Research Projects

For this work an adaptive numerical method is employed to simulate shear instabilities in open-ocean internal solitary-like gravity waves. The method is second-order accu- rate, employs block-structured adaptive mesh refinement (AMR), solves the incompressible Navier-Stokes equations, and allows for the simulation of all of the length scales of interest by dynamically tracking important regions with recursively nested finer grids. Simulations are performed that allow us to assess the conditions under which the shear instabilities in the waves occur, including a method to evaluate the critical Richardson number for instability based on the bulk wave parameters. Our results show that, although the Richardson number is well below the canonical value of 1/4 in all simulations, this value is not a sufficient condi- tion for instability, but instead a much lower Richardson number of 0.1 is required. When the Richardson number falls below 0.1, shear instabilities develop and grow into two-dimensional Kelvin-Helmholtz type billows, see Figure 1. The instability mechanism is validated by pre- senting a scaling relationship between the amplitude of the disturbances and the interface thickness. It is demonstrated that the instability is a strong function of the variability of the stratification and shear along the pycnocline. An eigendecomposition of the rate of strain tensor is performed to show that the pycnocline thickness increases within the wave due to pycnocline-normal strain and not due to diffusion, which has important ramifications for stability. A three-dimensional simulation is presented in Figure 2 to demonstrate that the primary instability is two-dimensional, and that secondary, three-dimensional instabilities occur thereafter and lead to strong dissipation and mixing.

This project is funded by a the ONR Physical Oceanography program and the NSF Mathematical Sciences Postdoctoral Research Fellowship program.

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