GLOBAL MODES IN FALLING CAPILLARY JETS

The global linear stability analysis of falling capillary jets is carr ied our when the density of ambient gas is negligible. The jet is assu med to be dominated by inertia (i.e. Re = ROUO/v >> 1 and epsilon = gR (O)/U-O(2) << 1, where g is the gravity, R-O and U-O are the radius an d the speed of the jet at the orifice, v is the viscosity of the liqui d) so that it evolves on a larger scale than Rayleigh instability wave lengths. If the basic jet is approximately an axisymmetric plug profil e in each section, it becomes locally absolutely unstable at the orifi ce for a critical value W-a approximate to 0.32 of the Weber number W- O = gamma/rho ROUO2 where gamma is the surface tension between the liq uid and the gas, and rho the liquid density. Just above that value, it is demonstrated that there exists a discrete number of unstable globa l modes, i.e. time-harmonic perturbations satisfying homogeneous bound ary conditions at the orifice and causal conditions at infinity. These modes differ from the Airy-type global modes obtained by Monkewitz et al. (1993): They are composed of three spatial branches interacting a t the orifice. The critical Weber number for the global transition is obtained as a function of epsilon and Re. it is computed for the jet o f water in air For Reynolds numbers ranging from 100 to 200; and compa red to experimental data for the transition to dripping. The conjectur e by Monkewitz (1990) that the transition to dripping could be related to a global instability is discussed in light of these results.