Non-modal stability of round viscous jets

Hydrodynamic stability of round viscous fluid jets is considered within the framework of the non-modal approach. Both the jet fluid and surrounding gas are assumed to be incompressible and Newtonian; the effect of surface capillary pressure is taken into account. The linearized Navier-Stokes equations coupled with boundary conditions at the jet axis, interface and infinity are reduced to a system of four ordinary differential equations for the amplitudes of disturbances in the form of spatial normal modes. The eigenvalue problem is solved by using the orthonormalization method with Newton iterations and the system of least stable normal modes is found. Linear combinations of modes (optimal disturbances) leading to the maximum kinetic energy at a specified set of governing parameters are found. Parametric study of optimal disturbances is carried out for both an air jet and a liquid jet in air. For the velocity profiles under consideration, it is found that the non-modal instability mechanism is significant for non-axisymmetric disturbances. The maximum energy of the optimal disturbances to the jets at the Reynolds number of 1000 is found to be two orders of magnitude larger than that of the single mode. The largest growth is gained by the streamwise velocity component.