| Abstract: |
| This talk investigates the surface dynamics and stability of solitary waves on an inviscid ferrofluid jet. We begin by establishing a proof of the Hamilton principle for the axisymmetric system and deriving a unique homogeneous expansion of the Dirichlet-Neumann operator (DNO), offering a formulation distinct from that of Guyenne \& Parau (2016). Within a unified Hamiltonian/Lagrangian framework, we introduce a systematic methodology for deriving reduced model equations across multiple scales. In particular, we propose a nonlinear model with full dispersion by truncating the DNO expansion at the cubic order. We demonstrate that this model accurately captures the speed-amplitude and speed-energy bifurcations inherent in the full Euler equations. Utilizing this reduced model, we examine the stability of solitary waves under longitudinal disturbances. Our findings indicate that stability exchange occurs at the stationary points of the speed-energy bifurcation curve, providing an axisymmetric parallel to the stability criteria established by Saffman (1985). Extensions of these results to the full Euler equations will be discussed as time allows. |
|