scholarly journals Reflection and transmission of high-frequency acoustic, electromagnetic and elastic waves at a distinguished class of irregular, curved boundaries

2019 ◽  
Vol 84 (6) ◽  
pp. 1203-1219
Author(s):  
Anthony Radjen ◽  
Gabriele Gradoni ◽  
Richard Tew
Keyword(s):  
High Frequency ◽  
Two Dimensions ◽  
Wave Number ◽  
Small Scale ◽  
Linear Wave ◽  
Incoming Wave ◽  
Reflection And Transmission ◽  
Large Wave ◽  
Irregular Boundary ◽  
Arbitrary Profile

Abstract Reflection and transmission phenomena associated with high-frequency linear wave incidence on irregular boundaries between adjacent acoustic or electromagnetic media, or upon the irregular free surface of a semi-infinite elastic solid, are studied in two dimensions. Here, an ‘irregular’ boundary is one for which small-scale undulations of an arbitrary profile are superimposed upon an underlying, smooth curve (which also has an arbitrary profile), with the length scale of the perturbation being prescribed in terms of a certain inverse power of the large wave-number of the incoming wave field. Whether or not the incident field has planar or cylindrical wave-fronts, the associated phase in both cases is linear in the wave-number, but the presence of the boundary irregularity implies the necessity of extra terms, involving fractional powers of the wave-number in the phase of the reflected and transmitted fields. It turns out that there is a unique perturbation scaling for which precisely one extra term in the phase is needed and hence for which a description in terms of a Friedlander–Keller ray expansion in the form as originally presented is appropriate, and these define a ‘distinguished’ class of perturbed boundaries and are the subject of the current paper.

Bottomless harbours

1970 ◽  
Vol 43 (3) ◽  
pp. 433-449 ◽  
Author(s):  
C. J. R. Garrett
Keyword(s):  
Simultaneous Equations ◽  
Wave Number ◽  
Incoming Wave ◽  
Large Wave ◽  
Resonant Wave ◽  
Incident Plane ◽  
Wave Numbers ◽  
Open Circular ◽  
Harbour Oscillations ◽  
Infinite Set

Does the harbour of an artificial island need a bottom? The excitation of waves inside a partially immersed open circular cylinder is considered. An incident plane wave is expanded in Bessel functions and for each mode the problem is formulated in terms of the radial displacement on the cylindrical interface below the cylinder. The solution is obtainable either from an infinite set of simultaneous equations or from an integral equation. It is shown that the phase of the solution is independent of depth and resonances are found at wave-numbers close to those of free oscillations in a cylinder extending to the bottom. If the resonances of the cylinder are made sharper (by increasing the depth of immersion) the peak response of the harbour increases, but the response to a continuous spectrum remains approximately constant. Numerical results are obtained by minimizing the least squares error of a finite numberNof simultaneous equations. Convergence is slow, but the error is roughly proportional to 1/Nand this is exploited. The solution obtained from a variational formulation using the incoming wave as a trial function is found to give a very good approximation for small wave-numbers, but is increasingly inaccurate for large wave-numbers. Away from resonance the amplitude of the harbour oscillation is less than 10% of the amplitude of the incoming wave provided the depth of the cylinder is greater than about ¼ wavelength, and it is argued that in practice at the resonant wave-number oscillations excited through the bottom of the harbour will leak out through the entrance before they can reach large amplitudes. In an appendix the excitation of harbour oscillations through the harbour entrance is discussed, and some results of Miles & Munk (1961) on an alleged harbour paradox are re-interpreted.

scholarly journals Asymptotic solutions of the Helmholtz equation: Generalised Friedlander–Keller ray expansions of fractional order

2018 ◽  
Vol 31 (1) ◽  
pp. 1-25 ◽  
Author(s):  
R. H. TEW
Keyword(s):  
Helmholtz Equation ◽  
Boundary Value ◽  
Fractional Power ◽  
Boundary Curve ◽  
Asymptotic Solutions ◽  
Wave Number ◽  
Small Scale ◽  
Scattering Problems ◽  
Large Wave ◽  
Exponential Factor

