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Open Access Publications from the University of California

Turbulence and internal waves in tidal flow over topography

  • Author(s): Gayen, Bishakhdatta
  • et al.
Abstract

Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) are used to investigate and quantify the dynamical processes underlying turbulence formed during the generation of an internal wave beam and its subsequent interaction with a realistically stratified upper ocean. As a part of the thesis, a three-dimensional mixed spectral/finite difference code was developed, parallelized, validated and employed to study several geophysical problems relevant to internal tide generation and its nonlinear breaking. The thesis research has four phases. In the first phase, a study of a stratified non- sloping bottom boundary layer under an oscillating tide was completed. The focus is on the boundary layer response to an external stratification based on LES. Flow instabilities and turbulence in the bottom boundary layer are found to excite internal gravity waves that propagate away into the ambient with phase angle varying over the tidal cycle. Subsequent studies as part of the second phase consider a stratified oscillating flow over a sloping bottom wall to mimic the generation of baroclinic internal waves (IW) from the tide-topography interaction at a model continental slope. The DNS study shows transition to turbulence, which is present along the entire extent of the near-critical region of the slope in the regime of low background excursion number and Reynolds number. The transition is found to be initiated by a convective instability, which is closely followed by shear instability. The peak value of the near-bottom velocity is found to increase with increasing length of the critical region of the topography. The scaling law that is observed to link the near-bottom peak velocity to slope length is explained by an analytical boundary layer solution that incorporates an empirically obtained turbulent viscosity. As an extension of the second phase, the objective of the third phase work is to numerically model a near-bottom beam with a larger, more realistic width using LES and characterize its turbulence statistics. Maximum turbulent kinetic energy and dissipation rate are found just after the zero velocity point when flow reverses from downslope to upslope motion. The phasing and other characteristics of the turbulent mixing in the present simulations show remarkable similarity with that observed off Kaena Ridge in Hawaii taken during the hawaiian ocean mixing experiment (HOME), and may be explained by the beam-scale convective overturns found here. The objective of the final phase is to understand the interaction process between an IW beam and an upper ocean pycnocline and to further characterize the cascade to small scales in the context of IW beam degradation observed in the ocean

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