Double Kelvin waves with continuous depth profiles

1968 ◽  
Vol 34 (1) ◽  
pp. 49-80 ◽  
Author(s):  
M. S. Longuet-Higgins
Keyword(s):  
Group Velocity ◽  
Transition Zone ◽  
Kelvin Wave ◽  
Trapped Modes ◽  
Full Account ◽  
Higher Modes ◽  
Depth Profiles ◽  
Different Depths ◽  
Bounded Below ◽  
Asymptotic Forms

The possibility of long waves in a rotating ocean being trapped along a straight discontinuity in depth was demonstrated in a recent paper (Longuet-Higgins 1968). The analysis is now extended to the situation where the depth varies continuously, in a zone separating two regions of different depths. The trapping of waves in the transition zone is investigated, taking full account of the horizontal divergence of the motion.If the profile of the depth is assumed to be monotonic, then it is shown that the trapped waves always travel along the transition zone with the shallower water to their right in the northern hemisphere and to their left in the southern hemisphere. The wave period must always exceed a pendulum-day. The period is also bounded below by a quantity depending inversely on the maximum bottom gradient.By allowing the width W of the transition zone to vary, asymptotic forms for the trapped modes are obtained, both as W → 0 and as W → ∞. In the limit as W → 0 the depth becomes discontinuous, and it is shown that the lowest mode then becomes a double Kelvin wave (Longuet-Higgins 1968) propagated along the discontinuity. The periods of the higher modes, on the other hand, all tend to infinity; these modes become steady currents.Numerical calculations of the trapped modes are presented for two different laws of depth in the transition zone. It is found that as W → 0 the lowest mode is insensitive to the form of the depth profile. Higher modes depend on the details of the profile. Hence the lowest mode is the most likely to be observed in the real ocean.The dispersion relation is also investigated. It is shown that the group-velocity of all modes must change sign at some point in the range of wave-numbers, if the divergence is taken into account. When the divergence was neglected the lowest mode appeared to be exceptional, in that the group-velocity was always in the same direction. This anomaly is now removed.

scholarly journals The Hybrid Kelvin–Edge Wave and Its Role in Tidal Dynamics

2010 ◽  
Vol 40 (12) ◽  
pp. 2757-2767 ◽  
Author(s):  
Ziming Ke ◽  
Alexander E. Yankovsky
Keyword(s):  
Group Velocity ◽  
Wave Energy ◽  
Numerical Experiments ◽  
Tidal Energy ◽  
Ocean Modeling ◽  
Edge Wave ◽  
Kelvin Wave ◽  
Regional Ocean Modeling System ◽  
Offshore Wave ◽  
Zero Group

Abstract A full set of long waves trapped in the coastal ocean over a variable topography includes a zero (fundamental) mode propagating with the coast on its right (left) in the Northern (Southern) Hemisphere. This zero mode resembles a Kelvin wave at lower frequencies and an edge wave (Stokes mode) at higher frequencies. At the intermediate frequencies this mode becomes a hybrid Kelvin–edge wave (HKEW), as both rotational effects and the variable depth become important. Furthermore, the group velocity of this hybrid mode becomes very small or even zero depending on shelf width. It is found that in midlatitudes a zero group velocity occurs at semidiurnal (tidal) frequencies over wide (∼300 km), gently sloping shelves. This notion motivated numerical experiments using the Regional Ocean Modeling System in which the incident HKEW with a semidiurnal period propagates over a wide shelf and encounters a narrowing shelf so that the group velocity becomes zero at some alongshore location. The numerical experiments have demonstrated that the wave energy increases upstream of this location as a result of the energy flux convergence while farther downstream the wave amplitude is substantially reduced. Instead of propagating alongshore, the wave energy radiates offshore in the form of Poincaré modes. Thus, it is concluded that the shelf areas where the group velocity of the HKEW becomes zero are characterized by an increased tidal amplitude and (consequently) high tidal energy dissipation, and by offshore wave energy radiation. This behavior is qualitatively consistent with the dynamics of semidiurnal tides on wide shelves narrowing in the direction of tidal wave propagation, including the Patagonia shelf and the South China Sea.

Resonant acoustic frequencies of a tandem cascade. Part 1. Zero relative motion

1999 ◽  
Vol 393 ◽  
pp. 215-240 ◽  
Author(s):  
B. M. WOODLEY ◽  
N. PEAKE
Keyword(s):  
Acoustic Scattering ◽  
Axial Flow ◽  
Acoustic Resonance ◽  
Front Face ◽  
Trapped Modes ◽  
Full Account ◽  
Low Frequencies ◽  
Wide Range ◽  
Analytic Expressions ◽  
Parameter Values

