Robust and efficient identification of optimal mixing perturbations using proxy multiscale measures

Area of Science:

• Fluid dynamics
• Transport phenomena
• Mathematical physics

Background:

• Passive scalar mixing is fundamental in environmental and industrial fluid flows.
• Optimizing mixing, especially at finite Péclet numbers, presents computational challenges.
• Identifying initial perturbations for efficient mixing requires advanced methods.

Purpose of the Study:

• To identify optimal initial perturbations for passive scalar mixing in a diffusive fluid flow.
• To develop computationally efficient methods for finding perturbations that thoroughly mix scalar distributions.
• To analyze the relationship between initial perturbations, flow structures, and mixing efficiency.

Main Methods:

• Utilized an idealized two-dimensional flow on a torus.
• Employed the 'direct-adjoint looping' method to identify optimal initial perturbations.
• Focused on minimizing 'mix-norms' over finite time horizons.

Main Results:

• Minimizing mix-norms over short horizons efficiently identifies perturbations for long-term mixing.
• Optimal perturbations trigger coherent vortical flow structures that enhance mixing.
• The characteristics of these structures depend on Péclet number and time horizon.

Conclusions:

• The direct-adjoint looping method combined with mix-norm minimization offers a robust approach to optimize passive scalar mixing.
• Coherent vortical structures are key to efficient mixing, with their properties tunable by flow parameters.
• This method provides a computationally tractable solution for a fundamental fluid dynamics problem.