Lagrangian coherent structures

Lagrangian coherent structures (LCS) are like paths in a river that show us where things will move based on the way the water is flowing. Imagine you are playing in a stream with a lot of sticks and leaves. If you pour food coloring into the water upstream of where you are playing, you will notice that the colors will mix and move around in different ways as they get closer to you. Some of the colors will move faster than others, and some will move in circles or even stop moving altogether.

LCS help us track and predict where these colors (or anything else that flows, like air or pollutants) will go by looking at the patterns in the flow of the water. LCS are like invisible lines that show us where the water is flowing in a very organized and predictable way.

Imagine if you could "paint" the water with invisible paint that only shows up when the water moves in a certain pattern. For example, if the water is moving in a "swirling" pattern, the invisible paint would show up and create a shape. This shape would be an LCS. LCS can help us understand how things move in different types of fluid, whether it's in a stream, ocean, or even the air.