Slender elliptical jets

The structure of steady hydrodynamic jets is investigated. The slender-jet method is employed to determine the changes in the cross-section with distance, beginning from a subsonic flow, progressing through a nozzle and subsequently reaching highly supersonic speeds. Gravity, a confining ambient pressure, and a streamline-dependent Bernoulli constant (equivalent to a variation in the injection energy or entropy across the jet) are included. A jet with an elliptical cross section either flattens into a sheet or beomes circular, according to a simple condition. The progress to a sheet is slowed in the nozzle region where the major axis flips 90° (the aspect ratio passing just once through unity). Gravity influences the final direction of flattening, but its main effect is to separate the transonic and nozzle locations. A volume instability distorts the shape of the jets, which flattens if the Bernoulli streamline constant is globally constant. This leads to jet splitting or stranding with the bifurcation mode prominent. In the more general case, it is the radial variation in the Bernoulli constant which determines the jet stability: the rule is that a negative gradient stabilizes the jet, and a positive gradient leads to a small-scale disintegration via a fragmenting sheath. Hence jet survival depends crucially on how the entropy is distributed, with a higher entropy along the axis stabilizing the flow. An important exception is that of jets in which the ambient pressure falloff with distance is slow. Then the jet flattens into a sheet of decreasing thickness. This sheet is unstable for all distributions of the Bernoulli constant. The conclusion is that a steady flow in which the jet opening angle does not increase with distance can only occur if (1) the external pressure is proportional to z-q with ? < q < 2?, where ? is the adiabatic index, and (2) the total specific energy is highest along the jet axis. The model discussed here is relevant to hot outflows from stars and galaxies as well as extragalactic jets.