Hamiltonian discontinuous Galerkin FEM for linear, stratified (in)compressible Euler equations: internal gravity waves

Oers, Alexander M. van; Maas, Leo R. M.; Bokhove, Onno

doi:10.1016/j.jcp.2016.10.032

Cited by 4 publications

(1 citation statement)

References 27 publications

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“…), the methods are proving useful also in partial differential equations, see e.g. [46,47,48,49] or [50], where even Jacobi identity on the discrete level is recovered. Combination of reversible and irreversible dynamics with geometric integration was recently presented in [51], [22], [52] (being essentially different from the approach in this manuscript).…”

Section: Relation To Literaturementioning

confidence: 99%

Ehrenfest regularization of Hamiltonian systems

Pavelka

Klika

Grmela

2019

Physica D: Nonlinear Phenomena

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Imagine a freely rotating rigid body. The body has three principal axes of rotation. It follows from mathematical analysis of the evolution equations that pure rotations around the major and minor axes are stable while rotation around the middle axis is unstable. However, only rotation around the major axis (with highest moment of inertia) is stable in physical reality (as demonstrated by the unexpected change of rotation of the Explorer 1 probe). We propose a general method of Ehrenfest regularization of Hamiltonian equations by which the reversible Hamiltonian equations are equipped with irreversible terms constructed from the Hamiltonian dynamics itself. The method is demonstrated on harmonic oscillator, rigid body motion (solving the problem of stable minor axis rotation), ideal fluid mechanics and kinetic theory. In particular, the regularization can be seen as a birth of irreversibility and dissipation. In addition, we discuss and propose discretizations of the Ehrenfest regularized evolution equations such that key model characteristics (behavior of energy and entropy) are valid in the numerical scheme as well.

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Section: Relation To Literaturementioning

confidence: 99%

Ehrenfest regularization of Hamiltonian systems

Pavelka

Klika

Grmela

2019

Physica D: Nonlinear Phenomena

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In situ measurement of wave attractor induced forces

Oers

Maas

2021

Exp Fluids

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An underwater force sensor for internal waves is presented. Using this sensor, we measure forces at a location near the surface of a fluid. The sensor performs a point measurement with a high temporal resolution. We perform measurements in a density-stratified fluid contained in a trapezoidal basin. By shaking this basin longitudinally, internal gravity waves are generated. Controlling the frequency with which the basin oscillates, these waves propagate toward a wave attractor whose shape varies from complicated to rectangular. We measure the force exerted by these waves on a plate that is partially submerged into the fluid. We observe the formation and decay of wave attractors. When a surface reflection of a wave attractor is near our sensor we measure (relatively) strong forces. We confirm our findings with simulations. We observe an asymmetry in the direction of the force. This asymmetry leads to a net force and could imply the driving of a mean flow. Graphical Abstract

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