RLM: Rearranged level-set method - An efficient approach for calculating temporally continuous Lagrangian Residual Velocities

Abstract

The Lagrangian Residual Velocity (LRV) is the subtidal residual current extracted from oscillating tidal water motions to depict the coastal circulation. Since the LRVs are sensitive to the initial time, the most widely used particle tracking method (PTM) must be used repeatedly to obtain temporally continuous LRVs. A new method, the rearranged level-set method (RLM), is introduced to efficiently obtain temporally continuous LRVs. Compared with the analytical solution of LRVs in a long narrow bay, both the RLM-LRVs and the PTM-LRVs can reproduce multiple gyre structures. However, the region of directional bias above 60° in the RLM-LRVs is limited to the narrow gyre conjunction region, while that in the PTM-LRVs extends up to half the bay width and 10% of the bay length. In particular, the RLM can produce temporally continuous LRVs with much higher computational efficiency than the PTM. The RLM also performs well in complex coastal sea areas, such as a cape with a staircase topography, rectangular coastline, and Jiaozhou Bay (JZB), a realistic small waterbody with complex coastline and topography. The RLM-derived temporally continuous LRVs can illustrate the evolution of the two small gyres perturbed by the staircase topography in the cape, and the two gyre cores embedded in the large dominant counterclockwise gyre move separately along the deep channels in the JZB while the PTM cannot. In conclusion, the RLM is a fast and accurate method for calculating temporally continuous LRVs.