Effect of density step on stirring properties of a strain flow

TL;DR

This paper analyzes how a sharp density gradient affects stirring in a strain flow, revealing complex interactions between vorticity, strain, and scalar gradient evolution through an exact analytical approach.

Contribution

It provides an exact analytical solution for the flow with a density step and examines its impact on stirring properties and scalar gradient dynamics.

Findings

Density ratio influences effective rotation and flow topology.

Scalar gradient alignment is altered by the density step.

Strain intensity jump affects scalar gradient growth.

Abstract

The influence of steep density gradient upon stirring properties of a strain flow is addressed by considering the problem in which an interface separating two regions with different constant densities is stabilised within a stagnation-point flow. The existence of an analytic solution for the two-dimensional incompressible flow field allows the exact derivation of the velocity gradient tensor and of parameters describing the local flow topology. Stirring properties are affected not only through vorticity production and jump of strain intensity at the interface, but also through rotation of strain principal axes resulting from anisotropy of pressure Hessian. The strain persistence parameter, which measures the respective effects of strain and effective rotation (vorticity plus rotation rate of strain basis), reveals a complex structure. In particular, for large values of the density ratio it indicates dominating effective rotation in a restricted area past the interface. Information on flow structure derived from the Okubo-Weiss parameter, by contrast, is less detailed. The influence of the density step on stirring properties is assessed through the Lagrangian evolution of the gradient of a passive scalar. Even for a moderate density ratio, alignment of the scalar gradient and growth rate of its norm are deeply altered. Past the interface effective rotation indeed drives the scalar gradient to align with a direction determined by the local strain persistence parameter, away from the compressional strain direction. The jump of strain intensity at the interface, however, opposes the lessening effect of the latter mechanism on the growth rate of the scalar gradient norm and promotes the rise of the gradient.