scholarly journals Wave Patterns of Gravity-Capillary Waves from Moving Localized Sources

2020 ◽  
Author(s):  
Vladimir Gnevyshev ◽  
Sergei Badulin
Keyword(s):  
Group Velocity ◽  
Threshold Current ◽  
Capillary Waves ◽  
Dispersive Waves ◽  
Localized Source ◽  
Wave Patterns ◽  
Wake Patterns ◽  
Ship Wakes ◽  
Pure Gravity ◽  
Localized Sources

We study wave patterns of gravity-capillary waves from moving localized sources within the classic setup of the problem of ship wakes. The focus is made on the co-existence of two wave systems with opposite signatures of group velocity relative to the localized source. It leads to the problem of choice of signs for phase functions of the gravity (“slow”) and capillary (“fast”) branches of the dispersion relation: the question generally ignored when constructing phase patterns of the solutions. We detail characteristic angles of the wake patterns: (i) angle of demarcation of gravity and capillary waves – “the phase Mach” cone, (ii) angle of the minimal group velocity of gravity-capillary waves – “the group Mach” cone, (iii, iv) angles of cusps of isophases that appear after a threshold current speed. The outer cusp cone is naturally associated with the classic cone of Kelvin for pure gravity waves. The inner one results from the effect of capillarity and tends to the “group Mach” pattern at high speeds of current. Amplitudes of the wave patterns are estimated within the recently proposed approach of reference functions for the problem of propagation of packets of linear dispersive waves. The effect of shape is discussed for elliptic reference sources.

scholarly journals Wave Patterns of Gravity–Capillary Waves from Moving Localized Sources

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 219
Author(s):  
Vladimir Gnevyshev ◽  
Sergei Badulin
Keyword(s):  
Group Velocity ◽  
Threshold Current ◽  
Capillary Waves ◽  
Dispersive Waves ◽  
Localized Source ◽  
Wave Patterns ◽  
Wake Patterns ◽  
Ship Wakes ◽  
Pure Gravity ◽  
Localized Sources

We study wave patterns of gravity–capillary waves from moving localized sources within the classic setup of the problem of ship wakes. The focus is on the co-existence of two wave systems with opposite signatures of group velocity relative to the localized source. It leads to the problem of choice of signs for phase functions of the gravity (“slow”) and capillary (“fast”) branches of the dispersion relation: the question generally ignored when constructing phase patterns of the solutions. We detail characteristic angles of the wake patterns: (i) angle of demarcation of gravity and capillary waves—“the phase Mach” cone, (ii) angle of the minimal group velocity of gravity–capillary waves—“the group Mach” cone, (iii, iv) angles of cusps of isophases that appear after a threshold current speed. The outer cusp cone is naturally associated with the classic cone of Kelvin for pure gravity waves. The inner one results from the effect of capillarity and tends to the “group Mach” pattern at high speeds of current. Amplitudes of the wave patterns are estimated within the recently proposed approach of reference functions for the problem of propagation of packets of linear dispersive waves. The effect of shape is discussed for elliptic reference sources.

Weakly nonlinear dispersive waves: group velocity

1982 ◽  
Vol 27 (3) ◽  
pp. 507-514
Author(s):  
Bhimsen K. Shivamoggi
Keyword(s):  
Group Velocity ◽  
Acoustic Waves ◽  
Specific Problem ◽  
Electron Plasma ◽  
Hot Electron ◽  
Ion Acoustic Waves ◽  
Dispersive Waves ◽  
Weakly Nonlinear ◽  
Longitudinal Waves ◽  
Wave Trains

For slowly varying wave trains in a linear system, it is known that a quantity proportional to the square of the amplitude propagates with the group velocity. It is shown here, by considering a specific problem of longitudinal waves in a hot electron-plasma and using an asymptotic analysis, that this result continues to be valid even when weak nonlinearities are introduced into the system provided they produce slowly varying wave trains. The method of analysis fails, however, for weakly nonlinear ion-acoustic waves.

scholarly journals On the Interpretation of the Doppler Spectra of Ionospherically Propagated Ground Backscatter Echoes

1975 ◽  
Vol 28 (5) ◽  
pp. 575
Author(s):  
JA Bennett
Keyword(s):  
Simple Model ◽  
Acoustic Wave ◽  
Group Velocity ◽  
Realistic Model ◽  
Directional Antennas ◽  
Doppler Spectrum ◽  
Sea Waves ◽  
Dispersive Waves ◽  
Time Changes ◽  
The Way

