Alignment dynamics of diffusive scalar gradient in a two-dimensional model flow

Abstract

The Lagrangian two-dimensional approach of scalar gradient kinematics is revisited accounting for molecular diffusion. Numerical simulations are performed in an analytic, parameterized model flow, which enables considering different regimes of scalar gradient dynamics. Attention is especially focused on the influence of molecular diffusion on Lagrangian statistical orientations and on the dynamics of scalar gradient alignment.A number of basic and practical questions in fluid dynamics are connected to the transport of vectors [1, 2], an issue therefore relevant to many fields -process engineering, reacting flows, mixing, astrophysical flows, etc. Vectors defining material lines or surfaces, vorticity, the vorticity gradient in two-dimensional flows, gradients of scalar quantities such as concentration or temperature, the magnetic field vector in magnetohydrodynamics, are transported vectors.Most often, analyses are with regard the growth -or decay -of the magnitude of the transported vector. The growth of the scalar gradient, for example, indicates the production of small scales in the scalar field; addressing the dynamo effect needs to determine the physical conditions in which the magnetic field vector is amplified. The bare kinematics of vector amplification -in non-diffusive tracer advection, kinematic dynamo, or inviscid vortex stretching -is a matter of strain level and orientation within the strain eigenframe. Just like strain intensity, vector orientation is essential to the process and was investigated in many studies [3][4][5][6][7] (see [2] for more references).

The Equilibrium Orientation of Scalar Gradient in a Lagrangian Model of Three-dimensional Turbulence

“…4) Better still, the preferential alignment of scalar gradient predicted in two-dimensional turbulence 2) is thereby confirmed in the three-dimensional case. As shown in a two-dimensional flow, 10) the equilibrium direction is the attracting alignment for the scalar gradient. This feature is checked in the equilibrium sample by comparing S eq = −sgn{cos (n (eq) , G)} • F eq and S c = −sgn{cos (e (3) , G)} • F c , where…”