Тезисы докладов

Доклады иностранных участников

Inadequacy of eigenvalues analysis has been recently recognised in assessing stability or instability of many shear dominated flows. In the case the governing operator is non-normal, in fact, even in subcritical ranges of the involved parameters, the potential of a substantial growth in the energy of small amplitude perturbations over short time or space scales exists, which is not amenable to be highlighted by the sole study of eigenvalues. Physical mechanisms involved in transient growth have been generally linked to the presence of a crosswise gradient in the basic flow velocity profile due to shear. On the other hand, in analysing the behaviour of homogeneous and heterogeneous plane jets, present authors highlighted the occurrence of energy transient growth although a uniform velocity, exhibiting a discontinuity at the free surface according to the so-called top hat profile, was considered. Such a velocity discontinuity ( the tangential stress being on the contrary continuous ), would thus constitute a further mechanism leading to transient growth which adds to the aforementioned continuous crosswise nonuniformity due to shear. The present work is aimed to weight importance of the two different mechanisms by evaluating their relative contribution to energy growth for a family of basic flow velocity profiles which are not uniform in the crosswise direction, all preserving the discontinuity at the free interface. Computation bases on eigenfunctions expansion determined by means of a spectral discretization of the governing equations, which are written in vector form in terms of the normal velocity and normal vorticity. While for the top hat profile dependent variables are no forced by each others, a coupling operator arises in the other cases when the spanwise wavenumber is different from zero, implying vorticity to be forced by velocity. Conditions for no energy growth, the time dependence of the growth and the way it is affected by the streamwise and spanwise wavenumbers and flow parameters, namely Weber and Reynolds numbers as well as the external to internal fluid density ratio, are taken under consideration. Iso-level curves of the maximum energy growth function are used to individuate the possible most dangerous disturbances and to make a tentative comparison with available experimental data concerning the conditions for which jet break-up occurs. The numerical results include plots of the numerical range as well as of the pseudospectra iso-level curves characterising the governing operator.

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