Effect of deceleration on jet instability

A non-parallel analysis of time-oscillatory instability of conical jets reveals important features not found in prior studies. Flow deceleration significantly enhances the shear-layer instability for both swirl-free and swirling jets. In swirl-free jets, flow deceleration causes the axisymmetric instability (absent in the parallel approximation). The critical Reynolds number Re_a for this instability is an order of magnitude smaller than the critical Re_a predicted before for the helical instability (where Re_a = rv_a/v, r is the distance from the jet source, v_a is the jet maximum velocity at a given r, and v is the viscosity). Swirl, intensifying the divergence of streamlines, induces an additional, divergent instability (which occurs even in shear-free flows). For the swirl Reynolds number Re_s (circulation to viscosity ratio) exceeding 3, the critical Re_a for the single-helix counter-rotating mode becomes smaller than those for axisymmetric and multi-helix modes. Since the critical Re_s is less than 10 for the near-axis jets, the boundary-layer approximation (used before) is invalid, as is Long's Type II boundary-layer solution (whose stability has been extensively studied). Thus, the non-parallel character of jets strongly affects their stability. Our results, obtained in a far-field approximation allowing reduction of the linear stability problem to ordinary differential equations, are more valid for short wavelengths.