The study is devoted to the development of the full Lagrangian approach for describing the evolution and the formation of singularities of differential characteristics of passive-admixture fields in various hydro- and gasdynamic flows. As a passive scalar one may regard an arbitrary physical quantity which is transported at the carrier-flow velocity and makes no impact on the carrier-flow velocity field. The diffusion transport of the scalar is ignored. The differential characteristics of the passive admixture may include, for instance, different differential parameters of a dispersed phase in two-phase flows, such as gradients of density and temperature, derivatives of the velocity components, vorticity, etc. The method is also applicable to the investigation of such parameters as temperature gradients in single-phase flows with a high Peclet number, the vorticity in inviscid flows, the frozen magnetic field, the electric charge, weak density nonuniformities in fast flows of stratified fluids, etc.
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