2 results
Reynolds stress turbulence modelling of surf zone breaking waves
- Yuzhu Li, Bjarke Eltard Larsen, David R. Fuhrman
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- Journal:
- Journal of Fluid Mechanics / Volume 937 / 25 April 2022
- Published online by Cambridge University Press:
- 22 February 2022, A7
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Computational fluid dynamics is increasingly used to investigate the inherently complicated phenomenon of wave breaking. To date, however, no single model has proved capable of accurately simulating the breaking process across the entirety of the surf zone for both spilling and plunging breakers. The present study newly considers the Reynolds stress–$\omega$ turbulence closure model for this purpose, where $\omega$ is the specific dissipation rate. Novel stability analysis proves that, unlike two-equation closures (at least in their standard forms), the stress–$\omega$ model is neutrally stable in the idealized potential flow region beneath surface waves. It thus naturally avoids unphysical exponential growth of turbulence prior to breaking, which has plagued numerous prior studies. The analysis is confirmed through simulation of a progressive surface wave train. The stress–$\omega$ model is then applied to simulate a turbulent wave boundary layer, demonstrating superior accuracy relative to a two-equation model, especially during flow deceleration. Finally, the stress–$\omega$ model is employed to simulate spilling and plunging breaking waves, with seemingly unprecedented accuracy. Specifically, the present work marks the first time that a single turbulence closure model collectively: (1) avoids turbulence over-production prior to breaking, (2) accurately predicts the breaking point, (3) provides reasonable evolution of turbulent normal stresses, while also (4) yielding accurate evolution of undertow velocity structure and magnitude across the surf zone, for both spilling and plunging cases. Differences in the predicted Reynolds shear stresses (hence flow resistance) are identified as key to the improved inner surf zone performance, relative to a state-of-the-art two-equation model.
On the over-production of turbulence beneath surface waves in Reynolds-averaged Navier–Stokes models
- Bjarke Eltard Larsen, David R. Fuhrman
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- Journal:
- Journal of Fluid Mechanics / Volume 853 / 25 October 2018
- Published online by Cambridge University Press:
- 23 August 2018, pp. 419-460
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In previous computational fluid dynamics studies of breaking waves, there has been a marked tendency to severely over-estimate turbulence levels, both pre- and post-breaking. This problem is most likely related to the previously described (though not sufficiently well recognized) conditional instability of widely used turbulence models when used to close Reynolds-averaged Navier–Stokes (RANS) equations in regions of nearly potential flow with finite strain, resulting in exponential growth of the turbulent kinetic energy and eddy viscosity. While this problem has been known for nearly 20 years, a suitable and fundamentally sound solution has yet to be developed. In this work it is demonstrated that virtually all commonly used two-equation turbulence closure models are unconditionally, rather than conditionally, unstable in such regions. A new formulation of the $k$–$\unicode[STIX]{x1D714}$ closure is developed which elegantly stabilizes the model in nearly potential flow regions, with modifications remaining passive in sheared flow regions, thus solving this long-standing problem. Computed results involving non-breaking waves demonstrate that the new stabilized closure enables nearly constant form wave propagation over long durations, avoiding the exponential growth of the eddy viscosity and inevitable wave decay exhibited by standard closures. Additional applications on breaking waves demonstrate that the new stabilized model avoids the unphysical generation of pre-breaking turbulence which widely plagues existing closures. The new model is demonstrated to be capable of predicting accurate pre- and post-breaking surface elevations, as well as turbulence and undertow velocity profiles, especially during transition from pre-breaking to the outer surf zone. Results in the inner surf zone are similar to standard closures. Similar methods for formally stabilizing other widely used closure models ($k$–$\unicode[STIX]{x1D714}$ and $k$–$\unicode[STIX]{x1D700}$ variants) are likewise developed, and it is recommended that these be utilized in future RANS simulations of surface waves. (In the above $k$ is the turbulent kinetic energy density, $\unicode[STIX]{x1D714}$ is the specific dissipation rate, and $\unicode[STIX]{x1D700}$ is the dissipation.)