Applications of a WKBJ-type ‘ray ansatz’ to obtain asymptotic solutions of the Helmholtz equation in the high-frequency limit are now standard and underpin the construction of ‘geometrical optics’ ray diagrams in many electromagnetic, acoustic and elastic reflection, transmission and other scattering problems. These applications were subsequently extended by Keller to include other types of rays – called ‘diffracted’ rays – to provide an accessible and impressively accurate theory which is relevant in wide-ranging sets of circumstances. Friedlander and Keller then introduced a modified ray ansatz to extend yet further the scope of ray theory and its applicability to certain other classes of diffraction problems (tangential ray incidence upon an obstructing boundary, for instance) and did so by the inclusion of an extra term proportional to a power of the wave number within the exponent of the initial ansatz. Our purpose here is to generalise this further still by the inclusion of several such terms, ordered in a natural sequence in terms of strategically chosen fractional powers of the large wave number, and to derive a systematic sequence of boundary value problems for the coefficient phase functions that arise within this generalised exponent, as well as one for the leading-order amplitude occurring as a pre-exponential factor. One particular choice of fractional power is considered in detail, and waves with specified radially symmetric or planar wavefronts are then analysed, along with a boundary value problem typifying two-dimensional radiation whereby arbitrary phase and amplitude variations are specified on a prescribed boundary curve. This theory is then applied to the scattering of plane and cylindrical waves at curved boundaries with small-scale perturbations to their underlying profile.

Dynamical evolution of two-dimensional unstable shear flows

1971 ◽  
Vol 47 (2) ◽  
pp. 353-379 ◽  
Author(s):  
N. J. Zabusky ◽  
G. S. Deem
Keyword(s):  
Stokes Equations ◽  
Flow Direction ◽  
Harmonic Component ◽  
Two Dimensions ◽  
Wave Number ◽  
Spectral Energy ◽  
Mean Flow ◽  
Flat Plates ◽  
Large Wave ◽  
Flow Profiles

A direct numerical integration of the time-dependent, incompressible Navier-Stokes equations is used to treat the nonlinear evolution of perturbed, linearly unstable, nearly parallel shear flow profiles in two dimensions. Calculations have been made for infinite (inviscid) and finite Reynolds numbers. The latter results are compared with laboratory measurements of Sato & Kuriki for wakes behind thin flat plates, and many of the detailed features are in excellent agreement, including mean flow profiles with ‘overshoot’ development, first harmonic energy profiles with off-axis nulls, and first harmonic phase profiles. The linear instability saturates by forming a vortex street consisting of elliptical vortex pairs. The solutions are followed for times up to eleven linear exponentiation times of the unstable disturbance. A new low-frequency non-linear oscillation is found, which explains the features of the above experiment, including the nearly periodic phase inversions in the first harmonic component of the longitudinal velocity. It results from a nutation of the elliptical vortices with respect to the mean flow direction. Inertial range spectral energy properties are also examined. Inviscid solutions have large wave-number spectral energies obeying the approximate power law, Ek ∼ k−μ, where μ lies between 3 and 4.

Can Values of Honesty, Hard Work, Loyalty and Discipline Predict Entrepreneurial Orientation of Muslim Owner Managers?

2015 ◽  
Vol 3 (1) ◽  
pp. 31 ◽  
Author(s):  
Rohani Mohd ◽  
Badrul Hisham Kamaruddin ◽  
Khulida Kirana Yahya ◽  
Elias Sanidas
Keyword(s):  
Entrepreneurial Orientation ◽  
Two Dimensions ◽  
Hard Work ◽  
Small Scale ◽  
Sampling Frame ◽  
Policy Makers ◽  
Learning Institutions ◽  
Innovative Orientation ◽  
The Impact ◽  
True Values

The purpose of the present study is twofold: first, to investigate the true values of Muslim owner managers; second, to examine the impact of these values on entrepreneurial orientations of Muslim small-scale entrepreneurs. 850 Muslim owner managers were selected randomly using the sampling frame provided by MajlisAmanah Rakyat Malaysia (MARA). 162 completed questionnaires were collected and analyzed. For this paper only two dimensions of entrepreneurial orientations were analyzed: proactive orientation and innovative orientation. Interestingly, the findings revealed that Muslim businessmen/women are honest, loyal, disciplined and hard working. Loyalty and honesty are positively related to proactive orientation, while discipline and hard-work are positively related to innovative orientation. The findings provide implications for existing relevant theories, policy makers, practitioners and learning institutions. 

