  Hydrodynamic instabilities in miscible fluids are ubiquitous, from natural
phenomena up to geological scales, to industrial and technological
applications, where they represent the only way to control and promote mixing
at low Reynolds numbers, well below the transition from laminar to turbulent
flow. As for immiscible fluids, the onset of hydrodynamic instabilities in
miscible fluids is directly related to the physics of their interfaces. The
focus of this review is therefore on the general mechanisms driving the growth
of disturbances at the boundary between miscible fluids, under a variety of
forcing conditions. In the absence of a regularizing mechanism, these
disturbances would grow indefinitely. For immiscible fluids, interfacial
tension provides such a regularizing mechanism, because of the energy cost
associated to the creation of new interface by a growing disturbance. For
miscible fluids, however, the very existence of interfacial stresses that mimic
an effective surface tension is debated. Other mechanisms, however, may also be
relevant, such as viscous dissipation. We shall review the stabilizing
mechanisms that control the most common hydrodynamic instabilities,
highlighting those cases for which the lack of an effective interfacial tension
poses deep conceptual problems in the mathematical formulation of a linear
stability analysis. Finally, we provide a short overview on the ongoing
research on the effective, out of equilibrium interfacial tension between
miscible fluids.
