Analogy in interactions of electronic beams and hydrodynamic flows with fields of resonators and periodic structures. Part 1

The hydrodynamic equations of inviscid compressible fluid are converted to a form suitable for development of self-consistent theory of interaction of hydrodynamic flows with resonators and periodic structures by analogy with the theory of microwave electronics devices with crossed electric and magnetic fields. We consider excitation of the acoustic velocity fields by the sources provided by vorticity in the flow. For twodimensional problems, neglecting by nonlinearity of natural acoustic oscillations and by compressibility of the fluid in the domain of vortex motion, we obtain the excitation equations of acoustic resonators in a form entirely analogous to the equations for resonators in electrodynamics. For three-dimensional resonators there is no complete analogy, but we provide a derivation corresponding to the electrodynamics theory in general structure. To illustrate solutions of self-consistent equations we consider dynamics of a flat vortex tape interacting with a comb-type periodic structure. Also we consider the self-consistent problem for the case of interaction of the vortex flow with an arbitrary periodic structure. The dispersion equation is obtained, and on the basis of its analysis some designs of hydrodynamic devices are suggested analogous to the electronic beam devices with crossed fields.