Generation of internal waves from rest: extended use of complex coordinates, for a sphere but not a disk

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.229 ◽

2012 ◽

Vol 703 ◽

pp. 374-390 ◽

Cited By ~ 1

Author(s):

Anthony M. J. Davis

Keyword(s):

Solution Structure ◽

Direct Calculation ◽

Relative Magnitude ◽

Analytic Solutions ◽

Careful Consideration ◽

Phase Changes ◽

Energy Propagation ◽

Scattering Problems ◽

Frequency Space ◽

Inviscid Case

AbstractThe anisotropy created by stratification and or rotation places restrictions, severe if viscosity is present, on the construction of analytic solutions to wave generation and scattering problems. Consequently, much literature is devoted to frequency space and so careful consideration of oscillatory motion generated from rest is advisable. Moreover, the use of complex coordinates in the inviscid case has been incompletely presented. The detailed inversion of the Fourier time transform for a breathing or heaving sphere demonstrates an expanded, perhaps more crucial, role for the complex coordinates and shows that the known phase changes in the energy propagation regions are present throughout the St Andrew’s cross that circumscribes the sphere. However, the different solution structure for the heaving disk requires and allows a more direct calculation. Though the inclusion of rotation does not affect the dynamics, it enables the significance of their relative magnitude to be identified and reference to rotation only results achieved.

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Extended local Rytov Fourier migration method

Geophysics ◽

10.1190/1.1444657 ◽

1999 ◽

Vol 64 (5) ◽

pp. 1535-1545 ◽

Cited By ~ 36

Author(s):

Lian‐Jie Huang ◽

Michael C. Fehler ◽

Peter M. Roberts ◽

Charles C. Burch

Keyword(s):

Phase Changes ◽

Fast Fourier Transform Algorithm ◽

Scalar Wave ◽

Depth Migration ◽

Frequency Space ◽

Rytov Approximation ◽

Migration Method ◽

The Stability ◽

Wavefield Extrapolation ◽

Lateral Variations

We develop a novel depth‐migration method termed the extended local Rytov Fourier (ELRF) migration method. It is based on the scalar wave equation and a local application of the Rytov approximation within each extrapolation interval. Wavefields are Fourier transformed back and forth between the frequency‐space and frequency‐wavenumber domains during wavefield extrapolation. The lateral slowness variations are taken into account in the frequency‐space domain. The method is efficient due to the use of a fast Fourier transform algorithm. Under the small angle approximation, the ELRF method leads to the split‐step Fourier (SSF) method that is unconditionally stable. The ELRF method and the extended local Born Fourier (ELBF) method that we previously developed can handle wider propagation angles than the SSF method and account for the phase and amplitude changes due to the lateral variations of slowness, whereas the SSF method only accounts for the phase changes. The stability of the ELRF method is controlled more easily than that of the ELBF method.

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Salvesen’s Method for Added Resistance Revisited

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.4050213 ◽

2021 ◽

Vol 143 (5) ◽

Author(s):

Mostafa Amini-Afshar

Keyword(s):

Direct Calculation ◽

Wave Resistance ◽

The Body ◽

Ship Motions ◽

Exact Equation ◽

Added Resistance ◽

Scattering Problems ◽

Correct Treatment ◽

Long Wave ◽

Strip Theory

Abstract Almost 4 years after the appearance of Salvesen–Tuck–Faltinsen (STF) strip theory (Salvesen et al., 1970, “Ship Motions and Sea Loads,” Annual Meeting of the Society of Naval Architecture and Marine Engineers (SNAME), New York, Nov. 12–13), Salvesen in 1974 published his popular method for calculation of added resistance (Salvesen, 1974, “Second-Order Steady State Forces and Moments on Surface Ships in Oblique Regular Waves,” Vol. 22; Salvesen, 1978, “Added Resistance of Ships in Waves,” J. Hydronautics, 12(1), pp. 24–34). His method is based on an exact near-field formulation; however, he applied the long-wave and the weak-scatterer assumptions to present his approximate method using the integrated quantities (hydrodynamic and geometrical coefficients). Considering the available computational powers in the 1970s, both of these assumptions were absolutely justifiable. The intention of this paper is to disseminate the results of a recent study at the Technical University of Denmark, whereby the Salvesen’s formulation has been revisited and the added resistance is computed from the original exact equation without invoking the weak-scatterer or the long-wave assumptions. This is performed using the solutions of the radiation and the scattering problems, obtained by a low-order boundary element method and the two-dimensional free-surface Green function inside our in-house STF theory implementation (Bingham and Amini-Afshar, 2020, DTU_Strip Theory Solver). The weak-scatterer assumption is then removed through a direct calculation of the x-derivatives of the velocity potentials and the normal vectors along the body. Knowing the velocity potentials over each panel, the long-wave assumption is also avoided by a piece-wise analytical integration of sectional Kochin Function (Kochin, 1936, “On the Wave Resistance and Lift of Bodies Submerged in Fluid,” Transactions of the Conference on the Theory of Wave Resistance, Moscow.). The presented results for five ship geometries testify that the correct treatment of the original equation is achieved only after both of the above-mentioned assumptions are removed. Implemented in this manner, Salvesen’s method proves to be relatively more accurate and robust than has been generally perceived during all these years.

