Stokes Drift and Meshless Wave Modeling

This dissertation is loosely organized around efforts to improve vertical ocean mixing in global climate models and includes an in-depth analysis of Stokes drift, optimization of a new global climate model wave component, and development of a meshless spectral wave model. Stokes drift (hereafter SD) is an important vector component that appears often in wave-averaged dynamics. Mathematically, SD is the mean difference between Eulerian and Lagrangian velocities and intuitively can be thought of as the near-surface ocean current induced from wave motion. Increasingly, spectral wave models are being used to calculate SD globally. These models solve a 5D wave action balance equation and typically require large computational resources to make short to medium-range forecasts of the sea state. In the first part, a hierarchy of SD approximations are investigated and new approximations that remove systematic biases are derived. A new 1D spectral approximation is used to study the effects of multidirectional waves and directional wave spreading on SD. It is shown that these effects are largely uncorrelated and affect both the magnitude and direction of SD in a nonlinear fashion that is sensitive with depth. In the second part, efforts to add a wave model component to the NCAR Community Earth System Model are discussed. This coupled component will serve as the backbone to a new Langmuir mixing parameterization and uses a modified version of NOAA WAVEWATCH III (a third-generation spectral wave model). In addition, the governing wave action balance equation is reviewed and several variations are derived and formulated. In the third part, construction of a monochromatic spectral wave model using RBF-generated finite differences is described. Several numerical test cases are conducted to measure performance and guide further development. In kinematic comparisons with WAVEWATCH III, the meshless prototype is approximately 70–210 times more accurate and uses a factor of 12 to 17 less unknowns

Remote monitoring of shallow turbulent flows based on the Doppler spectra of airborne ultrasound

Traditional flow monitoring techniques where the sensors are immersed in the flow are costly, and often need frequent maintenance. Non-contact measurement techniques can be used to determine the hydraulic conditions of free surface flows based on a characterisation of the air-water interface. They are robust, relatively cheap, and can be safely operated, but their applications in shallow turbulent flows such as rivers and open channels are limited by the limited understanding of the free surface roughness behaviour. This research aims at characterising the rough moving surface of shallow turbulent water flows and its interaction with airborne acoustic waves. The purpose of this work is to facilitate the development of accurate and reliable non-contact sensors that can measure the mean surface velocity of shallow turbulent flows from the Doppler spectrum of airborne backscattered ultrasonic waves. The dynamics of the free surface were characterised experimentally in a laboratory flume with a homogeneously rough flat bed, over a range of subcritical flow conditions. The three-dimensional patterns on the free surface can be represented by a model of gravity-capillary waves with random phase. These patterns and their statistics are dominated by the spatial and temporal scales of the stationary waves generated by the interaction with the rough bed in all conditions where the mean surface velocity is larger than the minimum phase velocity of gravity-capillary waves. When the mean surface velocity is smaller than the minimum phase velocity of gravity-capillary waves, the surface shows patterns that travel at the mean surface velocity and can be generated by the non-resonant interaction with turbulence inside the flow. In these conditions, the effects of coherent turbulent structures on the surface dynamics are negligible. A simplified linear model of the free surface dynamics was implemented in two different models of acoustic scattering based on the Kirchhoff approximation. The numerical predictions of the acoustic Doppler spectra in the backscattering and in the forward scattering configuration were compared with the experimental measurements in the same flow conditions. The comparison allows the rigorous interpretation of the measured Doppler spectra, and helps to identify the factors that link them to the behaviour of the free surface. The results can inform the design of more reliable non-contact measurement sensors with applications in shallow turbulent flows. There are important implications for modelling of the interaction between a homogeneously rough bed and the free surface, and for the study of transport and mixing phenomena near the interface