Evolution and decay of cylindrical and spherical nonlinear acoustic waves generated by a sinusoidal source

The present work gives a comprehensive numerical study of the evolution and decay of cylindrical and spherical nonlinear acoustic waves generated by a sinusoidal source. Using pseudospectral and predictor–corrector implicit finite difference methods, we first reproduced the known analytic results of the plane harmonic problem to a high degree of accuracy. The non-planar harmonic problems, for which the amplitude decay is faster than that for the planar case, are then treated. The results are correlated with the known asymptotic results of Scott (1981) and Enflo (1985). The constant in the old-age formula for the cylindrical canonical problem is found to be 1.85 which is rather close to 2, ‘estimated’ analytically by Enflo. The old-age solutions exhibiting strict symmetry about the maximum are recovered; these provide an excellent analytic check on the numerical solutions. The evolution of the waves for different source geometries is depicted graphically.

Accelerating Waves in Polar Coronal Holes as Seen by EIS and SUMER

We present EIS/Hinode and SUMER/SOHO observations of propagating disturbances detected in coronal lines in inter-plume and plume regions of a polar coronal hole. The observation was carried out on 2007 November 13 as part of the JOP196/HOP045 program. The SUMER spectroscopic observation gives information about fluctuations in radiance and on both resolved (Doppler shift) and unresolved (Doppler width) line-of-sight velocities, whereas EIS 40 `'wide slot images detect fluctuations only in radiance but maximize the probability of overlapping field of view between the two instruments. From distance-time radiance maps, we detect the presence of propagating waves in a polar inter-plume region with a period of 15-20 minutes and a propagation speed increasing from 130 +/- 14 km s(-1) just above the limb to 330 +/- 140 km s(-1) around 160 `' above the limb. These waves can be traced to originate from a bright region of the on-disk part of the coronal hole where the propagation speed is in the range of 25 +/- 1.3 to 38 +/- 4.5 km s(-1), with the same periodicity. These on-disk bright regions can be visualized as the base of the coronal funnels. The adjacent plume region also shows the presence of propagating disturbances with the same range of periodicity but with propagation speeds in the range of 135 +/- 18 to 165 +/- 43 km s(-1) only. A comparison between the distance-time radiance map of the two regions indicates that the waves within the plumes are not observable (may be getting dissipated) far off-limb, whereas this is not the case in the inter-plume region. A correlation analysis was also performed to find out the time delay between the oscillations at several heights in the off-limb region, finding results consistent with those from the analysis of the distance-timemaps. To our knowledge, this result provides first spectroscopic evidence of the acceleration of propagating disturbances in the polar region close to the Sun (within 1.2 R/R-circle dot), which provides clues to the understanding of the origin of these waves. We suggest that the waves are likely either Alfvenic or fast magnetoacoustic in the inter-plume region and slow magnetoacoustic in the plume region. This may lead to the conclusion that inter-plumes are a preferred channel for the acceleration of the fast solar wind.

Modified linear prediction method for directions of arrival estimation of narrow-band plane waves

A modified linear prediction (MLP) method is proposed in which the reference sensor is optimally located on the extended line of the array. The criterion of optimality is the minimization of the prediction error power, where the prediction error is defined as the difference between the reference sensor and the weighted array outputs. It is shown that the L2-norm of the least-squares array weights attains a minimum value for the optimum spacing of the reference sensor, subject to some soft constraint on signal-to-noise ratio (SNR). How this minimum norm property can be used for finding the optimum spacing of the reference sensor is described. The performance of the MLP method is studied and compared with that of the linear prediction (LP) method using resolution, detection bias, and variance as the performance measures. The study reveals that the MLP method performs much better than the LP technique.

Capillary-gravity waves against a corrugated vertical cliff

An analysis involving a transformation of the velocity potential and a Fourier Sine Transform technique is described to study the effect of surface tension on incoming surface waves against a vertical cliff with a periodic wall perturbation. Known results are recovered as particular cases of the general problem considered. An analytical expression is derived for the surface elevation, at far distances from the shore-line, by using Watson's lemma and a representative table of numerical values of the coefficients of the resulting asymptotic expansion is also presented.

Effects of capillary waves on the thickness of wetting layers

The free energy contribution of capillary waves is calculated to show its significant dependence on the thickness of the liquid layer, when the thickness is very small. It is shown that these oscillations can play an important role in determining the thermodynamic stability of a wetting layer, close to the critical point of a binary liquid mixture in the case of both short range and long range forces. In particular, the thickness of the wetting layer goes to zero as the temperature T approaches Tc.

