Propagation of axi-symmetric nonlinear shallow water waves over slowly varying depth

Killen, S. M.; Johnson, R. S.

doi:10.1016/s0378-4754(00)00294-9

Cited by 6 publications

(3 citation statements)

References 16 publications

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“…Mass “leaks” into this shelf, so there is an inherent dissipation associated with the spreading. The leading order term, or primary wave, in a suitable expansion looking for such solutions is [ Grimshaw , ; Killen and Johnson , ]:

η = \frac{B_{0}}{{false(r / r_{0} false)}^{2 / 3}} {sech}^{2} true{\sqrt{\frac{μ B_{0}}{12 δ {false(r / r_{0} false)}^{2 / 3}}} true(r - r_{0} - c_{0} t - μ \frac{B_{0} r_{0}}{c_{0}} true({false(r / r_{0} false)}^{1 / 3} - 1 true) true) true}

where the initial wave amplitude at a distance r 0 is B 0 .…”

Section: Discussionmentioning

confidence: 99%

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Internal wave generation from tidal flow exiting a constricted opening

Wang

Pawlowicz

2017

JGR Oceans

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The southern Strait of Georgia, British Columbia, often contains packets of large, near‐surface internal waves. Wave crests at the leading edge of the packet, spaced a few hundred meters apart, can have a longitudinal extent of more than 10 km. It has long been assumed that these waves are generated by tidal flow through narrow passages and channels at the Strait's southern boundaries, but no actual link has ever been made between these waves and a specific passage or generation mechanism. Here we identify the location and extent of a number of these large packets at specific times using mosaics of photogrammetrically rectified oblique air photos. Wave speeds are determined by analyzing a time sequence of images, with water column measurements used to subtract effects of tidal advection. The location and extent of these internal waves are then compared with the predicted location and extent of hypothetical waves generated in different passages, at different stages of the tide, which are then propagated through a predicted time‐varying barotropic flow field. It is found that the observed waves are most likely generated near or after the time of the peak flood tide, or peak inflow into the Strait. They are therefore inconsistent with generation mechanisms involving the release and upstream propagation of waves by the relaxation of an ebb tide. Instead they are probably associated with the nonlinear adjustment of conditions at the edge of an inflowing injection of relatively weakly stratified water.

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η = \frac{B_{0}}{{false(r / r_{0} false)}^{2 / 3}} {sech}^{2} true{\sqrt{\frac{μ B_{0}}{12 δ {false(r / r_{0} false)}^{2 / 3}}} true(r - r_{0} - c_{0} t - μ \frac{B_{0} r_{0}}{c_{0}} true({false(r / r_{0} false)}^{1 / 3} - 1 true) true) true}

where the initial wave amplitude at a distance r 0 is B 0 .…”

Section: Discussionmentioning

confidence: 99%

“…Mass ''leaks'' into this shelf, so there is an inherent dissipation associated with the spreading. The leading order term, or primary wave, in a suitable expansion looking for such solutions is [Grimshaw, 1998;Killen and Johnson, 2001]:…”

Section: Discussionmentioning

confidence: 99%

Internal wave generation from tidal flow exiting a constricted opening

Wang

Pawlowicz

2017

JGR Oceans

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“…On the other hand, the Lie group method is an effective method for studying conservation laws, performing Lie symmetry analysis, and finding exact solutions to nonlinear partial differential equations. In some recent findings, the symmetric analysis of spherical and cylindrical KdV has been discussed in detail [19,20]. For our purpose, we have applied a standard reductive perturbation technique and obtained the Korteweg-De Vries (KdV) equation, which admits the excitation of phase-shaped solitons.…”

Section: Introductionmentioning

confidence: 99%

Higher Order Non-Planar Electrostatic Solitary Potential in a Streaming Electron-Ion Magnetoplasma: Phase Plane Analysis

et al. 2023

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We investigate cylindrical and spherical solitons in electron-ion (EI) plasma that contains hot (cold) electrons with stationary ions. The magneto-hydrodynamic equations are solved with the aid of the reductive perturbation (RP) technique, leading to the modified Korteweg–De Vries (mKdV) equation for the non-linear behaviour of the solitary waves in EI plasma. By employing the reduced differential transform method (RDTM), an approximate solution of the mKdV is obtained for solitary waves. Phase plane analysis reveals that these excitations exhibit periodic oscillations. The phase plane and periodic behaviour of the obtained model are studied. It is observed that the amplitude and width of the electron acoustic waves (EAWs) are affected by a slight change in the cold to hot electron temperature ratio (σc) and the number density of the cold to hot electron ratio (α). The effect of the streaming speed u(0) and superthermality index κe are investigated. This study is important for understanding the symmetric properties of cylindrical and spherical plasma, relying on the bifurcation analysis, impacted by the streaming effect in the EI plasma.

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A note on the wave propagation in water of variable depth

Demı́ray

2011

Applied Mathematics and Computation

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Propagation of axi-symmetric nonlinear shallow water waves over slowly varying depth

Cited by 6 publications

References 16 publications

Internal wave generation from tidal flow exiting a constricted opening

Internal wave generation from tidal flow exiting a constricted opening

Higher Order Non-Planar Electrostatic Solitary Potential in a Streaming Electron-Ion Magnetoplasma: Phase Plane Analysis

A note on the wave propagation in water of variable depth

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