# Lamb Vector¶

The Lamb Vector filter computes the Lamb vector $L$ based on the velocity $v$, vorticity $\omega$ and the density $\rho$.

\begin{equation} L = \omega \times \boldsymbol{v} , \end{equation}

with vorticity as

\begin{equation} \omega = \nabla \times \boldsymbol{v} . \end{equation}

However, it is possible to compute the Lamb vector only based on the velocity, or on the velocity and the vorticity. If only the velocity is defined the vorticity is computed internally.

• The epsilonScaling Parameter scales the radial basis functions used for computing spatial derivatives. It controlls the "smoothness" of the basis function. The smoother the gauss-like surface is, the better the results will be BUT only until a certain number, when the matrix becomes to ill-contioned, which will result in very bada results. Typical values: 1e-1 - 1e-4.
• The kScaling parameter is an optional parameter and defines a constant term that is added to the radial basic function.
• The betaScaling parameter defines the slope of a linear term that is added to the radial basis function.
• The logEps Parameter enables a detailes console output (minimal distance, maximal distance, optimized parameters). Therefore, it should only be used if the spatial derivatives are investigated, because it totally spams the console
    <aeroacoustic type="AeroacousticSource_LambVector" inputFilterIds="..." id="...">
<RBF_Settings epsilonScaling="1e-4"  kScaling="" betaScaling="" logEps=false/>
<targetMesh>
<hdf5 fileName=..."/>
</targetMesh>
<ResultList>
<velocity resultName="..."/>
<vorticity/>
<density />  //NOT WORKING
<outputQuantity resultName="..."/>
</ResultList>
<regions>
<sourceRegions>
<region name="..."/>
</sourceRegions>
<targetRegions>
<region name="..."/>
</targetRegions>
</regions>
</aeroacoustic>


Note that the density Tag is currently not fully implemented and therefore not working. It is possible to enter results, however it will not alter the computed output quantity.

## Acknowledgement¶

Please provide an acknowledgement at the end of your publication using this software part for simulations

The computational results presented have been achieved [in part] using the software openCFS [FE-based Interpolation].