Adjoint Method-Based Algorithm for Calculating the Relative Dispersion Ratio in a Hydrodynamic System

• Published in: Journal of Ocean University of China Vol. 20; no. 4; pp. 790 - 802
• Main Authors: Ji, Fei, Jiang, Wensheng, Guo, Xinyu
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Science and Business Media LLC 01.08.2021; Science Press; Springer Nature B.V; Center for Marine Environmental Studies,Ehime University,Matsuyama 790-8577,Japan; State Key Laboratory of Satellite Ocean Environment Dynamics,Second Institute of Oceanography,Ministry of Natural Resources,Hangzhou 310012,China%Key Laboratory of Marine Environment and Ecology (Ministry of Education of China),Ocean University of China,Qingdao 266100,China%State Key Laboratory of Satellite Ocean Environment Dynamics,Second Institute of Oceanography,Ministry of Natural Resources,Hangzhou 310012,China
• Subjects: Algorithms; Consistency; Deviation; Dispersion; Earth and Environmental Science; Earth Sciences; Hydrodynamics; Mathematical analysis; Meteorology; Oceanography; Tracing; particle tracking; computational efficiency; relative dispersion; adjoint method
• ISSN: 1672-5182; 1993-5021; 1672-5174
• DOI: 10.1007/s11802-021-4493-x

Relative dispersion ratio (RDR) can be used to quantify the deviation behavior of a water parcel’s trajectory caused by a disturbance in a hydrodynamic system. It can be calculated by using a standard method for determining relative dispersion (RD), which accounts for the growth of the deviation of a cluster of particles from a specific initial time. However, the standard method for computing RD is time consuming. It involves numerous computations on tracing many water parcels. In this study, a new method based on the adjoint method is proposed to acquire a series of RDR fields in one round of tracing. Through this method, the continuous variation in the RDR corresponding to a time series of the disturbance time t can be obtained. The consistency and efficiency of the new method are compared with those of the standard method by applying it to a double-gyre flow and an unsteady Arnold-Beltrami-Childress flow field. Results show that the two methods have good consistency in a finite time span. The new method has a notable speedup for evaluating the RDR at multiple t .