Hydrodynamic stability of an annular liquid jet having a mantle solid axis using the energy principle (Q1108867)

The hydrodynamic stability of an annular liquid jet having a regular or irregular mantle solid axis, subjected to capillary and inertia forces, is presented. An eigenvalue relation valid for all modes of perturbation is derived, using the energy principle. The characteristics of the model are identified analytically, confirmed numerically and interpreted physically. The model is stable to all non-axisymmetric modes but it is unstable only to axisymmetric sausage modes whose wavelength is longer than the circumference of the liquid jet. However the maximum temporal amplification values prevailing of such model are far lower than of the full liquid jet. The greater the radius of the cylindrical solid axis; the slower the corresponding growth rate values but the greater the oscillation frequency values in the stability regions i.e., the thicker the solid mantle, the larger its stabilizing effect. The present results reduce to those of Rayleigh if we impose that the radius of the cylindrical solid axis tends to zero.