Resonant instability and nonlinear wave interactions in electrically forced jets

Nonlinear spatio-temporal instability regime for electrically forced viscous jets

“…The work of dyad resonant combined time and spatial instability that we consider in this paper is a research continuation of the work done in [21]. In contrast to the time evolving instability that was studied in [21], here we study particular realistic features of spatial and temporal instabilities of the modes that enhance significantly in space and time as observed in experiments [10].…”

“…In this paper, we consider the non-linear problem of the axisymmetric electrically driven jets with finite electrical conductivity and under the presence of a uniform and non-uniform applied electric field [9,10,19,21], but now we include realistic features that are found naturally in the jet flow including time and space evolving instabilities which are known to exist [8]. We approach the non-linear problem by considering combined space and time dyad resonant instability modes to study the non-linear wave interaction of such growing disturbances.…”

“…In regards to the resonant wave interactions in electrically driven jets, no investigation had been carried out for electrically driven jets prior to the work of Orizaga and Riahi [21,23]. They conducted the investigation of temporal linear instability of the modes that satisfy the dyad resonance conditions.…”

“…In this investigation in contrast with [21], we considered a more realistic study, which included two types of instabilities in a combined form for space and time. We modeled the combined spatial and temporal evolving instabilities for axisymmetric electrically driven jets, which are known to exist by the experiments done in [7,8,10].…”

“…Our mathematical modeling of the electrically driven jets is based on the governing electrohydrodynamic equations [8] for the mass conservation, momentum, charge conservation and for the electric potential, which are described in [9,10,19,21]. The work of dyad resonant combined time and spatial instability that we consider in this paper is a research continuation of the work done in [21].…”