1D source term interactions for shallow lakes in SWAN

1D source term interactions for shallow lakes in SWAN

Hartgring, Sebastian (TU Delft Civil Engineering and Geosciences)

Zijlema, M. (mentor)
Reniers, A.J.H.M. (graduation committee)

Delft University of Technology

Civil Engineering

2022-03-01

During the calibration of SWAN for shallow water lakes in the Netherlands, problems have been encountered. Especially the emergence of an unnatural, secondary peak in the low frequency part of the energy density spectrum poses problems. Therefore, this investigation aims to address the nonlinear shallow water source terms in SWAN that may introduce this artefact.

Firstly, the basics of linear wave theory and spectral modelling are introduced. Hereafter, these basics are extended to the modelling on nonlinear wave behaviour, as these phenomena form the basis of the relevant shallow water source terms.

The shallow water lake problem is reduced to a stationary, one dimensional problem, for which several model results are produced using varying parameters. Three main subjects can be identified: 1) the influence of depth-induced wave breaking using the BJ78-model or the $\beta-kd$-model, 2) the proportionality factor of the triad source term using the CCA-formulation, and 3) numerical properties such as frequency resolution and the magnitude of the flux limiter.

The results demonstrate that, for strong winds ($U_{10} = 40$ m/s) in shallow water ($d = 2.5$ m), source term interactions become complex as they are all of similar order of magnitude. Especially the interactions between triad wave-wave interactions and depth-induced wave breaking, and triads and quadruplets are important for determining the resulting wave spectrum. Increased wave breaking reduces the secondary peak but underestimates significant wave heights and dampens the spectrum. A more elaborate wave breaking formulation (the $\beta-kd$-model) showed improved performance, especially when it was set to allow younger wind waves (high $kd$) to develop.

Lowering the effect of the triad source term also removes the secondary peak, but may not be desirable as it is by definition a relevant shallow water source term. Reducing source term interactions by means of a stricter action limiter resulted in instabilities for the quadruplet source term and thus no convergence of the results.

A possible solution may be to investigate the possibility of reducing the effect of quadruplets for shallow water, as this term (together with the triad source term) contributes to the formation of the secondary peak. However, this has not been included in the scope of this investigation. Furthermore, improving the frequency resolution resulted in smoother spectra and less wiggles in the sum of the triad and quadruplet source terms. However, this may affect the performance of the quadruplet source term as this term has been calibrated for a fixed relative frequency resolution.

SWAN
nonlinear wave-wave interactions
Shallow water
nonlinear wave breaking

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© 2022 Sebastian Hartgring