Multiple Coherent Mode Interaction in a Developing Round Jet.

The integral energy method has been used in order to study the large-scale coherent wave mode interactions in a spatially developing round jet of a large Reynolds number. A flow quantity is split into two components; time-independent mean flow and large-scale coherent structure. The large-scale structure is decomposed into three fundamental wave modes (axisymmetric, first-order and second-order helical) and two subharmonic modes (axisymmetric and first -order helical). The streamwise development of a jet is obtained in terms of the mean flow shear layer momentum thickness, the wave mode kinetic energy and the wave mode phase angle. The results of the five mode interaction show that the axisymmetric and helical modes grow almost identically in the initial region until the energy densities of the fundamental modes reach peak values. When the initial energy densities of the fundamental and subharmonic modes are equal, the initial growth of the shear layer momentum thickness and the fundamental energy densities is mainly governed by the energy transfer from the mean flow to the fundamental modes. The subharmonic energy densities reach peak values at earlier or later steamwise positions than in the decoupled case depending upon the nonlinear mode -mode energy transfers. The nonlinear interaction between wave modes is strongly dependent on the phase angle difference between them. It is found that the initial phase angle differences between wave modes as well as the initial energy densities play a significant role in the streamwise evolution of the large-scale coherent wave modes and the mean flow. When the initial energy density of one wave mode is much higher than those of the other modes, the other wave modes do not affect the streamwise development of the mean flow and the forced mode until the energy density of the forced mode reaches a peak value. The jet development also can be predicted by two wave modes (fundamental and subharmonic) if their initial energy densities are much higher than those of the others.