The mechanism giVing rise to the backscatter Doppler spectrum is discussed by means of a simple model. Attention is focused on the effect of movement of the region contributing to the echo which arises from time changes in the group velocity within the ionosphere. It is shown that the influence of these changes on the spectrum can be separated into two parts: (1) A change in the maximum possible width of the spectrum as a result of the change of the time for which an indiVidual scatterer is contributing to the echo; this effect is independent of the scatterer distribution. (2) A possible narrowing of the spectrum as a result of the way in which the signals from individual scatterers combine; this effect depends upon scatterer distribution. Scatter from a fixed'scattering surface and from dispersive waves (e.g. sea waves) is considered. A tentative extrapolation of the results to a more realistic model suggests that neither effect is likely to be significant in practical highfrequency radio experiments (except at short ranges with highly directional antennas), although they may be significant in acoustic wave simulations of the radio case.

Phase patterns of dispersive waves from moving localized sources

2014 ◽  
Vol 184 (1) ◽  
pp. 89-100 ◽  
Author(s):  
Pavel N. Svirkunov ◽  
Maksim V. Kalashnik
Keyword(s):  
Dispersive Waves ◽  
Localized Sources

Perturbation theory of parametrically driven capillary waves at low viscosity

1997 ◽  
Vol 351 ◽  
pp. 301-344 ◽  
Author(s):  
PER LYNGSHANSEN ◽  
PREBEN ALSTRØM
Keyword(s):  
Perturbation Theory ◽  
Aspect Ratio ◽  
Standing Wave ◽  
High Aspect Ratio ◽  
Capillary Waves ◽  
Wave Analysis ◽  
Amplitude Equations ◽  
Low Viscosity ◽  
Wave Patterns ◽  
Hamiltonian Perturbation Theory

We present a critical review of the Hamiltonian and the Lagrangian theories of pattern formation in driven capillary waves at low viscosity and high aspect ratio. We construct a Hamiltonian perturbation theory in the spirit of Milner's (1991) formulation, and derive the amplitude equations and their coefficients relevant at the onset of surface waves. Our presentation is detailed, and we carefully point out the differences between our results for the nonlinear coefficients and the results obtained by others. From our standing wave analysis we find that the square pattern is subcritical. Among the supercritical standing wave patterns, we find that the eightfold quasi-crystalline pattern, observed by Christiansen et al. (1992) and by Bosch (1995), is more stable than both rolls and hexagons. We outline the high-aspect-ratio experimental results obtained so far, and discuss them in the light of the theory.

scholarly journals Variability in spatial patterns of long nonlinear waves from fast ferries in Tallinn Bay

2009 ◽  
Vol 16 (2) ◽  
pp. 351-363 ◽  
Author(s):  
T. Torsvik ◽  
I. Didenkulova ◽  
T. Soomere ◽  
K. E. Parnell
Keyword(s):  
High Speed ◽  
Wave Loads ◽  
S Waves ◽  
Ship Wave ◽  
Wake Patterns ◽  
Ship Wakes ◽  
Wave Heights ◽  
The Baltic ◽  
Sea Area ◽  
Intrinsic Feature

Abstract. High-speed ferries are known to generate wakes with unusually long periods, and occasionally large amplitudes which may serve as a qualitatively new forcing factor in coastal regions that are not exposed to a sea swell. An intrinsic feature of such wakes is their large spatial variation. We analyze the variability of wake conditions for the coasts of Tallinn Bay, the Baltic Sea, a sea area with very intense fast ferry traffic. The modelled ship wave properties for several GPS-recorded ship tracks reasonably match the measured waves in terms of both wave heights and periods. It is shown that the spatial extent of the wake patterns is very sensitive to small variations in sailing conditions. This feature leads to large variations of ship wave loads at different coastal sections with several locations regularly receiving high ship wave energy. The runup of the largest ship wakes on the beach increases significantly with an increase in wave height whereas shorter (period <2–5 s) waves merge into longer waves in the shoaling and runup process.

scholarly journals The Wavenumber–Frequency Content of Resonantly Excited Equatorial Waves