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RASCAS: RAdiation SCattering in Astrophysical Simulations

Astronomy and Astrophysics ◽

10.1051/0004-6361/201834961 ◽

2020 ◽

Vol 635 ◽

pp. A154 ◽

Cited By ~ 6

Author(s):

L. Michel-Dansac ◽

J. Blaizot ◽

T. Garel ◽

A. Verhamme ◽

T. Kimm ◽

...

Keyword(s):

Radiative Transfer ◽

Adaptive Mesh ◽

Analytic Solutions ◽

Resonant Line ◽

Frequency Space ◽

New Public ◽

Astrophysical Objects ◽

Process Simulations ◽

The Many ◽

Transfer Problems

Context. Resonant lines are powerful probes of the interstellar and circumgalactic medium of galaxies. Their transfer in gas being a complex process, the interpretation of their observational signatures, either in absorption or in emission, is often not straightforward. Numerical radiative transfer simulations are needed to accurately describe the travel of resonant line photons in real and in frequency space, and to produce realistic mock observations. Aims. This paper introduces RASCAS, a new public 3D radiative transfer code developed to perform the propagation of any resonant line in numerical simulations of astrophysical objects. RASCAS was designed to be easily customisable and to process simulations of arbitrarily large sizes on large supercomputers. Methods. RASCAS performs radiative transfer on an adaptive mesh with an octree structure using the Monte Carlo technique. RASCAS features full MPI parallelisation, domain decomposition, adaptive load-balancing, and a standard peeling algorithm to construct mock observations. The radiative transport of resonant line photons through different mixes of species (e.g. H I, Si II, Mg II, Fe II), including their interaction with dust, is implemented in a modular fashion to allow new transitions to be easily added to the code. Results. RASCAS is very accurate and efficient. It shows perfect scaling up to a minimum of a thousand cores. It has been fully tested against radiative transfer problems with analytic solutions and against various test cases proposed in the literature. Although it was designed to describe accurately the many scatterings of line photons, RASCAS may also be used to propagate photons at any wavelength (e.g. stellar continuum or fluorescent lines), or to cast millions of rays to integrate the optical depths of ionising photons, making it highly versatile.

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Over-reflection of internal-inertial waves from the mixed layer

Journal of Fluid Mechanics ◽

10.1017/s0022112084000793 ◽

1984 ◽

Vol 141 ◽

pp. 179-196 ◽

Cited By ~ 1

Author(s):

M. Kamachi ◽

R. Grimshaw

Keyword(s):

Mixed Layer ◽

Growth Rates ◽

Vertical Profile ◽

Body Force ◽

Inertial Waves ◽

Mean Flow ◽

Energy Propagation ◽

Frequency Space ◽

Wave Induced ◽

The Relationship

Near-inertial oscillations associated with downward energy propagation are commonly observed in the upper ocean. Stern (1977) has suggested that these observations may be internal-inertial waves over-reflected from the shear zone at the base of the mixed layer. In this paper we develop a criterion for over-reflection as a function of wavenumber and frequency for a class of shear flows in the mixed layer. By examining the vertical profile of the vertical wave action flux we demonstrate that the source of the over-reflection is the shear at the base of the mixed layer, which is maintained by the wind-induced turbulent Reynolds stress, here parametrized as a body force. The relationship between over-reflection and the wave-induced Lagrangian-mean flow is determined. We also determine a criterion for unstable waves, and show that these are contiguous in wavenumber-frequency space with points of resonant over-reflection. However, the growth rates of these unstable waves are quite small, and in practice unstable waves will be indistinguishable from waves generated by over-reflection.

