Some notes on periodic Beltrami fields in Cartesian geometry.

Some mathematical facts about Beltrami fields, which are time-independent solutions of the three-dimensional incompressible Euler equations with nontrivial helicity, are assembled. The linearization about an arbitrary, fixed Beltrami field is studied in a Hamiltonian framework. A factorization of this linearization is introduced and used to characterize null spaces for Beltrami fields with ergodic streamlines. An interesting property of unstable modes is noticed and its consequences concerning the nature of potential instabilities are discussed. [ABSTRACT FROM AUTHOR]