Effects of Stratification on Shoaling Internal Tidal Bores

Abstract

AbstractIdealized simulations of a shoaling internal tide on a gently sloping, linear shelf provide a tool to investigate systematically the effects of stratification strength, vertical structure, and internal wave amplitude on internal tidal bores. Simulations that prescribe a range of uniform or variable stratifications and wave amplitudes demonstrate a variety of internal tidal bores characterized by shoreward propagating horizontal density fronts with associated overturning circulations. Qualitatively, we observe three classes of solution: 1) bores, 2) bores with trailing wave trains, and 3) no bores. Very strong stratification (small wave) or very weak stratification (large wave) inhibits bore formation. Bores exist in an intermediate zone of stratification strength and wave amplitude. Within this intermediate zone, wave trains can trail bores if the stratification is relatively weak or wave amplitude large. We observe three types of bore that arise dependent on the vertical structure of stratification and wave amplitude: 1) a ‘backward’ downwelling front (near uniform stratification, small to intermediate waves), 2) a ‘forward’ upwelling front (strong pycnocline, small to large waves), and 3) a ‘double’ bore with leading up and trailing downwelling front (intermediate pycnocline, intermediate to large waves). Visualization of local flow structures explores the evolution of each of these bore-types. A frontogenetic diagnostic framework elucidates the previously undiscussed, yet, universal role of vertical straining of a stratified fluid that initiates formation of bores. Bores with wave trains exhibit strong non-hydrostatic dynamics. The results of this study suggest that mid-to-outer shelf measurements of stratification and cross-shore flow can serve as proxies to indicate the class of bore further inshore.