DesignTurb: Construction of Complex Vortices

Description

DesignTurb offers a versatile method for constructing the vorticity of vortex tubes with customizable centerline topology, differential twist, and variable thickness. This tool is ideal for designing classical turbulence fields, conceptualized with quantum vortex tangles as the core framework and complemented with customizable vortices as modular elements. This approach allows for free and precise adjustment on the distribution and shape of elemental vortices. The code is written in FORTRAN and supports MPI parallel computing. If you are interested in using the code for your own research, please contact [email protected] and [email protected] for more details.

How It Works

• Profile Shape: Modify the profile shape of vortices via the tpFunc subroutine.
• Thickness Distribution: Adjust the thickness along the centerlines in the sigmaFunc subroutine.
• Twist Distribution: Change the twist distribution along the centerlines using the etaFunc subroutine.
• Centerline Data: Input as discrete points, exemplified in TrefoilCenterline.dat for a trefoil knot and QTCenterline.dat for entangled vortices. Entangled centerline can be obtained from superfluid simulation based on the vortex filament method (see qvort on GitHub).

The code transforms discrete control points on centerlines into cubic spline curves, defined by polynomial parametric equations. It then constructs a 3D vorticity field for vortex tubes within a periodic box, translating curved cylindrical coordinates to Cartesian coordinates. The process ensures the vector field adheres to periodic boundary conditions.

Centerline Parameters

The centerline data file should be organized in order by the following parameters:

• nline: Total number of centerlines
• npointlist(i): Number of discrete points per centerline
• cxall(i): x-coordinates of discrete points
• cyall(i): y-coordinates of discrete points
• czall(i): z-coordinates of discrete points

References

W. Shen, J. Yao, and Y. Yang, "Designing turbulence with entangled vortices", Proc. Natl. Acad. Sci. U.S.A. (In Press). arXiv:2401.11149

W. Shen, J. Yao, F. Hussain, and Y. Yang, “Role of internal structures within a vortex in helicity dynamics”, J. Fluid Mech., 970, A26 (2023). JFM

W. Shen, J. Yao, F. Hussain, and Y. Yang, “Topological transition and helicity conversion of vortex knots and links”, J. Fluid Mech., 943, A41 (2022). JFM

S. Xiong, Y. Yang, “Effects of twist on the evolution of knotted magnetic flux tubes”, J. Fluid Mech., 895, A28 (2020). JFM

S. Xiong, Y. Yang, “Construction of knotted vortex tubes with the writhe-dependent helicity”, Phys. Fluids, 31, 047101 (2019). POF