Abstract
This work investigates the numerical time stability of the Lagrangian-averaged shallow water α model (SW-α). The main result is an analytical estimate for the maximum allowable time step. This estimate shows that as the grid is refined the time step becomes independent of the mesh spacing and instead depends on the length scale, α, a parameter of the model. The α model achieves this result through changes in the equations of motion that reduce the frequency of the linear waves at high wavenumbers. This type of reduction in the frequency of high-wavenumber waves is also a characteristic of time-implicit numerical methods. Consequently, an analogy is drawn between the two by comparing the numerical method's modified equation to the partial differential equation of the α model. Fourier analysis and numerical simulations are also used to compare a third-order Adams–Bashforth α model simulation to the well-known implicit numerical method of Dukowicz and Smith.
Corresponding author address: B. A. Wingate, Computer and Computational Sciences and Center for Nonlinear Studies, Los Alamos National Laboratory, MS B413, Los Alamos, NM 87545. Email: wingate@lanl.gov