In this paper we study the acoustic scattering between two flat-plate cascades, with the aim of investigating the possible existence of trapped modes. In practical terms this question is related to the phenomenon of acoustic resonance in turbomachinery, whereby such resonant modes are excited to large amplitude by unsteady processes such as vortex shedding. We use the Wiener–Hopf technique to analyse the scattering of the various wave fields by the cascade blades, and by considering the fields between adjacent blades, as well as between the cascades, we are able to take full account of the genuinely finite blade chords. Analytic expressions for the various scattering matrices are derived, and an infinite-dimensional matrix equation is formed, which is then investigated numerically for singularity. One advantage of this formulation is that it allows the constituent parts of the system to be analysed individually, so that for instance the behaviour of the gap between the blade rows alone can be investigated by omitting the finite-chord terms in the equations. We demonstrate that the system exhibits two types of resonance, at a wide range of parameter values. First, there is a cut-on/cut-off resonance associated with the gap between the rows, and corresponding to modes propagating parallel to the front face of the cascades. Second, there is a resonance of the downstream row, akin to a Parker mode, driven at low frequencies by a vorticity wave produced by trapped duct modes in the upstream row, and at higher frequencies by radiation modes (and the vorticity wave) between the blade rows. The predictions for this second set of resonances are shown to be in excellent agreement with previous experimental data. The resonant frequencies are also seen to be real for this twin cascade system, indicating that the resonances correspond to genuine trapped modes. The analysis in this paper is completed with non-zero axial flow but with zero relative rotation between the cascades – in Part 2 (Woodley & Peake 1999) we will show how non-zero rotation of the upstream row can be included.

Approximations to wave trapping by topography

1996 ◽  
Vol 325 ◽  
pp. 357-376 ◽  
Author(s):  
P. G. Chamberlain ◽  
D. Porter
Keyword(s):  
Water Waves ◽  
Two Dimensional ◽  
Trapped Modes ◽  
Wave Trapping ◽  
Mild Slope Equation ◽  
Precise Shape ◽  
Different Depths ◽  
Linear Water Waves ◽  
Local Irregularity

The trapping of linear water waves over two-dimensional topography is investigated by using the mild-slope approximation. Two types of bed profile are considered: a local irregularity in a horizontal bed and a shelf joining two horizontal bed sections at different depths. A number of results are derived concerning the existence of trapped modes and their multiplicity. It is found, for example, that the maximum number of modes which can exist depends only on the gross properties of the topography and not on its precise shape. A range of problems is solved numerically, to inform and illustrate the analysis, using both the mild-slope equation and the recently derived modified mild-slope equation.

On trapped waves over a continental shelf

1975 ◽  
Vol 69 (4) ◽  
pp. 689-704 ◽  
Author(s):  
John M. Huthnance
Keyword(s):  
Energy Density ◽  
Continental Shelf ◽  
Depth Profile ◽  
Kelvin Wave ◽  
Trapped Modes ◽  
Edge Waves ◽  
Trapped Waves ◽  
Shelf Waves ◽  
Continental Shelf Waves

Any straight continental shelf of monotonic depth profile is shown to have as its entire complement of barotropic trapped modes (i) an infinite discrete set of ‘continental-shelf waves’, (ii) a single ‘Kelvin wave’, and (iii) an infinite discrete set of ‘edge waves’. The decomposition of energy density and fluxes into modal constituents is discussed.

scholarly journals Difficulties in the isotopic indication of the genesis Yamal's massive ice. Part 2. Kharasavey

2020 ◽  
pp. 35-56
Author(s):  
Julia Nikolaevna Chizhova ◽  
Yurij Kirillovich Vasil'chuk
Keyword(s):  
Chemical Composition ◽  
Transition Zone ◽  
Fresh Water ◽  
Open System ◽  
Coastal Areas ◽  
Ice Formation ◽  
Chemical Characteristics ◽  
The Third ◽  
Different Depths ◽  
Geochemical Studies

Massive ice, located at different depths in the permafrost of the Kharasavey gas condensate field, many massive ice formations occurred in different forms such as layers, lenses and laccoliths. Massive ice near the Kharasavey village was repeatedly studied and tested in detail, and ice formations were found both within the first sea terrace and within the third sea terrace. The isotopic and chemical composition of massive ice can be explained by different ways. We believe that it indicates intrasedimental formation of massive ice. This study is based on data on the values of δ18О, δ2H and dexc in massive ice, as well as the chemical composition of the ice to establish possible conditions for the massive ice formation. Geochemical studies of sediments within the coastal areas of the Kharasavey showed that variability in the distribution of salts in sediments reaches a maximum here, especially in the transition zone from sea to land. The isotopic and chemical characteristics of the ice indicate that ice had been formed in an open system (i.e., with free flow of water from the reservoir). At the same time, the water in the reservoir was changed; at the first stages, it was most likely a mixture of sea and fresh water, which was subsequently desalinated more and more.

