Clebsch Maps for Visualization and Processing

Albert Chern, Felix Knöppel, Ulrich Pinkall, Peter Schröder



Clebsch maps encode velocity fields through functions. These functions contain valuable information about the velocity field. For example, closed integral curves of the associated vorticity field are level lines of the vorticity Clebsch map. This makes Clebsch maps useful for visualization and fluid dynamics analysis. Additionally they can be used in the context of simulations to enhance flows through the introduction of subgrid vorticity. Spherical Clebsch maps turned out to be particularly attractive. Elucidating their geometric structure, it is shown in [1] that such maps can be found as minimizers of a non-linear Dirichlet energy. To illustrate our approach a number of benchmark problems are used [2]. Code and a video can be found at .


  • Albert Chern, Felix Knöppel, and Peter Pinkall, Ulrich and​ ​Schröder.
    Inside Fluids: Clebsch Maps for Visualization and Processing.
    ACM Trans. Graph., 36(4):142:1–142:11, July 2017.
  • Albert Chern, Felix Knöppel, Peter Pinkall, Ulrich and​ ​Schröder, and Steffen Weißmann.
    Schrödinger's Smoke.
    ACM Trans. Graph., 35:77:1–77:13, July 2016.

Dr. Albert Chern   +

University: TU Berlin
E-Mail: chern[at]

Dr. Felix Knöppel   +

Projects: C07
University: TU Berlin
E-Mail: knoeppel[at]

Prof. Dr. Ulrich Pinkall   +

Projects: A05, C07
University: TU Berlin, Institut für Mathematik, MA 822
Address: Straße des 17. Juni 136, 10623 Berlin, GERMANY
Tel: +49 30 31424607
E-Mail: pinkall[at]

Prof. Dr. Peter Schröder   +