Coupling of surface acoustic waves propagating in two separated piezoelectric media

The coupling of surface acoustic waves propagating in two separated piezoelectric media is studied using the perturbation theory of Auld. The results of the analysis are applied to two configurations using Bi12GeO20 and CdS crystals. It is found that the loss due to coupling is about 7 dB at 50 MHz in the cases of (111)-cut, [110]-prop. Bi12GeO20 and Y-cut, 60°-X prop. CdS combination. On étudie le couplage des ondes acoustiques de surface se propageant sur deux milieux piezo-eléctriques par la théorie de perturbation de Auld. Les resultats d'analyse sont appliqué's aux deux configurations des cristanx Bi12GeO20 et CdS. On trouve que la perte par couplage est environ de 7 dB a 50 MHz dans le cas de combination de (111)-coupe, [110]-prop. Bi12GeO20 et Y-coupe, 60°-X prop. CdS.

Hydromagnetic surface waves in a compressible medium

The dispersive characteristic of hydromagnetic surface waves along a plasma-plasma interface when the upper fluid moves with a uniform velocity is discussed. The region of propagation of these waves is shifted above or below depending on whether the basic velocity (uniform)Ugl0.

Propagation of quasi-simple waves in a compressible rotating atmosphere

A class of self-propagating linear and nonlinear travelling wave solutions for compressible rotating fluid is studied using both numerical and analytical techiques. It is shown that, in general, a three dimensional linear wave is not periodic. However, for some range of wave numbers depending on rotation, horizontally propagating waves are periodic. When the rotation ohgr is equal to $$\sqrt {(\gamma - 1)/(4\gamma )}$$ , all horizontal waves are periodic. Here, gamma is the ratio of specific heats. The analytical study is based on phase space analysis. It reveals that the quasi-simple waves are periodic only in some plane, even when the propagation is horizontal, in contrast to the case of non-rotating flows for which there is a single parameter family of periodic solutions provided the waves propagate horizontally. A classification of the singular points of the governing differential equations for quasi-simple waves is also appended.

Propagation Of Vlf Electromagnetic-Waves In An Idealized Earth-Crust Wave-Guide With Overburden

Theoretical study of propagation characteristics of VLF electromagnetic waves through an idealised parallel-plane earth-crust waveguide with overburden, experimental verification of some of these characteristics with the aid of a model tank and use of range equation reveal the superiority of radio communication between land and a deeply submerged terminal inside a ocean via the earth-crust over direct link communication through the ocean.

Solution of a Boundary-Value Problem associated with Diffraction of Water Waves by a Nearly Vertical Barrier

An exact solution is derived for a boundary-value problem for Laplace's equation which is a generalization of the one occurring in the course of solution of the problem of diffraction of surface water waves by a nearly vertical submerged barrier. The method of solution involves the use of complex function theory, the Schwarz reflection principle, and reduction to a system of two uncoupled Riemann-Hilbert problems. Known results, representing the reflection and transmission coefficients of the water wave problem involving a nearly vertical barrier, are derived in terms of the shape function.

A mathematical analysis of nonlinear waves in a fluid filled visco-elastic tube

Our investigations in this paper are centred around the mathematical analysis of a ldquomodal waverdquo problem. We have considered the axisymmetric flow of an inviscid liquid in a thinwalled viscoelastic tube under certain simplifying assumptions. We have first derived the propagation space equations in the long wave limit and also given a general procedure to derive these equations for arbitrary wave length, when the flow is irrotational. We have used the method of operators of multiple scales to derive the nonlinear Schrödinger equation governing the modulation of periodic waves and we have elaborated on the ldquolong modulated wavesrdquo and the ldquomodulated long wavesrdquo. We have also examined the existence and stability of Stokes waves in this system. This is followed by a discussion of the progressive wave solutions of the long wave equations. One of the most important results of our paper is that the propagation space equations are no longer partial differential equations but they are in terms of pseudo-differential operators.Die vorliegenden Untersuchungen beziehen sich auf die mathematische Behandlung des ldquorModalwellenrdquo-Problems. Die achsensymmetrische Strömung einer nichtviskosen Flüssigkeit in einem dünnwandigen viskoelastischen Rohr, unter bestimmten vereinfachenden Annahmen, wird betrachtet. Zuerst werden die Gleichungen des Ausbreitungsraumes im Langwellenbereich abgeleitet und eine allgemeine Methode zur Herleitung dieser Gleichungen für beliebige Wellenlängen bei nichtrotierender Strömung angegeben. Eine Operatorenmethode mit multiplem Maßstab wird verwendet zur Herleitung der nichtlinearen Schrödinger-Gleichung für die Modulation der periodischen Wellen, und die ldquorlangmodulierten Wellenrdquo sowie die ldquormodulierten Langwellenrdquo werden aufgezeigt. Weiters wird die Existenz und die Stabilität der Stokes-Wellen im System untersucht. Anschließend werden die progressiven Wellenlösungen der Langwellengleichungen diskutiert. Eines der wichtigsten Ergebnisse dieser Arbeit ist, daß die Gleichungen des Ausbreitungsraumes keine partiellen Differentialgleichungen mehr sind, sondern Ausdrücke von Pseudo-Differentialoperatoren.