arXiv subjects

Conor T. Curtin

Publications and source records attributed to Conor T. Curtin.

2 recordsLinked to original sources

arXiv2026

Long interfacial internal waves with currents: current profiles with quadratic depth-dependence

Internal waves often propagate in the presence of currents. Internal waves and currents are widespread in the world's oceans. The equatorial internal waves and the equatorial undercurrent (EUC) are perhaps the most representative illustration of this phenomenon. The current profile in this study is a quadratic function of depth, which is in agreement with the known results of the EUC. With this assumption the integrable nonlinear Gardner's equation is derived as a model for the wave motion of the thermocline, separating the two layers of slightly different densities. In addition, we derive the generalised Gardner's equation in the case of variable bottom. We demonstrate that the coefficients of the equation are very sensitive with respect to the parameters of the EUC.

physics.flu-dyn↗

arXiv2024

The Lagrangian formulation for wave motion with a shear current and surface tension

The Lagrangian formulation for the irrotational wave motion is straightforward and follows from a Lagrangian functional which is the difference between the kinetic and the potential energy of the system. In the case of fluid with constant vorticity, which arises for example when a shear current is present, the separation of the energy into kinetic and potential is not at all obvious and neither is the Lagrangian formulation of the problem. Nevertheless, we use the known Hamiltonian formulation of the problem in this case to obtain the Lagrangian density function, and utilising the Euler-Lagrange equations we proceed to derive some model equations for different propagation regimes. While the long-wave regime reproduces the well known KdV equation, the short- and intermediate long wave regimes lead to highly nonlinear and nonlocal evolution equations.

physics.flu-dyn↗