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Dissipative Losses in Nonlinear Internal Waves Propagating across the Continental Shelf

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  • 1 College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon
  • | 2 Graduate School of Oceanography, University of Rhode Island, Kingston, Rhode Island
  • | 3 College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon
  • | 4 Scripps Institution of Oceanography, La Jolla, California
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Abstract

A single nonlinear internal wave tracked more than 100 wavelengths across Oregon’s continental shelf over a 12-h period exhibited nearly constant wave speed, c = 0.75 m s−1, and amplitude, a = 15 m. The wavelength L gradually decreased from 220 m in 170-m water depth to 60 m in 70-m water depth. As the water shallowed beyond 50 m, the wave became unrecognizable as such. The total energy decreased from 1.1 to 0.5 MJ m−1. The rate at which wave energy was lost, −dE/dt = 14 [7, 22] W m−1, was approximately equal to the energy lost to turbulence dissipation, ρε = 10 [7, 14] W m−1, as inferred from turbulence measurements in the wave cores plus estimates in the wave-induced bottom boundary layer. The approximate balance, dE/dt = −ρε, differs from the solibore model of Henyey and Hoering in which the potential energy across the wave balances ρε. However, other evidence suggests that the wave evolved from a solibore-like state to a dissipative solitary wavelike state over the observed propagation path.

Corresponding author address: J. N. Moum, College of Oceanic and Atmospheric Sciences, Oregon State University, COAS Admin. Bldg. 104, Corvallis, OR 97331-5503. Email: moum@coas.oregonstate.edu

Abstract

A single nonlinear internal wave tracked more than 100 wavelengths across Oregon’s continental shelf over a 12-h period exhibited nearly constant wave speed, c = 0.75 m s−1, and amplitude, a = 15 m. The wavelength L gradually decreased from 220 m in 170-m water depth to 60 m in 70-m water depth. As the water shallowed beyond 50 m, the wave became unrecognizable as such. The total energy decreased from 1.1 to 0.5 MJ m−1. The rate at which wave energy was lost, −dE/dt = 14 [7, 22] W m−1, was approximately equal to the energy lost to turbulence dissipation, ρε = 10 [7, 14] W m−1, as inferred from turbulence measurements in the wave cores plus estimates in the wave-induced bottom boundary layer. The approximate balance, dE/dt = −ρε, differs from the solibore model of Henyey and Hoering in which the potential energy across the wave balances ρε. However, other evidence suggests that the wave evolved from a solibore-like state to a dissipative solitary wavelike state over the observed propagation path.

Corresponding author address: J. N. Moum, College of Oceanic and Atmospheric Sciences, Oregon State University, COAS Admin. Bldg. 104, Corvallis, OR 97331-5503. Email: moum@coas.oregonstate.edu

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