# Internal Gerstner waves: applications to dead water

@article{Stuhlmeier2013InternalGW, title={Internal Gerstner waves: applications to dead water}, author={Raphael Stuhlmeier}, journal={Applicable Analysis}, year={2013}, volume={93}, pages={1451 - 1457} }

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.

## 12 Citations

### Internal Gerstner waves on a sloping bed

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### Instability of equatorially-trapped nonhydrostatic internal geophysical water waves

- Physics, Environmental ScienceWave Motion
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### Exact Pollard-like internal water waves

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We present a new exact solution describing progressive waves on a blunt interface based on Gerstner's trochoidal wave. The second-order irrotational theory is developed for a sharp interface, and…

### Nonhydrostatic Pollard-like internal geophysical waves

- Environmental ScienceDiscrete & Continuous Dynamical Systems - A
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We present a new exact and explicit Pollard-like solution describing internal water waves representing the oscillation of the thermocline in a nonhydrostatic model. The derived solution is a…

### Aspects of the Mathematical Analysis of Nonlinear Stratified Water Waves

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### Global diffeomorphism of the Lagrangian flow-map for Pollard-like solutions

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We present a rigorous analysis of the nonlinear surface waves in the presence of a zonal current under the effects of Earth’s rotation derived by Constantin and Monismith (J Fluid Mech 820:511–528,…

## References

SHOWING 1-10 OF 28 REFERENCES

### On the deep water wave motion

- Mathematics
- 2001

The problem of the propagation of surface waves over deep water is considered. We present a rigorous approach towards the only known (non-trivial) explicit solution to the governing equations for…

### Periodic Traveling Water Waves with Isobaric Streamlines

- Physics
- 2004

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

- Physics
- 2008

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

- Physics
- 2010

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

- Mathematics
- 2012

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

- Physics
- 2011

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,…

### The trajectories of particles in Stokes waves

- Mathematics
- 2006

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

- Physics
- 1979

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

- Physics
- 1982

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