SIMBAD references

We present the results of numerical simulations of the long-term evolution of Kelvin-Helmholtz instabilities of arbitrary symmetry for a 2-D fluid slab jet, focusing on the mechanisms governing the exchange of mass, momentum, and energy between the jet and its environment. Most of our novel results emerge from studies of the behavior of the anti-symmetric mode, which is believed to resemble that of the m=1 modes for a cylinder; for this reason, our 2-D results can give some insight into the computationally far more complex 3-D problem. The solution space explored by us is defined by the main control parameters describing our system - the flow Mach number M and the density ratio between the ambient medium and the jet, ν. Our results show that the evolution of the slab can be typically divided into four stages (rather than three stages, as earlier results suggested): An initial `linear' stage, during which the amplitude of unstable perturbations grows, leading to the formation of alternating shocks and to a growing deformation of the jet; an `acoustic' phase, during which the jet radiates acoustic waves and shock waves into the external medium, and by this means loses momentum and energy to the external medium; a `mixing' phase, during which we observe strong mixing between the jet and external material; and a final `quasi-steady' state. A key tool for distinguishing these stages is the concept of `tracer entropy', which we introduce in order to discriminate between turbulent and `molecular' mixing of the jet and ambient materials. One of the notable results which then emerges from our study is that a jet's loss of momentum and energy can be entirely decoupled from its loss of mass, that is, momentum and energy may be lost substantially before there is any significant material entrainment; whether this effect is important depends entirely on the details of the `acoustic' phase, during which no significant entrainment occurs. The characteristics of the ultimate quasi-steady state strongly depend on the two control parameters M and ν; which dominates is determined by the precise details characterizing the initial state. The most distinctive result is that while a light jet (ν≫1) is virtually disrupted after the `mixing' phase, the asymptotic state of an initially heavy jet (ν≤1) differs little in its velocity amplitude from its initial state.