2012 ◽  
Vol 42 (11) ◽  
pp. 1834-1858 ◽  
Author(s):  
Theodore S. Durland ◽  
J. Thomas Farrar
Keyword(s):  
Group Velocity ◽  
Gravity Waves ◽  
Wave Energy ◽  
Wave Structure ◽  
Physical Conditions ◽  
Total Wave ◽  
Zonal Wavenumber ◽  
Meridional Winds ◽  
Pure Gravity ◽  
Inertia Gravity Waves

Abstract The theoretical resonant excitation of equatorial inertia–gravity waves and mixed Rossby–gravity waves is examined. Contrary to occasionally published expectations, solutions show that winds that are broadband in both zonal wavenumber and frequency do not in general produce peaks in the wavenumber–frequency spectrum of sea surface height (SSH) at wavenumbers associated with vanishing zonal group velocity. Excitation of total wave energy in inertia–gravity modes by broadband zonal winds is virtually wavenumber independent when the meridional structure of the winds does not impose a bias toward negative or positive zonal wavenumbers. With increasing wavenumber magnitude |k|, inertia–gravity waves asymptote toward zonally propagating pure gravity waves, in which the magnitude of meridional velocity υ becomes progressively smaller relative to the magnitude of zonal velocity u and pressure p. When the total wave energy is independent of wavenumber, this effect produces a peak in |υ|2 near the wavenumber where group velocity vanishes, but a trough in |p|2 (or SSH variance). Another consequence of the shift toward pure gravity wave structure is that broadband meridional winds excite inertia–gravity modes progressively less efficiently as |k| increases and υ becomes less important to the wave structure. Broadband meridional winds produce a low-wavenumber peak in total wave energy leading to a subtle elevation of |p|2 at low wavenumbers, but this is due entirely to the decrease in the forcing efficiency of meridional winds with increasing |k|, rather than to the vanishing of the group velocity. Physical conditions that might alter the above conclusions are discussed.

Some effects of surface tension on steep water waves. Part 2

1980 ◽  
Vol 96 (3) ◽  
pp. 417-445 ◽  
Author(s):  
S. J. Hogan
Keyword(s):  
Surface Tension ◽  
Gravity Waves ◽  
Water Waves ◽  
Expansion Method ◽  
Capillary Waves ◽  
Maximum Wave Height ◽  
Pure Gravity ◽  
Wave Profiles ◽  
The Waves ◽  
Wave Properties

This paper continues an investigation of the effects of surface tension on steep water waves in deep water begun in Hogan (1979a). A Stokes-type expansion method is given which can be applied to most wavelengths. For capillary waves (2 cm or less) it is found that the surface of the highest wave encloses a bubble of air, as was found for pure capillary waves by Crapper (1957). For intermediate waves (20 cm) the wave profiles are similar to those of pure gravity waves and the wave properties increase monotonically. For gravity waves (200 cm) the wave properties all exhibit a maximum just short of the maximum wave height obtained by the method. The integral properties for all the waves are drawn and given in numerical form in the appendix.

scholarly journals Mechanistic targets for the ablation of atrial fibrillation

2017 ◽  
Vol 2017 (1) ◽  
Author(s):  
Junaid AB Zaman ◽  
Tina Baykaner ◽  
Amir A Schricker ◽  
David E Krummen ◽  
Sanjiv M Narayan
Keyword(s):  
Atrial Fibrillation ◽  
Clinical Studies ◽  
Optical Mapping ◽  
Ongoing Research ◽  
Localized Source ◽  
All Optical ◽  
Spatially Distributed ◽  
Basic Studies ◽  
Localized Sources

The mechanisms responsible for sustaining atrial fibrillation are a key debate in cardiovascular pathophysiology, and directly influence the approach to therapy including ablation. Clinical and basic studies have split AF mechanisms into two basic camps: ‘spatially distributed disorganization’ and ‘localized sources’. Recent data suggest that these mechanisms can also be separated by the method for mapping – with nearly all traditional electrogram analyses showing spatially distributed disorganization and nearly all optical mapping studies showing localized sources We will review this dichotomy in light of these recently identified differences in mapping, and in the context of recent clinical studies in which localized ablation has been shown to impact AF, also lending support to the localized source hypothesis. We will conclude with other concepts on mechanism-based ablation and areas of ongoing research that must be addressed to continue improving our knowledge and treatment of AF. 

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