11:15 AM - 11:30 AM
[ACG47-09] Numerical simulation of breaking waves by weakly compressible two-phase model
Keywords:wind wave, gas-liquid two phase flow, numerical simulation
The ocean we see always has surface waves. These waves, called wind waves, are generated and developed by receiving energy and momentum from the wind, and transport energy and momentum into the ocean currents through wave breaking. Since these waves are the boundary between the atmosphere and ocean, the atmosphere and ocean exchange momentum, heat, and materials through wind waves. Therefore, understanding interactions through wind waves is essential for understanding and predicting atmospheric and oceanic phenomena.
In the exchange process between the atmosphere and ocean, momentum exchange is represented by wind stress τ. This τ is often expressed as τ=ρCDU102 (CD is drag coefficient, U10 is the wind speed at z = 10 m above the sea surface) in coupled atmosphere-ocean models. CD depends on wave conditions, but many parameterizations are dependent on wind speed for practical purposes. Most of them have a tendency for CD to increase with wind speed, but recent studies have shown experimental results that CD saturates (Takagaki et al. 2012) and observational results that CD decreases (Shimura et al. 2024) during high winds, and the knowledge of drag coefficients for high winds is not unified.
In addition, the effect of breaking waves cannot be ignored. Takagaki et al. (2012) interpreted that wave breaking under intense winds suppresses the development of wind waves, which saturates CD by flattening the sea surface. Yang et al. (2018) performed numerical simulations of breaking waves under favorable winds and showed that plunging breakers tend to accelerate the airflow. Thus, wave breaking is one of the key determinants of momentum transport between the atmosphere and ocean.
Investigating momentum transport during wave breaking from observations and experiments is difficult due to the limitations of measurement techniques. Therefore, reproduction and quantitative investigation using numerical simulations that can represent wave breaking is expected. However, the computational resources are insufficient to precisely investigate the impact of wave breaking on air currents. A particular bottleneck in wave breaking calculations is the solution of the elliptic equation of pressure obtained from the incompressible condition. This elliptic equation is difficult to converge for gas-liquid two-phase flows with large density ratios, and much time is spent on calculating this equation. To overcome this problem, a method called weakly compressible scheme (Matsushita & Aoki 2021, etc.) has recently been proposed. This method introduces compressibility and reduces the sound velocity, allowing for completely explicit and fast calculation. This method may solve the problem of computational resources in wave breaking calculations.
Based on the above, in this study we constructed a weakly compressible model and performed numerical simulations of wave breaking. We employed the VOF method and the phase-field method for interface-capturing methods and compared the two methods. Simulations of the plunging and spilling breakers showed that the plunging breaker has a large effect on the airflow, while the spilling breaker has a smaller effect on the airflow, consistent with previous studies. Both the VOF and phase-field methods reproduced the breaking waves well. In the VOF method, tiny water droplets were suspended in the gas phase. The phase-field method tended to overestimate momentum transport due to the gas-liquid diffusive interface with a width of several grids. We also conducted numerical experiments with different values of the speed of sound to evaluate the validity of the weakly compressible approximation. In the presentation, we will report details of these results.
In the exchange process between the atmosphere and ocean, momentum exchange is represented by wind stress τ. This τ is often expressed as τ=ρCDU102 (CD is drag coefficient, U10 is the wind speed at z = 10 m above the sea surface) in coupled atmosphere-ocean models. CD depends on wave conditions, but many parameterizations are dependent on wind speed for practical purposes. Most of them have a tendency for CD to increase with wind speed, but recent studies have shown experimental results that CD saturates (Takagaki et al. 2012) and observational results that CD decreases (Shimura et al. 2024) during high winds, and the knowledge of drag coefficients for high winds is not unified.
In addition, the effect of breaking waves cannot be ignored. Takagaki et al. (2012) interpreted that wave breaking under intense winds suppresses the development of wind waves, which saturates CD by flattening the sea surface. Yang et al. (2018) performed numerical simulations of breaking waves under favorable winds and showed that plunging breakers tend to accelerate the airflow. Thus, wave breaking is one of the key determinants of momentum transport between the atmosphere and ocean.
Investigating momentum transport during wave breaking from observations and experiments is difficult due to the limitations of measurement techniques. Therefore, reproduction and quantitative investigation using numerical simulations that can represent wave breaking is expected. However, the computational resources are insufficient to precisely investigate the impact of wave breaking on air currents. A particular bottleneck in wave breaking calculations is the solution of the elliptic equation of pressure obtained from the incompressible condition. This elliptic equation is difficult to converge for gas-liquid two-phase flows with large density ratios, and much time is spent on calculating this equation. To overcome this problem, a method called weakly compressible scheme (Matsushita & Aoki 2021, etc.) has recently been proposed. This method introduces compressibility and reduces the sound velocity, allowing for completely explicit and fast calculation. This method may solve the problem of computational resources in wave breaking calculations.
Based on the above, in this study we constructed a weakly compressible model and performed numerical simulations of wave breaking. We employed the VOF method and the phase-field method for interface-capturing methods and compared the two methods. Simulations of the plunging and spilling breakers showed that the plunging breaker has a large effect on the airflow, while the spilling breaker has a smaller effect on the airflow, consistent with previous studies. Both the VOF and phase-field methods reproduced the breaking waves well. In the VOF method, tiny water droplets were suspended in the gas phase. The phase-field method tended to overestimate momentum transport due to the gas-liquid diffusive interface with a width of several grids. We also conducted numerical experiments with different values of the speed of sound to evaluate the validity of the weakly compressible approximation. In the presentation, we will report details of these results.