Recreating World-Class Surf Breaks: Applications of Numerical Modeling

In a practical sense, ocean engineering and surf park (or artificial reef) engineering are essentially the same subject matter. The techniques developed and used in conventional ocean engineering are directly applicable to surf park and artificial reef design by providing accurate, quantitative estimations for important surfability characteristics, predicted wave forces, and energy requirements.

Quantitative Analysis

Engineering is critical for any design, and is especially so for emergent technologies and industries as in the case of surf parks. The advantages of performing model analyses of the design wave conditions for any proposed surf park, lagoon or artificial reef is to provide the owner or developer with a basis for design and specification of the final desired feature, based on a quantitative oceanographic engineering approach. There are a number of ocean engineering tools available to assist with this objective. This article will focus on two of these tools.

The Boussinesq Model

During the conceptual design process, a greater degree of efficiency may be achieved by performing a numerical model analysis of selected preliminary pool, lagoon or reef alternatives, using a phase-resolving, shallow water wave model. The model, which was originally developed to investigate the propagation and transformation of waves in complicated shallow coastal regions, works via calculation of a set of Boussinesq wave equations using shallow water assumptions over a rectilinear grid developed from the site topography. The resolution of the model can be increased by adjusting the grid size upon which it is based, which is analogous to the way resolution can be increased with pixel count in an image. It is a very useful model, however it has a limitation in that it is depth-averaged (2-dimensional) and therefore does not simulate the full, complicated process of wave breaking.

Boussinesq modeling is valuable in this case primarily for its capability of realistically simulating complex wave shoaling, focusing, and reflection patterns over relatively wide areas. Wave transformation patterns over gradual slopes, steep reefs, or obstacles are effectively revealed by this model, as well as highlighting potential regions of unwanted reflection from boundaries (surfers see this as undesirable backwash and bounce); both of these are critical elements to control in designing a high quality artificial surf spot.

The analysis will illustrate many of the phenomena of interest in the surf park related to wave quality by producing a calculation-based visualization of wave behavior. The visual results will aid the designer in quickly refining or revising major features of the wave pool or lagoon layout, and indirectly indicate favorable changes in depth or shoreline configuration. The cues obtained from this model will be important to the designer in allowing constructive modifications to the prototype before committing to any particular layout or alternative (see video below).

Boussinesq model analysis additionally provides the designer with useful numerical data, including but not limited to: estimated wave height distribution at any location in the park with given input wave condition; determination of the input wave height required to create a resultant wave height at any specific location; a gross estimate of energy required for specific wave conditions; and, basic circulation patterns driven by the wave-generated currents.

The CFD Model

Taking the analysis a step further, a more detailed investigation of the breaking wave characteristics can be accomplished through a method known as computational fluid dynamics (CFD). This particular CFD model is a three dimensional, high-resolution numerical simulation of the physics behind fluid motion using a volume of fluids (VOF) solution to Reynolds-averaged Navier-Stokes (RANS) equations.

This model is able to simulate the complicated behavior of breaking waves, and reveals critical characteristics of the wave, including breaker height, peel angle, steepness, hollowness of the tube, and other detailed features. The detailed analysis will also highlight potentially negative phenomenon of a prototype wave pool such as the wobbling effects from turbulence or currents produced by previous waves, as well as the effects of backwash from the beach and excessive reflection from the reef or other shoreline boundaries.

Whereas the Boussinesq model is good for investigating the general wave response within a broad area such as an entire surf park, lagoon, or shoreline (scales on the order of thousands of feet), the CFD model is appropriate for up-close examination of areas down to the scale of a single surf spot takeoff zone (on the order of hundreds of feet). Yet even with the reduced area of computation, the high resolution and three-dimensionality add days to the computation cycle for this mode of analysis.

For example, the demonstration wave pool simulation shown above used a model domain composed of more than 4.5 million cells (think 3D pixels, elements roughly a 3-inch cube in size), each of which had to be solved for the governing equations at a time step of approximately once per 0.001 seconds for a total duration of 20 seconds. For every one of the cells at every time step, values for air and water particle velocity, momentum, pressure, and turbulence are calculated. On a standard dual-core desktop computer, this simulation ran for about a week, yet with higher-end quad core machines that time could be reduced to a number days, and likely hours in the near future with expected increases in processing power. Clearly CFD analysis is processor intensive, however, one look at the results shows that it is well worth it.

Added Value

A logical extension of this technology is its application to the design and optimization of wave generation devices, which is likely already employed to some degree. The CFD model is a powerful toolbox for solving complicated problems in the physics of fluid motion, and has the potential to simulate situations involving mechanical or pressure-based displacement modes of wave generation (i.e., wave paddles, travelling wedges, pressurized vaults, and so on). CFD model analysis provides the capability to model the wave from the mechanics of its generation through to its breaking at the pool shoreline or artificial reef. This approach to wave analysis could be a valuable exercise for artificial surf spot development by allowing a quantifiable measure of overall performance and providing the designer with accurate estimations of such variables as wave quality (i.e., height, hollowness, peel angle), gross power requirements for wave production, and dynamic wave forces on submerged structures in the park well before construction.

The Takeaway

In summary, with comprehensive ocean engineering evaluation and model analysis, wave quality and other surf park features can be designed, simulated and optimized before physical testing and construction, giving designers and stakeholders increased options and an added degree of confidence at an early stage in the project, as well as likely cost savings overall.