3:30 PM - 5:00 PM
[ACG38-P06] Development of wave-resolving two-phase numerical model for the study of microscale air-sea interaction
Keywords:Numerical model, Air-sea interaction, Ocean surface waves, Direct numerical simulation
The interaction of the atmosphere and the ocean, such as momentum exchange, is an essential part of the climate system. From a macroscopic point of view, the bulk formula is commonly used to model the momentum transfer from the atmosphere to the ocean. Its coefficient has been estimated from turbulence observations in the marine atmospheric boundary layer (MABL). However, the observed momentum flux shows a large scatter from the bulk formula. One of the reasons for such deviations is the impact of ocean swells, which are known to alter effective roughness and cause upward momentum transfer. However, the understanding of the swell-wind interaction processes is still limited.
To describe the processes from a microscopic viewpoint, numerical models that can simulate wave-influenced MABL turbulence are valuable.
In this study, we developed a numerical solver for the two-phase fluid motion to understand microscale air-sea interaction processes especially related to swells. The incompressible Navier-Stokes equation is solved for air and water confined in a rectangular domain with flat walls at the top and bottom, and doubly periodic horizontal boundaries. Their interface is assumed to be one-valued, so a turn-over of the water surface by wave breaking is not allowed. The sigma-coordinate-like surface-following coordinate is introduced for each phase.
The equations are solved following the numerical scheme of a previously developed free-surface model (Fujiwara, Yoshikawa, and Matsumura, 2020, Ocean Modelling). There, the instantaneous pressure variable is defined at cell centers, and they follow a Poisson equation demanded from the non-divergence of velocity tendency. In the present model, the pressure variable is located at the air-water interface in addition to cell centers. This additional degree of freedom allows us to demand strict continuity at the interface. Thanks to this feature, an accurate evaluation of air-water momentum and energy transfer are enabled. Furthermore, an adjunctive numerical formulation is derived that can simulate the air-side motion over a prescribed surface elevation. These two formulations allow us to study the sensitivity to the coupling between wind, wave, and surface currents.
The accuracy of the present model is studied in some inviscid cases where the analytic solutions are known. The phase speed of linear and weakly nonlinear interfacial gravity waves was well reproduced. Also, the growth rate of unstable waves such as Rayleigh-Taylor and Kelvin-Helmholtz instabilities is accurately reproduced with modest spatial resolution. Furthermore, the model could reproduce the growth rate of the monochromatic wind waves described by laminar Miles instability (Miles 1959). The effect of viscosity such as the attenuation of interfacial waves and momentum transfer from waves to surface currents is to be examined.
To describe the processes from a microscopic viewpoint, numerical models that can simulate wave-influenced MABL turbulence are valuable.
In this study, we developed a numerical solver for the two-phase fluid motion to understand microscale air-sea interaction processes especially related to swells. The incompressible Navier-Stokes equation is solved for air and water confined in a rectangular domain with flat walls at the top and bottom, and doubly periodic horizontal boundaries. Their interface is assumed to be one-valued, so a turn-over of the water surface by wave breaking is not allowed. The sigma-coordinate-like surface-following coordinate is introduced for each phase.
The equations are solved following the numerical scheme of a previously developed free-surface model (Fujiwara, Yoshikawa, and Matsumura, 2020, Ocean Modelling). There, the instantaneous pressure variable is defined at cell centers, and they follow a Poisson equation demanded from the non-divergence of velocity tendency. In the present model, the pressure variable is located at the air-water interface in addition to cell centers. This additional degree of freedom allows us to demand strict continuity at the interface. Thanks to this feature, an accurate evaluation of air-water momentum and energy transfer are enabled. Furthermore, an adjunctive numerical formulation is derived that can simulate the air-side motion over a prescribed surface elevation. These two formulations allow us to study the sensitivity to the coupling between wind, wave, and surface currents.
The accuracy of the present model is studied in some inviscid cases where the analytic solutions are known. The phase speed of linear and weakly nonlinear interfacial gravity waves was well reproduced. Also, the growth rate of unstable waves such as Rayleigh-Taylor and Kelvin-Helmholtz instabilities is accurately reproduced with modest spatial resolution. Furthermore, the model could reproduce the growth rate of the monochromatic wind waves described by laminar Miles instability (Miles 1959). The effect of viscosity such as the attenuation of interfacial waves and momentum transfer from waves to surface currents is to be examined.