Shallow Water Ray Tracing with Nonlinear Velocity Profiles

1972 ◽  
Vol 52 (3B) ◽  
pp. 1000-1010 ◽  
Author(s):  
N. L. Weinberg ◽  
T. Dunderdale
Keyword(s):  
Shallow Water ◽  
Ray Tracing ◽  
Velocity Profiles ◽  
Nonlinear Velocity

scholarly journals Wall roughness and nonlinear velocity profiles in granular shear flows

2017 ◽  
Vol 140 ◽  
pp. 03090 ◽  
Author(s):  
Paul Schuhmacher ◽  
Farhang Radjai ◽  
Stéphane Roux
Keyword(s):  
Shear Flows ◽  
Velocity Profiles ◽  
Wall Roughness ◽  
Granular Shear ◽  
Nonlinear Velocity

A ray method for near-shore plumes in a shallow-water flow

1991 ◽  
Vol 224 ◽  
pp. 227-239 ◽  
Author(s):  
Ronald Smith
Keyword(s):  
Shallow Water ◽  
Ray Tracing ◽  
Water Flow ◽  
Uniform Approximation ◽  
Contaminant Plume ◽  
Shallow Water Flow ◽  
Ray Method ◽  
Near Shore ◽  
Tracing Method ◽  
Ray Paths

Far from a shoreline, the spreading of a contaminant plume in a shallow-water flow can be predicted easily and accurately by a ray-tracing method. Unfortunately, the concentration predictions become singular at a beach, where the ray paths have a caustic. In this paper a uniform approximation is derived which remains valid at a beach. It is shown how the singular ray solutions corresponding to rays incident to and transmitted from the beach can be combined to construct the uniform approximation.

scholarly journals Ray tracing in a turbulent, shallow‐water channel

1998 ◽  
Vol 103 (5) ◽  
pp. 2751-2752 ◽  
Author(s):  
Christian Bjerrum‐Niese ◽  
René Lützen ◽  
Leif Bjo/rno/
Keyword(s):  
Shallow Water ◽  
Ray Tracing ◽  
Water Channel

scholarly journals Manifestation of the Berry curvature in geophysical ray tracing

2021 ◽  
Vol 477 (2248) ◽  
Author(s):  
N. Perez ◽  
P. Delplace ◽  
A. Venaille
Keyword(s):  
Shallow Water ◽  
Ray Tracing ◽  
Berry Phase ◽  
Wave Packets ◽  
Equations Of Motion ◽  
Cold Atom ◽  
Water Model ◽  
Local Geometry ◽  
Wave Polarization ◽  
Berry Curvature

Geometrical phases, such as the Berry phase, have proven to be powerful concepts to understand numerous physical phenomena, from the precession of the Foucault pendulum to the quantum Hall effect and the existence of topological insulators. The Berry phase is generated by a quantity named the Berry curvature, which describes the local geometry of wave polarization relations and is known to appear in the equations of motion of multi-component wave packets. Such a geometrical contribution in ray propagation of vectorial fields has been observed in condensed matter, optics and cold atom physics. Here, we use a variational method with a vectorial Wentzel–Kramers–Brillouin ansatz to derive ray- tracing equations for geophysical waves and to reveal the contribution of the Berry curvature. We detail the case of shallow-water wave packets and propose a new interpretation of their oscillating motion around the equator. Our result shows a mismatch with the textbook scalar approach for ray tracing, by predicting a larger eastward velocity for Poincaré wave packets. This work enlightens the role of the geometry of wave polarization in various geophysical and astrophysical fluid waves, beyond the shallow-water model.

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