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Full-Text Articles in Physical Sciences and Mathematics
On The Time Evolution Of Resonant Triads In Rotational Capillary-Gravity Water Waves, Rossen Ivanov, Calin Martin
On The Time Evolution Of Resonant Triads In Rotational Capillary-Gravity Water Waves, Rossen Ivanov, Calin Martin
Articles
We investigate an effect of the resonant interaction in the case of one-directional propagation of capillary-gravity surface waves arising as the free surface of a rotational water flow. Specifically, we assume constant vorticity in the body of the fluid which physically corresponds to an underlying current with a linear horizontal velocity profile. We consider the interaction of three distinct modes, and we obtain the dynamic equations for a resonant triad. Setting the constant vorticity equal to zero, we recover the well known integrable three-wave system.
On The Time-Evolution Of Resonant Triads In Rotational Capillary-Gravity Water Waves, Rossen Ivanov, Calin I. Martin
On The Time-Evolution Of Resonant Triads In Rotational Capillary-Gravity Water Waves, Rossen Ivanov, Calin I. Martin
Articles
We investigate an effect of the resonant interaction in the case of one-directional propagation of capillary-gravity surface waves arising as the free surface of a rotational water flow. Specifically, we assume a constant vorticity in the body of the fluid which physically corresponds to an underlying current with a linear horizontal velocity profile. We consider the interaction of three distinct modes and we obtain the dynamic equations for a resonant triad. Setting the constant vorticity equal to zero we recover the well known integrable three-wave system.
Hamiltonian Formulation Of 2 Bounded Immiscible Media With Constant Non-Zero Vorticities And A Common Interface, Alan Compelli
Hamiltonian Formulation Of 2 Bounded Immiscible Media With Constant Non-Zero Vorticities And A Common Interface, Alan Compelli
Articles
We examine a 2-dimensional water-wave system, with gravitationally induced waves, consisting of a lower medium bound underneath by an impermeable flat bed and an upper medium bound above by an impermeable lid such that the 2 media have a free common interface. Both media have constant density and constant (non-zero) vorticity. By examining the governing equations of the system we calculate the Hamiltonian of the system in terms of it's conjugate variables and per- form a variable transformation to show that it has canonical Hamiltonian structure.
Nearly-Hamiltonian Structure For Water Waves With Constant Vorticity, Adrian Constantin, Rossen Ivanov, Emil Prodanov
Nearly-Hamiltonian Structure For Water Waves With Constant Vorticity, Adrian Constantin, Rossen Ivanov, Emil Prodanov
Articles
We show that the governing equations for two-dimensional gravity water waves with constant non-zero vorticity have a nearly-Hamiltonian structure, which becomes Hamiltonian for steady waves.