LIMITATIONS ON RESISTIVITY METHODS AS INFERRED FROM THE BURIED SPHERE PROBLEM

Geophysics ◽  
1953 ◽  
Vol 18 (2) ◽  
pp. 423-433 ◽  
Author(s):  
Robert G. Van Nostrand
Keyword(s):  
Exact Solution ◽  
Coordinate System ◽  
Direct Current ◽  
Arbitrary Shape ◽  
Apparent Resistivity ◽  
Potential Problem ◽  
Depth Profiles ◽  
Conducting Sphere ◽  
Different Depths

The study of resistivity surveys over buried spheres is facilitated by the use of a bipolar coordinate system. Without solving the incident potential problem exactly, the author obtains an exact solution for the apparent resistivity as measured by the Wenner configuration of electrodes situated directly over a buried conducting sphere. From a study of depth profiles over a set of spheres buried at different depths, it is concluded that one cannot expect to find by direct current methods a sphere buried to a depth greater than the radius of the sphere. This result is generalized to include bodies of more arbitrary shape.

Interferometric (Fourier-Spectroscopic) Measurement of Electron Energy Distributions

1990 ◽  
Vol 48 (2) ◽  
pp. 110-111 ◽  
Author(s):  
F. Hasselbach ◽  
A. Schäfer
Keyword(s):  
Group Velocity ◽  
Wave Packets ◽  
Index Of Refraction ◽  
Electron Wave ◽  
Fringe Contrast ◽  
Faraday Cage ◽  
Optical Index ◽  
Wien Filter ◽  
Coherent Wave ◽  
Electric And Magnetic Fields

Möllenstedt and Wohland proposed in 1980 two methods for measuring the coherence lengths of electron wave packets interferometrically by observing interference fringe contrast in dependence on the longitudinal shift of the wave packets. In both cases an electron beam is split by an electron optical biprism into two coherent wave packets, and subsequently both packets travel part of their way to the interference plane in regions of different electric potential, either in a Faraday cage (Fig. 1a) or in a Wien filter (crossed electric and magnetic fields, Fig. 1b). In the Faraday cage the phase and group velocity of the upper beam (Fig.1a) is retarded or accelerated according to the cage potential. In the Wien filter the group velocity of both beams varies with its excitation while the phase velocity remains unchanged. The phase of the electron wave is not affected at all in the compensated state of the Wien filter since the electron optical index of refraction in this state equals 1 inside and outside of the Wien filter.

Preparation of Backthinned Ceramic Specimens

1985 ◽  
Vol 43 ◽  
pp. 182-183
Author(s):  
A. T. Fisher ◽  
P. Angelini
Keyword(s):  
Electron Microscopy ◽  
Analytical Electron Microscopy ◽  
Vacuum System ◽  
Back Surface ◽  
Surface Microstructure ◽  
Ion Milling ◽  
Near Surface ◽  
Depth Profiles ◽  
Analytical Electron ◽  
Ion Implanted

Analytical electron microscopy (AEM) of the near surface microstructure of ion implanted ceramics can provide much information about these materials. Backthinning of specimens results in relatively large thin areas for analysis of precipitates, voids, dislocations, depth profiles of implanted species and other features. One of the most critical stages in the backthinning process is the ion milling procedure. Material sputtered during ion milling can redeposit on the back surface thereby contaminating the specimen with impurities such as Fe, Cr, Ni, Mo, Si, etc. These impurities may originate from the specimen, specimen platform and clamping plates, vacuum system, and other components. The contamination may take the form of discrete particles or continuous films [Fig. 1] and compromises many of the compositional and microstructural analyses. A method is being developed to protect the implanted surface by coating it with NaCl prior to backthinning. Impurities which deposit on the continuous NaCl film during ion milling are removed by immersing the specimen in water and floating the contaminants from the specimen as the salt dissolves.

Multiple-fracturing and viewing of the same frozen sample at different depths using a low temperature FESEM

1996 ◽  
Vol 54 ◽  
pp. 820-821
Author(s):  
M.V. Parthasarathy ◽  
C. Daugherty
Keyword(s):  
Temperature Field ◽  
Low Temperature ◽  
Field Emission ◽  
Multiple Fracture ◽  
Precise Control ◽  
Cold Stage ◽  
Different Depths ◽  
Transfer Device

The versatility of Low Temperature Field Emission SEM (LTFESEM) for viewing frozen-hydrated biological specimens, and the high resolutions that can be obtained with such instruments have been well documented. Studies done with LTFESEM have been usually limited to the viewing of small organisms, organs, cells, and organelles, or viewing such specimens after fracturing them.We use a Hitachi 4500 FESEM equipped with a recently developed BAL-TEC SCE 020 cryopreparation/transfer device for our LTFESEM studies. The SCE 020 is similar in design to the older SCU 020 except that instead of having a dedicated stage, the SCE 020 has a detachable cold stage that mounts on to the FESEM stage when needed. Since the SCE 020 has a precisely controlled lock manipulator for transferring the specimen table from the cryopreparation chamber to the cold stage in the FESEM, and also has a motor driven microtome for precise control of specimen fracture, we have explored the feasibility of using the LTFESEM for multiple-fracture studies of the same sample.

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