing the transducers inside a cavity of arbitrary shape with some perfectly reflecting boundaries. In addition to time-reversal mirrors, the proposed concept could be integrated in the design of phased arrays and parametric arrays.     

Nonlinear frequency mixing in a resonant cavity: Numerical simulations in a bubbly liquid

The study of nonlinear frequency mixing for acoustic standing waves in a resonator cavity is presented. Two high frequencies are mixed in a highly nonlinear bubbly liquid filled cavity that is resonant at the difference frequency. The analysis is carried out through numerical experiments, and both linear and nonlinear regimes are compared. The results show highly efficient generation of the difference frequency at high excitation amplitude. The large acoustic nonlinearity of the bubbly liquid that is responsible for the strong difference-frequency resonance also induces significant enhancement of the parametric frequency mixing effect to generate second harmonic of the difference frequency.