Internal Gerstner waves: applications to dead water

@article{Stuhlmeier2014InternalGW,
  title={Internal Gerstner waves: applications to dead water},
  author={Raphael Stuhlmeier},
  journal={Applicable Analysis},
  year={2014},
  volume={93},
  pages={1451 - 1457}
}
  • R. Stuhlmeier
  • Published 12 March 2013
  • Mathematics
  • Applicable Analysis
We give an explicit solution describing internal waves with a still-water surface, a situation akin to the well-known dead-water phenomenon, on the basis of the Gerstner wave solution to the Euler equations. 
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12 Citations
Background Citations
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12 Citations

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  • M. Kluczek
  • Environmental Science
    Discrete & Continuous Dynamical Systems - A
  • 2019
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References

SHOWING 1-10 OF 28 REFERENCES

Periodic Traveling Water Waves with Isobaric Streamlines

Abstract It is shown that in water of finite depth, there are no periodic traveling waves with the property that the pressure in the underlying fluid flow is constant along streamlines. In the case…

On Gerstner’s Water Wave

Abstract We present a simple approach showing that Gerstner’s flow is dynamically possible: each particle moves on a circle, but the particles never collide and fill out the entire region below the…

On the Deep-Water Stokes Wave Flow

We prove a new result detailing the monotonicity of the horizontal velocity component of deep-water Stokes waves along streamlines.

ON PERIODIC WATER WAVES WITH CORIOLIS EFFECTS AND ISOBARIC STREAMLINES

In this paper we prove that solutions of the f-plane approximation for equatorial geophysical deep water waves, which have the property that the pressure is constant along the streamlines and do not…

ON EDGE WAVES IN STRATIFIED WATER ALONG A SLOPING BEACH

Building on previous investigations, we show that Gerstner's famous deep water wave and the related edge wave propagating along a sloping beach, found within the context of water of constant density,…

An exact solution for equatorial geophysical water waves with an underlying current

An exact solution for equatorially trapped waves

[1] We present an exact solution of the nonlinear governing equations for geophysical water waves in the β-plane approximation near the Equator. The solution describes in the Lagrangian framework…

The trajectories of particles in Stokes waves

Analyzing a free boundary problem for harmonic functions we show that there are no closed particle paths in an irrotational inviscid traveling wave propagating at the surface of water over a flat…

Edge Waves in a Rotating Stratified Fluid, an Exact Solution

Abstract Gerstner's exact solution for free-surface waves can be modified beyond the modifications given by Yih and Pollard, to describe edge waves in a rotating fluid with mean rotation and in the…

Allowable discontinuities in a Gerstner wave field

Velocity discontinuity surfaces can be inserted at will in a Gerstner edge wave on an inclined boundary in a rotating fluid.