TY - GEN A1 - Tyvand, Peder A. A1 - Mulstad, Camilla A1 - Bestehorn, Michael T1 - A nonlinear impulsive Cauchy–Poisson problem. Part 1. Eulerian description T2 - Journal of Fluid Mechanics N2 - 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. KW - Surface gravity waves KW - Air/sea interactions Y1 - 2021 UR - https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/nonlinear-impulsive-cauchypoisson-problem-part-1-eulerian-description/F353BA9CA7AD0059F023BE50B4942D64# U6 - https://doi.org/10.1017/jfm.2020.787 SN - 1469-7645 SN - 0022-1120 VL - 906 SP - A24-1 EP - A24-32 ER - TY - GEN A1 - Tyvand, Peder A. A1 - Mulstad, Camilla A1 - Bestehorn, Michael T1 - A nonlinear impulsive Cauchy–Poisson problem. Part 2. Lagrangian description T2 - Journal of Fluid Mechanics N2 - 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. KW - Air/sea interactions KW - Surface gravity waves Y1 - 2021 UR - https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/nonlinear-impulsive-cauchypoisson-problem-part-2-lagrangian-description/1934256B0F16ABDDAE313EF9FD9D3ADA U6 - https://doi.org/10.1017/jfm.2020.788 SN - 1469-7645 SN - 0022-1120 VL - 906 SP - A25-1 EP - A25-19 ER -