# 4.3.14.2. Lagrangian Coherent Structure (LCS) operator¶

The LCS operator utilizes Lyapunov Exponents based on the Cauchy-Green Tensor to highlight Lagrangian Coherent Structures in vector fields. When performing a Finite Time Lyapunov Exponent (FTLE) calculation, the time can be specified as one would for a traditional FTLE, and the resulting value will be based on the maximal Eigen value.

However, when performing the calculation with Finite Space Lyapunov Exponents (FSLE), instead of assuming a uniform mesh discretization and specifying the dispersion distance, we specify a dispersion factor. In a traditional FTLE, this is the dispersion distance divided by the initial distance. In the equivalent definition, the dispersion distance is the maximal Eigen value. Thus when the maximal Eigen value is greater than the specified dispersion factor, then the exponent is calculated.

More details can be found `in this paper`

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## 4.3.14.2.1. Source¶

The set of points that seed the integral curves that reveal the Lagrangian Coherent Structures. In addition to the Source attributes common to all ICS operators, the LCS operator supports the following attributes:

### 4.3.14.2.1.1. Source types¶

The source type controls how the seeds for curves are created. The user can seed the integral curves using the native mesh or define a rectilinear grid. The nodes of the mesh are the seed points.

### 4.3.14.2.1.2. Auxilary Grid¶

When calculating the Jacobian for the Cauchy-Green tensor, one can use the neighboring points from the native mesh or one can specify an auxiliary grid that allows for the detection of finer features but at greater computational expense. Using an auxiliary grid is advantageous because it is independent of the native mesh, so it gives more accurate results for higher order elements. For simulation flows, using the auxiliary grid for eigenvalue calculations gives better results.

## 4.3.14.2.2. Integration¶

Specify settings for numerical integrators. In addition to the Integration attributes common to all ICS operators, the LCS operator supports the following attributes:

### 4.3.14.2.2.1. Integration Direction¶

Sets the integration direction through time: either forward or backward.

## 4.3.14.2.3. Appearance¶

The appearance tab specifies how the LCS’s will be rendered. In addition to the Appearance attributes common to all ICS operators, the LCS operator supports the following attributes.

### 4.3.14.2.3.1. Seed Generation¶

Filter the number of seeds generated from the mesh (either native or rectilinear). There are various self-descriptive filtering options.

## 4.3.14.2.4. Advanced¶

In addition to the Advanced attributes common to all ICS operators, the LCS Operator supports the following attributes:

### 4.3.14.2.4.1. Warnings¶

- Issue warning if the advection limit is not reached
If the maximum time or distance is not reached, issue a warning.

- Issue warning if the spatial boundary is reached
If the integral curve reaches the spatial domain boundary, issue a warning.