The Maximum Allowable Time Step for the Shallow WaterαModel and Its Relation to Time-Implicit Differencing

• DOI: 10.1175/mwr2816.1
• Publication Date: 2004-12-17T18:32:30Z
• Authors: B. A. Wingate
• Keywords: Wavenumber; Shallow water equations

This work investigates the numerical time stability of Lagrangian-averaged shallow water α model (SW-α). The main result is an analytical estimate for maximum allowable step. shows that as grid refined step becomes independent mesh spacing and instead depends on length scale, α, a parameter model. achieves this through changes in equations motion reduce frequency linear waves at high wavenumbers. type reduction high-wavenumber also characteristic time-implicit methods. Consequently, analogy drawn between two by comparing method's modified equation to partial differential Fourier analysis simulations are used compare third-order Adams–Bashforth simulation well-known implicit method Dukowicz Smith.