On the structure of the internal wave field: the impact of the distribution of shear and strain variance in wavenumber-frequency space on mixing estimates

Abstract

Data from an archive of McLane Moored Profiler (MP) deployments are used to investigate the role of internal waves, and in general physical processes occupying this frequency range, on the dissipation of kinetic energy and to study how these processes work to shape the spectral characteristics of the wavefield. The data used come from 5 separate field programs, and by analyzing them as a set, provides the opportunity to not only compare and contrast an unprecedented range of different forcing regimes, but also supports the discovery of unique observations of physical processes at individual sites. This dissertation is composed of four separate chapters that address different aspects of this idea. First, two records, one to the North (MP1) and one to the South (MP2), of Mindoro strait, which lies between the South China Sea and the Sulu Sea, were used to study the processes driving mixing in the Strait. The records are dominated by near inertial variability and internal tides at both the diurnal and semidiurnal frequencies. Analysis of the velocity records from MP1 reveals suggestive evidence for the presence of parametric subharmonic instability of the diurnal tide as well as curious rectilinear bottom trapped near inertial waves. Diffusivities estimated via Thorpe scale analysis at MP1 reveal weak mixing over much of the water column that increases nearly an order of magnitude near the bottom and is strongly tied to the tides. Average mixing rates are found to be insufficient to produce observed changes in water mass properties suggesting additional processes are at play. Second, variability in the shear to strain ratio (R$_\omega$) is investigated with the goal of understanding the factors that influence R$_\omega$ variability, quantifying its time and space scales, and determining how variability impacts estimates of parameterized diffusivity. Time mean R$_\omega$ from each of the sites spans a range from 1 to 10 and within each record, temporal variability around the mean is sufficient to produce a factor of 2-3 change in parameterized diffusivity. Vertical structure of R$_\omega$ appears strongly tied to topographic properties and wind forcing. In general, sites can be categorized as having R$_\omega$ controlled by shear or by strain. Finally, we find that with sufficient characterization of a site, a predictive model of R$_\omega$ can be made that reduces error in R$_\omega$ values relative to assuming R$_\omega=3$ by over 30\%. Third, aspects of the the wavenumber frequency spectrum are explored. We find that while a separable representation of the spectrum can be made that has the same level of variance, the observed structure cannot be modeled with a single form in vertical wavenumber. Narrow band peaks attenuate to match the background continuum by wavenumbers of approximately $k=10^{-2}$ cpm. At frequencies $\omega<5$ cpd and wavenumbers $k>10^{-2}$ cpm, we find that the spectrum is nearly white in frequency and that nearly all frequency bands have collapsed to this same structure. Background continuum spectral levels of velocity vary as a linear function of $N$. The background continuum spectrum, with peaks removed, displays significant deviations from GM at low wavenumbers. Addition of the narrow band peaks improves the consistency of the total spectrum with GM at low wavenumbers implying that the often observed GM spectral shape is dependent on the presence of internal tides. Fourth, the impact of the inherent sawtooth sampling pattern in time and depth space of profiling instruments on resolved variance is examined through the use of virtual instruments profiling through an idealized wavefield. By creating a wavefield that has an exactly GM velocity spectrum, the variance resolved by various profiling schemes can be determined. We find that variance resolved, as computed from a spectrum from gridded profile data, can be represented as a linear function of mean time between profile and latitude. A functional dependence is defined such that one can estimate a priori the impact of their sampling patterns. Additionally, the spectral response and bandwidth of the half inertial differencing operation is examined. It is found that the while half inertial differencing does eliminate even multiples of the inertial frequency and alias in odd multiples, the pass band of the filter is quite broad meaning there is potential for significant aliasing of non inertial signals into the inertial band estimates from the half inertial difference filter.