PhD Dissertation Defense: Simulation- and Model-Based Analysis of Turbulent Wind over Waves
Speaker:
Ziyan Ren, PhD student in Lian Shen's group
Committee Members:
Prof. Lian Shen (Advisor, ME)
Prof. Sungyon Lee (Chair, ME)
Prof. Michele Guala (CEGE)
Prof. Maziar Hemati (AEM)
Abstract:
The interaction between turbulent wind and ocean surface waves plays an important role in the exchange of mass, momentum and heat between the atmosphere and oceans, which is critical to a wide range of applications, including weather forecasting, climate modelling and offshore wind energy. This thesis investigates how travelling water waves influence the air turbulence above them, using simulation-based and model-based analysis.
The first part of the thesis investigates the amplitude modulation phenomenon in wind turbulence overlying water waves, which represents a nonlinear effect of waves on the airflow. Data from wave-phase-resolved large-eddy simulations (LES) of both monochromatic wave and broadband wave field conditions are used. Triple decomposition is applied to the instantaneous airflow field to separate the mean, wave-induced and turbulence components.
It is found that the envelope of the turbulence motions exhibits coherence with the wave field and the envelope structure follows the wave dispersion relation, indicating the existence of wave-induced amplitude modulation embedded in the turbulence. Our analysis shows that amplitude modulation originates from wave–turbulence triadically consistent scales, and manifests itself in the wave-phase variation in turbulence velocity variance. The modulation is further quantified by a transport-based amplitude modulation coefficient, which exhibits similar behaviour across different wave conditions and indicates a phase-leading tendency of the envelope relative to the wave-induced velocity.
In the second part, we develop a Floquet-theory-based resolvent framework to analyse coherent turbulent structures in airflow over water waves. These structures are modelled as a family of Floquet response modes separated by the wavenumber of water waves, kw, which arises from the amplification of harmonic forcing governed by the linearised Navier–Stokes equations. The equations are formulated in a wave-boundary-fitted coordinate system and linearised about the phase-averaged velocity obtained from LES of airflow over monochromatic wave trains, thereby directly incorporating the effects of both the undulating geometry and the wave-induced airflow motions. At representative energetic scales near the wave surface, the most amplified response consists of a dominant central Floquet mode and subdominant sideband modes shifted by kw. Our Floquet–resolvent framework reveals two coexisting mechanisms of wave–turbulence interaction. The central Floquet mode, which contains most of the energy in the response mode, is sustained primarily by intrinsic linear amplification, similar to that in canonical wall-bounded turbulence. Meanwhile, the wave introduces cross-mode coupling, generating the sidebands and producing a wave-phase-dependent amplitude modulation of the response. The key characteristics of the resolvent-predicted envelope are consistent with the observations in LES.
These results provide a new, mechanistic and model-based interpretation of how surface waves modulate overlying airflow turbulence. We believe our findings can benefit the analysis and modelling of turbulence over waves.