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# Animations comparing surface wave simulations with standard and "stabilized" two-equation turbulence models

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posted on 2019-05-29, 11:43 authored by Bjarke Eltard LarsenBjarke Eltard Larsen, David R. FuhrmanDavid R. FuhrmanThis data set contains animations comparing the performance of standard and "stabilized" (as described in Larsen and Fuhrman, 2018) two-equation turbulence closures. Two animations are included, involving simulation of:

1. A simple wave train

2. Spilling breaking test of Ting and Kirby (1994)

Both tests utilize incident waves with:

*kH*=0.207 and*kh*=0.664, where*k*is the wave number,*H*is the wave height, and*h*=0.4 m is the water depth. In the spilling breaking test the waves propagate up a 1:35 slope. The set ups are as described in Larsen and Fuhrman (2018).The tests demonstrate the characteristic instability (exponential growth) of the turbulent kinetic energy beneath non-breaking surface waves exhibited by all widely-used two equation turbulence closures. This is proved unconditionally by Larsen and Fuhrman (2018), which built on the prior conditional proof of Mayer and Madsen (2000). This problem is removed entirely by the "stabilized" closures of Larsen and Fuhrman (2018), where significant turbulence is limited to the boundary layer region and/or surf zone (breaking waves).

It is emphasized that

__of the simulations shown in these animations (as well as__**all**__results shown in Larsen and Fuhrman, 2018, as indicated on their p. 434) have the buoyancy production term active in the__**all***k*-equation, as suggested recently in this context by e.g. Devolder et al. (2017). This only creates a local sink in the turbulent kinetic energy near the air-water interface, but clearly does not stabilize the models. This is because the problem of over-production of turbulence in two-equation models is not confined to the near-surface region; Rather the__, as again proved unconditionally by Larsen and Fuhrman (2018). It is the simple modification of the eddy viscosity, coupled with its elimination from either the \omega or \epsilon production term, which formally stabilizes the models, as shown therein.__**entirety of the nearly-potential flow region beneath the surface waves is unstable**Simulations have been made in OpenFOAM, with waves generated by waves2Foam (Jacobsen et al., 2012).

Stabilized turbulence models are available in the open-source stabRAS repository (announced here: https://www.cfd-online.com/Forums/openfoam-community-contributions/208312-new-contribution-stabras.html).

Please cite this as:

Larsen, B.E. and Fuhrman, D.R. (2019) Animations comparing surface wave simulations with standard and "stabilized" two-equation turbulence models. figshare. Media. DOI: 10.11583/DTU.8180708

References

Devolder, B., Rauwoens, P. and Troch, P. (2017) Application of a buoyancy-modified k-omega turbulence model to simulate wave run-up around a monopile subject to regular waves using OpenFOAM. Coast. Eng. 125, 81-94. DOI: 10.1016/j.coastaleng.2017.04.004

Jacobsen, N.G., Fuhrman, D.R. and Fredsøe, J. (2012) A wave generation toolbox for the open-source CFD library: OpenFoam. Int. J. Numer. Meth. Fluids. 70, 1073-1088. DOI: 10.1002/fld.2726

Larsen, B.E. and Fuhrman, D.R. (2018) On the over-production of turbulence beneath surface waves in Reynolds-averaged Navier-Stokes models. J. Fluid Mech. 853, 419-460. DOI: 10.1017/jfm.2018.577

Mayer, S. and Madsen, P.A. (2000) Simulation of breaking waves in the surf zone using a Navier-Stokes solver. In: Proc. 27th Int. Conf. Coast. Eng., pp. 928-941, Sydney, Australia. DOI: 10.1061/40549(276)72

Ting, F.C.K. and Kirby, J.T. (1994) Observations of undertow and turbulence in a laboratory surf zone. Coast. Eng. 24, 51-80. DOI: 10.1016/0378-3839(94)90026-4

## Funding

### SWASH: Simulating WAve Surf-zone Hydrodynamics and sea bed morphology

Danish Agency for Science and Higher Education

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