Grid-based calculation of the Lagrangian mean

• Main Author: Kafiabad, H.A (Author)
• Format: Article
• Language: English
• Published: Cambridge University Press 2022
• Subjects: computational methods; Equations of motion; Eulerian; Geostrophic balance; Grid-based; Iterative methods; Lagrange multipliers; Lagrangian; Numerical methods; Numerical models; ocean circulation; Ocean circulation; Oceanography; Reduced model; Slow dynamics; Slow flow; Two time scale; waves in rotating fluids; Waves in rotating fluids
• Online Access: View Fulltext in Publisher

 Lagrangian averaging has been shown to be more effective than the Eulerian mean in separating waves from slow dynamics in two time scale flows. It also appears in many reduced models that capture the wave feedback on the slow flow. Its calculation, however, requires tracking particles in time, which imposes several difficulties in grid-based numerical simulations or estimation from fixed-point measurements. To circumvent these difficulties, we propose a grid-based iterative method to calculate the Lagrangian mean without tracking particles in time, which also reduces computation, memory footprint and communication between processors in parallelised numerical models. To assess the accuracy of this method several examples are examined and discussed. We also explore an application of this method in the context of shallow-water equations by quantifying the validity of wave-averaged geostrophic balance - a modified form of geostrophic balance accounting for the effect of strong waves on slow dynamics. ©