The stirring and mixing properties of one-phase coaxial jets, with large outer (annular)
to inner velocity ratio ru = u2/u1
are investigated. Mixing is contemplated according
to its geometrical, statistical and spectral facets with particular attention paid to
determining the relevant timescales of the evolution of, for example, the interface
area generation between the streams, the emergence of its scale-dependent (fractal)
properties and of the mixture composition after the mixing transition. The two key
quantities are the vorticity thickness of the outer, fast stream velocity profile which
determines the primary shear instability wavelength and the initial size of the lamellar
structures peeled-off from the slow jet, and the elongation rate
γ = (u2 − u1)/e
constructed with the velocity difference between the streams and the gap thickness
e of the annular jet. The kinetics of evolution of the interface corrugations, and the
rate at which the mixture evolves from the initial segregation towards uniformity is
prescribed by γ−1. The mixing time ts,
that is the time needed to bring the initial
scalar lamellae down to a transverse size where molecular diffusion becomes effective,
and the corresponding dissipation scale s(ts) are
formula here
where Re and Sc denote the gap Reynolds number and the Schmidt number, respectively.
The persistence of the large-scale straining motion is also apparent from the
spectra of the scalar fluctuations which exhibit a k−1 shape on the inertial range of
scales.