@misc{BestehornTyvand, author = {Bestehorn, Michael and Tyvand, Peder A.}, title = {Merging and colliding bores}, language = {en} } @misc{TyvandBestehorn, author = {Tyvand, Peder A. and Bestehorn, Michael}, title = {Diffraction of Poincare waves by a change in ocean depth}, language = {en} } @misc{BestehornTyvandMichelitsch, author = {Bestehorn, Michael and Tyvand, Peder A. and Michelitsch, Thomas M.}, title = {Dimension-Reduced Model for Deep-Water Waves}, series = {Journal of Applied Mathematics and Physics}, volume = {7}, journal = {Journal of Applied Mathematics and Physics}, number = {1}, issn = {2327-4379}, doi = {10.4236/jamp.2019.71007}, pages = {72 -- 92}, abstract = {Starting from the 2D Euler equations for an incompressible potential flow, a dimension-reduced model describing deep-water surface waves is derived. Similar to the Shallow-Water case, the z-dependence of the dependent variables is found explicitly from the Laplace equation and a set of two one- dimensional equations in x for the surface velocity and the surface elevation remains. The model is nonlocal and can be formulated in conservative form, describing waves over an infinitely deep layer. Finally, numerical solutions are presented for several initial conditions. The side-band instability of Stokes waves and stable envelope solitons are obtained in agreement with other work. The conservation of the total energy is checked.}, language = {en} } @misc{TyvandMulstadBestehorn, author = {Tyvand, Peder A. and Mulstad, Camilla and Bestehorn, Michael}, title = {A nonlinear impulsive Cauchy-Poisson problem. Part 1. Eulerian description}, series = {Journal of Fluid Mechanics}, volume = {906}, journal = {Journal of Fluid Mechanics}, issn = {1469-7645}, doi = {10.1017/jfm.2020.787}, pages = {A24-1 -- A24-32}, abstract = {A nonlinear Cauchy-Poisson problem with impulsive surface forcing is investigated analytically and numerically. An incompressible liquid with an initially horizontal surface is instantaneously put into motion by an impulsive surface pressure distribution turned on and off during an infinitesimal time interval. We consider symmetric, antisymmetric and asymmetric pressure impulses based on dipoles and quadrupoles. The subsequent inviscid free-surface flow is governed by fully nonlinear surface conditions, which are solved exactly to third order in a small-time expansion. The small-time expansion applies to flows dominated by inertia. Such flows are generated by relatively strong pressure impulses, measured in gravitational units. We solve the problem numerically and find that only relatively weak pressure impulses will lead to oscillatory waves. The free surface will break before a full gravitational oscillation is completed when the amplitude of the pressure impulse exceeds one gravitational unit.}, language = {en} } @misc{TyvandMulstadBestehorn, author = {Tyvand, Peder A. and Mulstad, Camilla and Bestehorn, Michael}, title = {A nonlinear impulsive Cauchy-Poisson problem. Part 2. Lagrangian description}, series = {Journal of Fluid Mechanics}, volume = {906}, journal = {Journal of Fluid Mechanics}, issn = {1469-7645}, doi = {10.1017/jfm.2020.788}, pages = {A25-1 -- A25-19}, abstract = {A fully nonlinear Cauchy-Poisson problem is investigated analytically by a small-time expansion. The inviscid incompressible fluid layer has an initially horizontal surface. The fluid is forced into motion by an impulsive surface pressure. The early nonlinear free-surface problem is solved to second order in a small-time expansion by the Lagrangian description of motion. Comparisons are made with two other solution procedures for the same nonlinear problem in the absence of gravity: a third-order small-time expansion and a numerical solution, based on full nonlinearity according to the standard Eulerian description. Good agreement is found between the present second-order Lagrangian solution and the previous third-order Eulerian solution, until both these asymptotic expansions diverge rather abruptly at the same time.}, language = {en} } @misc{TyvandBestehorn, author = {Tyvand, Peder A. and Bestehorn, Michael}, title = {Nonlinear wave resonance from bottom vibrations in uniform open-channel flow}, series = {European Journal of Mechanics. B, Fluids}, volume = {79}, journal = {European Journal of Mechanics. B, Fluids}, issn = {1873-7390}, doi = {10.1016/j.euromechflu.2019.07.004}, pages = {74 -- 86}, abstract = {It is known from linear theory that bottom oscillations in uniform open-channel flow can produce resonant surface waves with zero group velocity and diverging amplitude (Tyvand and Torheim 2012). This resonance exists for Froude numbers smaller than one, at a critical frequency dependent on the Froude number. This resonance phenomenon is studied numerically in the time domain, with fully nonlinear free-surface conditions. An oscillatory 2D bottom source is started, and the local elevation at resonance grows until it may reach a saturation amplitude. Four waves exist at subcritical Froude numbers, where resonance represents the third and the fourth wave merging. In the zero-frequency limit, the dispersive second and fourth wave merge into a steady wave with finite group velocity and amplitude, and no other periodic waves exist. In the time-dependent nonlinear analysis at zero frequency, a transient undular bore may emerge as the dominating phenomenon.}, language = {en} }