Toward Regional Characterizations of the Oceanic Internal Wavefield

Many major oceanographic internal wave observational programs of the last 4 decades are reanalyzed in order to characterize variability of the deep ocean internal wavefield. The observations are discussed in the context of the universal spectral model proposed by Garrett and Munk. The Garrett and Munk model is a good description of wintertime conditions at Site-D on the continental rise north of the Gulf Stream. Elsewhere and at other times, significant deviations in terms of amplitude, separability of the 2-D vertical wavenumber - frequency spectrum, and departure from the model's functional form are noted. Subtle geographic patterns are apparent in deviations from the high frequency and high vertical wavenumber power laws of the Garrett and Munk spectrum. Moreover, such deviations tend to co-vary: whiter frequency spectra are partnered with redder vertical wavenumber spectra. Attempts are made to interpret the variability in terms of the interplay between generation, propagation and nonlinearity using a statistical radiative balance equation. This process frames major questions for future research with the insight that such integrative studies could constrain both observationally and theoretically based interpretations

Weighted-norm preconditioners for a multilayer tide model

We derive a linearized rotating shallow water system modeling tides, which can be discretized by mixed finite elements. Unlike previous models, this model allows for multiple layers stratified by density. Like the single-layer case [R. C. Kirby and T. Kernell, Comput. Math. Appl., 82 (2021), pp. 212–227], a weighted-norm preconditioner gives a (nearly) parameter-robust method for solving the resulting linear system at each time step, but the all-to-all coupling between the layers in the model poses a significant challenge to efficiency. Neglecting the inter-layer coupling gives a preconditioner that degrades rapidly as the number of layers increases. By a careful analysis of the matrix that couples the layers, we derive a robust method that requires solving a reformulated system that only involves coupling between adjacent layers. Numerical results obtained using Firedrake [F. Rathgeber et al., ACM Trans. Math. Software, 43 (2016), 24] confirm the theory

Long nonlinear internal waves

Author Posting. © Annual Reviews, 2006. This article is posted here by permission of Annual Reviews for personal use, not for redistribution. The definitive version was published in Annual Review of Fluid Mechanics 38 (2006): 395-425, doi:10.1146/annurev.fluid.38.050304.092129.Over the past four decades, the combination of in situ and remote sensing observations has demonstrated that long nonlinear internal solitary-like waves are ubiquitous features of coastal oceans. The following provides an overview of the properties of steady internal solitary waves and the transient processes of wave generation and evolution, primarily from the point of view of weakly nonlinear theory, of which the Korteweg-de Vries equation is the most frequently used example. However, the oceanographically important processes of wave instability and breaking, generally inaccessible with these models, are also discussed. Furthermore, observations often show strongly nonlinear waves whose properties can only be explained with fully nonlinear models.KRH acknowledges support from NSF and ONR and an Independent Study Award from the Woods Hole Oceanographic Institution. WKM acknowledges support from NSF and ONR, which has made his work in this area possible, in close collaboration with former graduate students at Scripps Institution of Oceanography and MIT

Internal tide generation by tall ocean ridges

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2009Internal tides are internal waves of tidal period generated by tidal currents flowing over submarine topography. Tall ridges that are nominally two-dimensional (2-D) are sites of particularly strong generation. The subsequent dissipation of internal tides contributes to ocean mixing, thereby playing an important role in the circulation of the ocean. Strong internal tides can also evolve into internal wave solitons, which affect acoustic communication, offshore structures and submarine navigation. This thesis addresses the generation of internal tides by tall submarine ridges using a combined analytical and experimental approach. The first part of the thesis is an experimental investigation of a pre-existing Green function formulation for internal tide generation by a tall symmetric ridge in a uniform density stratification. A modal decomposition technique was developed to characterize the structure of the experimental wave fields generated by 2D model topographies in a specially configured wave tank. The theory accurately predicts the low mode structure of internal tides, and reasonably predicts the conversion rate of internal tides infinite tidal excursion regimes, for which the emergence of non-linearities was notable in the laboratory. In the second part of the thesis, the Green function method is advanced for asymmetric and multiple ridges in weakly non-uniform stratifications akin to realistic ocean situations. A preliminary investigation in uniform stratification with canonical asymmetric and double ridges reveals asymmetry in the internal tide that can be very sensitive to the geometric configuration. This approach is then used with realistic topography and stratification data to predict the internal tide generated by the ridges at Hawaii and at the Luzon Strait. Despite the assumption of two-dimensionality, there is remarkably good agreement between field data, simulations and the new theory for the magnitude, asymmetry and modal content of the internal tide at these sites. The final part of the thesis investigates the possibility of internal wave attractors in the valley of double-ridge configurations. A one-dimensional map is developed to identify the existence and stability of attractors as a function of the ridge geometry. The Green function method is further advanced to include a viscous correction to balance energy focusing and dissipation along an attracting orbit of internal wave rays, and very good agreement is obtained between experiment and theory, even in the presence of an attractor.My Ph. D. and the work in this thesis have been generously funded by the National Science Foundation under grants OCE 0645529 and OCE 04-25283 and the Office of Naval Research under grants N00014-08-0390, N00014-05-1-0573 and N00014-09-0282