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

Rodríguez-Sanjurjo, Adrián

doi:10.1007/s10231-018-0749-5

Cited by 9 publications

(7 citation statements)

References 28 publications

(32 reference statements)

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“…This is an important property of the Lagrangian flow description. We note that for both, the two-dimensional Gerstners wave [7,19] and a number of three-dimensional generalizations [32,33,34], a mixture of analytical and topological methods can be applied to prove that the Lagrangian flow-map describing these exact solutions is a global diffeomorphism, with the result that the flow is globally dynamically possible. In Eq.…”

Section: Anatoly Abrashkinmentioning

confidence: 99%

Wind generated equatorial Gerstner-type waves

Abrashkin

2019

Discrete &Amp; Continuous Dynamical Systems - A

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A class of non-stationary surface gravity waves propagating in the zonal direction in the equatorial region is described in the f-plane approximation. These waves are described by exact solutions of the equations of hydrodynamics in Lagrangian formulation and are generalizations of Gerstner waves. The wave shape and non-uniform pressure distribution on a free surface depend on two arbitrary functions. The trajectories of fluid particles are circumferences. The solutions admit a variable meridional current. The dynamics of a single breather on the background of a Gerstner wave is studied as an example.

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Section: Anatoly Abrashkinmentioning

confidence: 99%

Wind generated equatorial Gerstner-type waves

Abrashkin

2019

Discrete &Amp; Continuous Dynamical Systems - A

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“…A Pollard-like solution for the surface waves in the presence of mean currents and rotation was derived in a recent research paper [12], with an instability analysis of the Pollard-like solution presented in [26]. Moreover, the surface wave solution is globally dynamically possible [36]. Our purpose is to modify Pollard's solution to obtain a valid model describing the nonlinear internal water waves.…”

Section: Introductionmentioning

confidence: 99%

Exact Pollard-like internal water waves

Kluczek¹

2021

JNMP

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In this paper we construct a new solution which represents Pollard-like three-dimensional nonlinear geophysical internal water waves. The Pollard-like solution includes the effects of the rotation of Earth and describes the internal water wave which exists at all latitudes across Earth and propagates above the thermocline. The solution is provided in Lagrangian coordinates. In the process we derive the appropriate dispersion relation for the internal water waves in a stable stratification and discuss the particles paths. An analysis of the dispersion relation for the constructed model identifies one mode of the internal water waves.

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“…Consequently, the wave-current interactions in Pollard's solution for surface waves are described in [14] by including in the exact solution an underlying depthinvariant current interpreted as the mean flow velocity. Moreover, an instability of this solution is available in [27,28] and the solution has been proven to be globally dynamically possible [40].…”

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confidence: 99%

Nonhydrostatic Pollard-like internal geophysical waves

Kluczek¹

2019

Discrete &Amp; 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 modification of Pollard's surface wave solution in order to describe internal water waves at general latitudes. The novelty of this model consists in the embodiment of transitional layers beneath the thermocline. We present a Lagrangian analysis of the nonlinear internal water waves and we show the existence of two modes of the wave motion.2010 Mathematics Subject Classification. Primary: 35F50, 76B15; Secondary: 86A05.

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

Cited by 9 publications

References 28 publications

Wind generated equatorial Gerstner-type waves

Wind generated equatorial Gerstner-type waves

Exact Pollard-like internal water waves

Nonhydrostatic Pollard-like internal geophysical waves

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