Transient formation of the passive scalar spectrum at a turbulent interface

We consider the transport of a passive scalar through the turbulent-turbulent interface between two decaying isotropic turbulent flows with different kinetic energy. Although the concentration of a passive substance exhibits a complex behaviour that shows many phenomenological parallels with the turbulent velocity field, the statistical properties of passive scalar turbulence are in part decou­pled from those of the underlying velocity [1,2]. In our numerical experiment, the passive scalar is initially uniform in each of the two isotropic regions. The interaction of the two isotropic flows generates a high scalar variance region in the centre of the mixing layer and two intermittent scalar fronts arise at the margins of the mixing layer. The velocity field instead presents one front only which is placed in the part of the field where the kinetic energy is lower [3,4] or, in case the ener­gy is uniform but the correlation is varying, where the integral scale is lower [5]. In the central part of the mixing layer, between the two intermittent fronts, the spectrum of the scalar fluctuation shows a full range of scales just after one eddy turnover time (see figure below). Moreover, the scalar spectrum shows a more prominent inertial range region than the velocity spectrum – a wider range with a scaling exponent closer to -5/3 – a feature which has been observed also in ho­mogeneous flows at moderate Reynolds numbers, see [6,7]. This feature is preserved for about ten eddy turnover times, during which the scalar variance decays slower than the velocity fluctuation.