Computing Lagrangian means

Lagrangian averaging plays an important role in the analysis of wave–mean-flow interactions and other multiscale fluid phenomena. The numerical computation means, e.g. from simulation data, is, however, challenging. Typical implementations require tracking a large number particles to construct time series, which are then averaged using low-pass filter. This has drawbacks that include memory demands, particle clustering complications parallelisation. We develop novel approach means various fields (including positions) computed by solving partial differential equations (PDEs) integrated over successive intervals. propose two strategies, distinguished their spatial independent variables. first, generalises algorithm Kafiabad ( J. Fluid Mech. , vol. 940, 2022, A2), uses end-of-interval positions; second directly mean positions. PDEs can be discretised variety ways, same discretisation as employed for governing dynamical equations, solved on-the-fly minimise footprint. illustrate new with pseudo-spectral implementation rotating shallow-water model. Two applications flows combine vortical turbulence Poincaré waves demonstrate superiority Eulerian wave–vortex separation.