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Computation of the Streamfunction and Velocity Potential for Limited and Irregular Domains

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  • 1 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California
  • | 2 Department of Atmospheric Science, and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Los Angeles, California
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Abstract

An algorithm is proposed for the computation of streamfunction and velocity potential from given horizontal velocity vectors based on solving a minimization problem. To guarantee the uniqueness of the solution and computational reliability of the algorithm, a Tikhonov regularization is applied. The solution implies that the obtained streamfunction and velocity potential have minimal magnitude, while the given velocity vectors can be accurately reconstructed from the computed streamfunction and velocity potential. Because the formulation of the minimization problem allows for circumventing the explicit specification of separate boundary conditions on the streamfunction and velocity potential, the algorithm is easily applicable to irregular domains. By using an advanced minimization algorithm with the use of adjoint techniques, the method is computationally efficient and suitable for problems with large dimensions. An example is presented for coastal oceans to illustrate the practical application of the algorithm.

* Additional affiliation: Raytheon Technical Services Co. LLC, Pasadena, California

Corresponding author address: Dr. Zhijin Li, Jet Propulsion Laboratory, California Institute of Technology, M/S 300-323, 4800 Oak Grove Dr., Pasadena, CA 91109. Email: zhijin.li@jpl.nasa.gov

Abstract

An algorithm is proposed for the computation of streamfunction and velocity potential from given horizontal velocity vectors based on solving a minimization problem. To guarantee the uniqueness of the solution and computational reliability of the algorithm, a Tikhonov regularization is applied. The solution implies that the obtained streamfunction and velocity potential have minimal magnitude, while the given velocity vectors can be accurately reconstructed from the computed streamfunction and velocity potential. Because the formulation of the minimization problem allows for circumventing the explicit specification of separate boundary conditions on the streamfunction and velocity potential, the algorithm is easily applicable to irregular domains. By using an advanced minimization algorithm with the use of adjoint techniques, the method is computationally efficient and suitable for problems with large dimensions. An example is presented for coastal oceans to illustrate the practical application of the algorithm.

* Additional affiliation: Raytheon Technical Services Co. LLC, Pasadena, California

Corresponding author address: Dr. Zhijin Li, Jet Propulsion Laboratory, California Institute of Technology, M/S 300-323, 4800 Oak Grove Dr., Pasadena, CA 91109. Email: zhijin.li@jpl.nasa.gov

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