1. Turbulence is common to consider as the last unresolved problem of classical physics [1-16]. For years its complexity and universality assisted engineers and practitioners, nourished enthusiasm of scientists, and fascinated mathematicians [1-16]. Similarity and isotropy are fundamental hypotheses that advanced our understanding of turbulent processes. Still the problem withstands the efforts applied thus indicating a need in new concepts to better control the irregular dynamics [3,4]. Turbulent motions of realistic fluids are often characterized by non-equilibrium heat transport, sharp changes of density and pressure, and may be a subject to spatially varying and time-dependent acceleration and rotation [1-16]. Turbulent mixinginduced by the Rayleigh-Taylor instability (RTI) is generic problem, which we encounter when trying to extend our knowledge of turbulent processes beyondthe limit of idealizedconsideration[3,4].
2. Rayleigh-Taylor (RT) turbulent mixing is an extensive interfacial mixing process which develops when fluids of different densities are accelerated against a density gradient [1,2]. It governs a broad variety of natural phenomena spanning macroscopic to atomistic scales and high to low energy density regimes, and plays an important role in technological applications in aerodynamics and aeronautics [5-13]. Examples include instabilities of plasmas, light-material interaction, material transformation under high strain rate, atmospheric flows, shock-turbulence interaction, non-canonical wall-bounded flows, scramjet combustors, liquid atomization and free-space optical telecommunications [5-13]. Rayleigh-Taylor mixing is a multi-scale, heterogeneous, anisotropic and statistically unsteady turbulent process with non-local interactions among the many scales [3,4]. Its development is usually associated with the conditions of strong gradients of pressure and density and may also include spatially varying and time-dependent acceleration, diffusion of species, heat release, and chemical reactions [17-28,29-39]. These conditions depart from those under which canonical Kolmogorov turbulence is expected to occur [14-16,40]. Capturing the properties of Rayleigh-Taylor mixing can enable a better understanding of realistic turbulent flows and can further improve the methods of their mitigation and control [40]. Here we discuss the influence of momentum transport on fundamental properties of turbulent mixing, and outline some new ideas that may help to better control the mixingprocess inthe applications[5-13].
3. Arising in a variety of diverse circumstances, RT flows exhibit some similar features of their evolution [3,4]. The mixing starts to develop when the fluid interface is slightly perturbed near its equilibrium state. The flow transitions from an initial stage, where the perturbation amplitude grows relatively quickly [e.g. exponentially in time, if the fluids are incompressible and immiscible and are to sustained acceleration or gravity g], to a nonlinear stage, where the growth-rate slows and the interface is transformed into a composition of a large-scale coherent structure and small-scale irregular structures driven by shear, andthenfinally toa stage of turbulent mixing, whose dynamics is believedtobe self-similar [41-58].
4. penetrating the heavy (light) fluid in bubbles (spikes) [3,4]. The dynamics of the structure is governed by two, in general independent, length scales: the amplitude h~ in the direction of gravity and the spatial periodλ in the normal plane [3,4,59-62]. The horizontal scaleλ is set by the mode of fastest-growth or by the initial conditions [3,4]. It may increase, if the flow is two-dimensional and the initial perturbation is broad-band and incoherent [43-49]. The vertical scale h~ growsaspower-lawwithtime,anditisbelievedthatinthemixingregime
5. h , g = g [41-58]. This scale can be regarded as an integral scale, which represents cumulative contributions of small-scale structures in the flow dynamics [3,4,59-62]. The small-scale vortical structures are produced by the KelvinHelmholtz instabilities at the fluidinterface [17-39]. In miscible fluids, the small-scale structures diffuse from the interface into the bulk, and the mixing process is slowing down. Some other features are induced in the dynamics by compressibility, high energy density conditionsand non-uniformacceleration[5-13].