Open rabernat opened 3 years ago
Many of the LCS methods are based on "velocity gradient tensor"
In 2D this is
$$ \nabla \mathbf{u} = \begin{bmatrix} \frac{\partial u}{\partial x} & \frac{\partial u}{\partial y} \ \frac{\partial v}{\partial x} & \frac{\partial v}{\partial y} \end{bmatrix} $$
This can be decomposed into a couple of different components. A key one is the divergence
$$ \delta = \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} $$
This is always ZERO for QG flow and for geostrophic flow in general it is approximately zero.
Another component is vorticity
$$ \zeta = -\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x} $$
A final one is strain
All of these quantities can be averaged along particle paths and are the foundation for many LCS methods.
I need to write some notes on this to be more specific about what we want to calculate.
Many of the LCS methods are based on "velocity gradient tensor"
In 2D this is
$$ \nabla \mathbf{u} = \begin{bmatrix} \frac{\partial u}{\partial x} & \frac{\partial u}{\partial y} \ \frac{\partial v}{\partial x} & \frac{\partial v}{\partial y} \end{bmatrix} $$
This can be decomposed into a couple of different components. A key one is the divergence
$$ \delta = \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} $$
This is always ZERO for QG flow and for geostrophic flow in general it is approximately zero.
Another component is vorticity
$$ \zeta = -\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x} $$
A final one is strain
All of these quantities can be averaged along particle paths and are the foundation for many LCS methods.