Inversion of Wave-number Spectrum from Simulated Bistatic High-frequency Radar Data

2011 ◽  
Vol 33 (10) ◽  
pp. 2477-2482
Author(s):  
Huan He ◽  
Heng-yu Ke ◽  
Xian-rong Wan ◽  
Fang-zhi Geng
Keyword(s):  
High Frequency ◽  
Radar Data ◽  
Wave Number ◽  
High Frequency Radar

scholarly journals Causality and stability conditions of a conformal charged fluid

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Farid Taghinavaz
Keyword(s):  
Chemical Potential ◽  
Second Law Of Thermodynamics ◽  
Dense Medium ◽  
Wave Number ◽  
Second Law ◽  
Stability Conditions ◽  
Charged Fluid ◽  
Large Wave ◽  
The Stability ◽  
Large Wave Number

Abstract In this paper, I study the conditions imposed on a normal charged fluid so that the causality and stability criteria hold for this fluid. I adopt the newly developed General Frame (GF) notion in the relativistic hydrodynamics framework which states that hydrodynamic frames have to be fixed after applying the stability and causality conditions. To do this, I take a charged conformal matter in the flat and 3 + 1 dimension to analyze better these conditions. The causality condition is applied by looking to the asymptotic velocity of sound hydro modes at the large wave number limit and stability conditions are imposed by looking to the imaginary parts of hydro modes as well as the Routh-Hurwitz criteria. By fixing some of the transports, the suitable spaces for other ones are derived. I observe that in a dense medium having a finite U(1) charge with chemical potential μ0, negative values for transports appear and the second law of thermodynamics has not ruled out the existence of such values. Sign of scalar transports are not limited by any constraints and just a combination of vector transports is limited by the second law of thermodynamic. Also numerically it is proved that the most favorable region for transports $$ {\tilde{\upgamma}}_{1,2}, $$ γ ˜ 1 , 2 , coefficients of the dissipative terms of the current, is of negative values.

A Numerical Analysis of the Weak Galerkin Method for the Helmholtz Equation with High Wave Number

2017 ◽  
Vol 22 (1) ◽  
pp. 133-156 ◽  
Author(s):  
Yu Du ◽  
Zhimin Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimates ◽  
Phase Error ◽  
Three Dimensions ◽  
Wave Number ◽  
Weak Galerkin ◽  
High Wave Number ◽  
Large Wave ◽  
Element Method

AbstractWe study the error analysis of the weak Galerkin finite element method in [24, 38] (WG-FEM) for the Helmholtz problem with large wave number in two and three dimensions. Using a modified duality argument proposed by Zhu and Wu, we obtain the pre-asymptotic error estimates of the WG-FEM. In particular, the error estimates with explicit dependence on the wave numberkare derived. This shows that the pollution error in the brokenH1-norm is bounded byunder mesh conditionk7/2h2≤C0or (kh)2+k(kh)p+1≤C0, which coincides with the phase error of the finite element method obtained by existent dispersion analyses. Herehis the mesh size,pis the order of the approximation space andC0is a constant independent ofkandh. Furthermore, numerical tests are provided to verify the theoretical findings and to illustrate the great capability of the WG-FEM in reducing the pollution effect.

Assessment of GRACE-FO Laser Ranging Interferometer measurements

2021 ◽  
Author(s):  
Athina Peidou ◽  
Felix Landerer ◽  
David Wiese ◽  
Matthias Ellmer ◽  
Eugene Fahnestock ◽  
...  
Keyword(s):  
High Frequency ◽  
Signal To Noise Ratio ◽  
Small Scale ◽  
Laser Ranging ◽  
High Signal ◽  
Measurement Sensitivity ◽  
One Year ◽  
Mass Transfers ◽  
Gravity Recovery ◽  
System Errors

<p>The performance of Gravity Recovery and Climate Experiment Follow‐On (GRACE-FO) laser ranging interferometer (LRI) system is assessed in both space and frequency domains. With LRI’s measurement sensitivity being as small as 0.05 nm/s<sup>2</sup> at GRACE-FO altitude we perform a thorough assessment on the ability of the instrument to detect real small-scale high-frequency gravity signals. Analysis of range acceleration measurements along the orbit for nearly one year of daily solutions suggests that LRI can detect signals induced by mass perturbation up to 26 mHz, i.e., ~145 km spatial resolution. Additionally, high frequency signals that are not adequately modeled by dealiasing models are clearly detected and their magnitude is shown to reach 2-3 nm/s<sup>2</sup>. The alternative K‐band microwave ranging system (KBR) is also examined and results demonstrate the inability of KBR to retrieve signals above 15mHz (i.e., shorter than ~200 km) as the noise of the KBR range acceleration increases rapidly. Overall, the first stream of LRI measurements shows that the high signal to noise ratio allows for detection of mass transfers in finer scales, however the ability to fully exploit the high-quality signal measured by the LRI in Level 2 products is still constrained by noise of background models and other onboard instrumentation and measurement system errors.</p><p>Copyright Acknowledgment: This work was performed at the California Institute of Technology's Jet Propulsion Laboratory under a contract with the National Aeronautics and Space Administration's Cryosphere Science Program.</p>

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