Journal of Nonlinear Mathematical Physics

Volume 22, Issue 4, November 2015

1. Preface

Adrian Constantin
Pages: 474 - 474
Research Article

2. An ocean undercurrent, a thermocline, a free surface, with waves: a problem in classical fluid mechanics

R. S. Johnson
Pages: 475 - 493
We describe a problem that can be tackled more-or-less routinely using the ideas of classical fluid mechanics, but it is a complex flow and even the linearised problem involves considerable algebraic complexity. The presentation here emphasises the approach that we adopt in order to formulate an accessible...
Research Article

3. On Symmetric Water Waves with Constant Vorticity

Florian Kogelbauer
Pages: 494 - 498
We prove that a solution to the gravity water wave problem with constant vorticity, whose wave profile as well as its horizontal velocity component at the free surface are symmetric at any instant of time, is given by a traveling wave. The proof is based on maximum principles and structural properties...
Research Article

4. Internal equatorial water waves in the f−plane

David Henry
Pages: 499 - 506
In this paper we describe an exact, and explicit, three-dimensional nonlinear solution for geophysical internal ocean waves in the Equatorial region which incorporates a transverse-Equatorial meridional current.
Research Article

5. Particle paths in Stokes’ edge wave

Raphael Stuhlmeier
Pages: 507 - 515
We treat the particle motion in Stokes’ linear edge wave along a uniformly sloping beach. By a rotation of the coordinate frame, we show that there is no particle motion in the direction orthogonal to the sloping beach, and conclude that particles have a longshore drift in the direction of wave propagation...
Research Article

6. Dynamics of the thermocline in the equatorial region of the Pacific ocean

Calin Iulian Martin
Pages: 516 - 522
This paper is devoted to the subsurface current dynamics in equatorial regions, where the hallmark of a strong stratification is a sharp interface (thermocline), separating two layers of different density, and whose depth is dependent upon the strength of the winds above the ocean's surface. We...
Research Article

7. On Pollard's wave solution at the Equator

Delia Ionescu-Kruse
Pages: 523 - 530
In this paper we present a dynamical study of the exact nonlinear Pollard wave solution to the geophysical water-wave problem in the f-plane approximation. We deduce an exact dispersion relation and we discuss some properties of this solution.
Research Article

8. On the dynamics of internal waves interacting with the equatorial undercurrent

Alan Compelli, Rossen Ivanov
Pages: 531 - 539
The interaction of the nonlinear internal waves with a nonuniform current with a specific form, characteristic for the equatorial undercurrent, is studied. The current has no vorticity in the layer, where the internal wave motion takes place. We show that the nonzero vorticity that might be occuring...
Research Article

9. On the Existence of Benthic Storms

Ronald Quirchmayr
Pages: 540 - 544
We study a model for the wind-induced current field of the Pacific ocean in order to demonstrate that currents in the surface layer are carried down to the deepest regions above the abyssal sea floor, which indicates the existence of the phenomenon of comparably strong currents in bottom regions as a...
Research Article

10. Symmetric waves are traveling waves for a shallow water equation modeling surface waves of moderate amplitude

Anna Geyer
Pages: 545 - 551
Following a general principle introduced by Ehrnström, Holden and Raynaud in 2009, we prove that for an equation modeling the free surface evolution of moderate amplitude waves in shallow water, all symmetric waves are traveling waves.