Comparison of Lagrangian Coherent Structures and Relative Dispersion in a Mixing Layer

Abstract

Lagrangian coherent structures (LCS) and relative dispersion are two widely used tools to study mixing and have been successfully applied to a wide variety of flows. Their computation requires particle advection by numerical integration of the velocity field. We have developed a CUDA-based 2D flow solver using a Fourier-spectral method with a second-order Adams-Bashforth time-stepping method to solve the Navier-Stokes and scalar diffusion equations for a perturbed, temporally-growing, two-dimensional incompressible mixing layer. The resulting simulation data are used to compute LCS and relative dispersion $R^2$. LCS is computed using finite time Lyapunov exponents ($\sigma$). Contours plots are used to visualize these two scalar fields and it is found that maximum dispersion ($R^2$) values correspond to the ridges in the FTLE field. We further compute normalized relative dispersion ($\lambda_d$) and compare it with $\sigma$. It is shown that $\lambda_d$ and $\sigma$ provide qualitatively the same information. Another quantity $\Gamma$, defined as the ratio of $\lambda_d$ and $\sigma$, is computed to relate the two quantities. The implications and future directions of our research are suggested