Advances on linear instability analysis method of jet breakup

Linear instability analysis is one of the most commonly used theoretical methods for investigating the breakup of single jet and compound jets with cylindrical shapes. The method employs the linearized small perturbations and the normal mode method based on the governing equations and boundary conditions of fluid dynamics to perform relevant investigations, and is able to predict different flow phenomena and rules observed in experiments. The principle of linearized small perturbation method can be characterized by decomposing physical quantities involved in nonlinear problems into zero-order approximations and small perturbations, substituting the results into the original nonlinear equations and omitting the high-order small quantities. Thus the nonlinear problems can be transformed into the first-order approximation of linear definite solution problem. The normal mode method is to decompose small disturbances into a series of modal superposition that meets the linear system. In this way, the problem of linear definite solution is transformed into the problem of solving generalized eigenvalue problem. The normal mode method is suitable for symmetric flow fields and can be divided into different modes in temporal domain, in spatial domain, and in spatio-temporal domain according to the evolution of small disturbances. In this review, the main content and the specific implementation steps of the linear instability analysis method on single jet and compound jets are analyzed. Taking the flow focusing that can generate microjets as an example, the practical applications of the linear instability analysis method are discussed. Finally, the related achievements are also summarized.