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The response of a stratified rapidly rotating flow to a pulsating topography

Journal of Fluid Mechanics ◽

10.1017/s0022112087000995 ◽

1987 ◽

Vol 177 ◽

pp. 359-379 ◽

Cited By ~ 3

Author(s):

S. N. Brown ◽

H. K. Cheng

Keyword(s):

Large Scale ◽

Internal Gravity Wave ◽

Wave Theory ◽

Internal Gravity Waves ◽

Relative Magnitude ◽

Far Field ◽

Energy Propagation ◽

Propagating Waves ◽

Finite Distance ◽

Full Solution

A theoretical study is made of the disturbance produced by an oscillating, shallow topographical feature in horizontal relative motion in a rapidly rotating, linearly stratified, unbounded fluid. For a sinusoidal surface oscillation, an explicit solution is obtained in terms of wavenumber spectra of the topography. The oscillating far-field behaviour is shown to consist of a large-scale, cyclonic component above the topography and a system of inertial waves behind the caustics, which spreads predominantly in the downstream direction. A significant property of the flow field is its dependence on a frequency threshold familiar from classical works on internal gravity waves in the absence of rotation, determined by the Brunt-Väisälä value. When the frequency is supercritical, a prominent circle of maximum disturbance appears in the far field, which provides the transition boundary between two distinct cyclonic structures and an upstream barrier to the propagating waves ahead of the obstacle. The circle has a radius depending on the relative magnitude of the pulsating frequency and the Brunt-Väisälä value, and is distinctly marked also by a phase jump in pressure and velocities. These features are substantiated by numerical examples of the full solution at a large but finite distance above the obstacle at supercritical frequencies. The circle of maximum disturbance signifies a preferential direction for energy propagation unaccounted for by group velocity. Its relation to the classical result of Görtler in the homogeneous case and that in the classical internal-gravity-wave theory are examined.

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Enumeration, orthogonality and completeness of the incompressible Coriolis modes in a sphere

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.27 ◽

2015 ◽

Vol 766 ◽

pp. 468-498 ◽

Cited By ~ 13

Author(s):

D. J. Ivers ◽

A. Jackson ◽

D. Winch

Keyword(s):

Incompressible Flows ◽

Dimensional Space ◽

Bounded Operator ◽

Neumann Boundary ◽

Analytic Solutions ◽

Careful Consideration ◽

Finite Dimensional Space ◽

Rotating Boundary ◽

Spherical Polynomial ◽

Polynomial Flows

AbstractWe consider incompressible flows in the rapid-rotation limit of small Rossby number and vanishing Ekman number, in a bounded volume with a rigid impenetrable rotating boundary. Physically the flows are inviscid, almost rigid rotations. We interpret the Coriolis force, modified by a pressure gradient, as a linear operator acting on smooth inviscid incompressible flows in the volume. The eigenfunctions of the Coriolis operator $\boldsymbol{{\mathcal{C}}}$ so defined are the inertial modes (including any Rossby modes) and geostrophic modes of the rotating volume. We show $\boldsymbol{{\mathcal{C}}}$ is a bounded operator and that $-\text{i}\boldsymbol{{\mathcal{C}}}$ is symmetric, so that the Coriolis modes of different frequencies are orthogonal. We prove that the space of incompressible polynomial flows of degree $N$ or less in a sphere is invariant under $\boldsymbol{{\mathcal{C}}}$. The symmetry of $-\text{i}\boldsymbol{{\mathcal{C}}}$ thus implies the Coriolis operator is non-defective on the finite-dimensional space of spherical polynomial flows. This enables us to enumerate the Coriolis modes, and to establish their completeness using the Weierstrass polynomial approximation theorem. The fundamental tool, which is required to establish invariance of spherical polynomial flows under $\boldsymbol{{\mathcal{C}}}$ and completeness, is that the solution of the polynomial Poisson–Neumann problem, i.e. Poisson’s equation with a Neumann boundary condition and polynomial data, in a sphere is a polynomial. We also enumerate the Coriolis modes in a sphere, with careful consideration of the geostrophic modes, directly from the known analytic solutions.

