FTLE Operator
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The analysis of time-dependent dynamical systems can be done with the Finite-time Lyapunov exponents (FTLE) Operator. We direct interested users to the excellent tutorial on Lagrangian Coherent Structures page for more details.
We reproduce here the simple (time-independent) example from section 7 of the LCS tutorial, with Epsilon=0
An input grid is required. We use a trivial 2D Cartesian grid in ASCII VTK format. Simply copy the 7 lines below in a text file called ftle_input.vtk:
# vtk DataFile Version 3.0 vtk output ASCII DATASET STRUCTURED_POINTS DIMENSIONS 101 51 1 SPACING 0.02 0.02 1 ORIGIN 0 0 0
This VTK file represents a grid with Spatial Extents [0, 2, 0, 1] to fit the example's requirements.
We then create a vector field with two components, u and v, defining the following expressions:
DefineVectorExpression("velocity", "{u,v}") DefineScalarExpression("u", "-3.141592*1*sin(3.141592*coord(mesh)[0])*cos(3.141592*coord(mesh)[1])") DefineScalarExpression("v", "3.141592*1*cos(3.141592*coord(mesh)[0])*sin(3.141592*coord(mesh)[1])") DefineScalarExpression("vel_mag", "magnitude(velocity)")
Finally, we plot both the velocity glyphs and the FTLE output with the code:
OpenDatabase("ftle_input.vtk") AddPlot("Vector", "velocity", 0, 0) AddPlot("Pseudocolor", "velocity") AddOperator("FTLE", 0) opAtts = FTLEAttributes() opAtts.regionType = opAtts.NativeResolutionOfMesh # NativeResolutionOfMesh, RegularGrid opAtts.direction = opAtts.Forward # Forward, Backward opAtts.flowType = opAtts.Steady # Unsteady, Steady SetOperatorOptions(opAtts) DrawPlots() # Set the view view = View2DAttributes() view.windowCoords = (0, 2, 0, 1) view.viewportCoords = (0.2, 0.95, 0.15, 0.95) view.fullFrameActivationMode = view.Auto # On, Off, Auto view.fullFrameAutoThreshold = 100 view.xScale = view.LINEAR # LINEAR, LOG view.yScale = view.LINEAR # LINEAR, LOG view.windowValid = 1 SetView2D(view)
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