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Impact of Annealing on the Thermoelectric Properties of Ge2Sb2Te5 Films

MRS Proceedings ◽

10.1557/opl.2012.1573 ◽

2012 ◽

Vol 1490 ◽

pp. 223-228

Author(s):

Jaeho Lee ◽

Takashi Kodama ◽

Yoonjin Won ◽

Mehdi Asheghi ◽

Kenneth E. Goodson

Keyword(s):

Phase Change ◽

Thermoelectric Power ◽

Thermoelectric Properties ◽

Power Factor ◽

Effective Medium Theory ◽

Careful Consideration ◽

Phase Changes ◽

Face Centered Cubic ◽

Thermoelectric Power Factor ◽

Medium Theory

ABSTRACTThermoelectric phenomena strongly influence the behavior of chalcogenide materials in nanoelectronic devices including phase-change memory cells. This paper presents the annealing temperature and phase dependent thermoelectric properties of Ge2Sb2Te5 films including the thermoelectric power factor and the figure of merit. The Ge2Sb2Te5 films annealed at different temperatures contain varying fractions of the amorphous and crystalline phases which strongly influence the thermoelectric properties. The thermoelectric power factor increases fom 3.2 μW/mK2 to 65 μW/mK2as the crystal phase changes from face-centered cubic to hexagonal close-packed. The data are consistent with modeling based on effective medium theory and suggest that careful consideration of phase purity is needed to improve the figures of merit for phase change memories and potentially for thermoelectric energy conversion applications.

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Determination of the Best Emulsion for the Microscopy of Crystals

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100096886 ◽

1981 ◽

Vol 39 ◽

pp. 32-33

Author(s):

David A. Grano ◽

Kenneth H. Downing

Keyword(s):

Spatial Frequency ◽

Information Transfer ◽

Signal To Noise Ratio ◽

Experimental Situation ◽

Photographic Emulsion ◽

Modulation Transfer ◽

Signal To Noise ◽

Frequency Space ◽

Noise Ratio

The retrieval of high-resolution information from images of biological crystals depends, in part, on the use of the correct photographic emulsion. We have been investigating the information transfer properties of twelve emulsions with a view toward 1) characterizing the emulsions by a few, measurable quantities, and 2) identifying the “best” emulsion of those we have studied for use in any given experimental situation. Because our interests lie in the examination of crystalline specimens, we've chosen to evaluate an emulsion's signal-to-noise ratio (SNR) as a function of spatial frequency and use this as our critereon for determining the best emulsion.The signal-to-noise ratio in frequency space depends on several factors. First, the signal depends on the speed of the emulsion and its modulation transfer function (MTF). By procedures outlined in, MTF's have been found for all the emulsions tested and can be fit by an analytic expression 1/(1+(S/S0)2). Figure 1 shows the experimental data and fitted curve for an emulsion with a better than average MTF. A single parameter, the spatial frequency at which the transfer falls to 50% (S0), characterizes this curve.

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The Interpretation of Crystal Lattice Images

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010009600x ◽

1972 ◽

Vol 30 ◽

pp. 550-551

Author(s):

J. M. Cowley ◽

Sumio Iijima

Keyword(s):

Crystal Orientation ◽

Diffraction Theory ◽

Phase Changes ◽

Electron Wave ◽

Crystal Lattices ◽

Heavy Atoms ◽

Lattice Images ◽

The Right ◽

Intuitive Interpretation ◽

Suitable Approximation

The imaging of detailed structures of crystal lattices with 3 to 4Å resolution, given the correct conditions of microscope defocus and crystal orientation and thickness, has been used by Iijima (this conference) for the study of new types of crystal structures and the defects in known structures associated with fluctuations of stoichiometry. The image intensities may be computed using n-beam dynamical diffraction theory involving several hundred beams (Fejes, this conference). However it is still important to have a suitable approximation to provide an immediate rough estimate of contrast and an evaluation of the intuitive interpretation in terms of an amplitude object.For crystals 100 to 150Å thick containing moderately heavy atoms the phase changes of the electron wave vary by about 10 radians suggesting that the “optimum defocus” theory of amplitude contrast for thin phase objects due to Scherzer and others can not apply, although it does predict the right defocus for optimum imaging.

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