Spectral Analysis of the Efficiency of Vertical Mixing in the Deep Ocean due to Interaction of Tidal Currents with a Ridge Running down a Continental Slope

¹ Pacific Northwest National Laboratory, Richland, WA 99352, USA
² School of Geosciences, Department of Mathematics and Statistics University of South Florida, Tampa, FL
³ Lead Mathematician, Applied Statistics Lab, GE Global Research 1 Research Circle Niskayuna, NY 12309

^⋆ Corresponding author. E-mail: ibrranis@gmail.com

Abstract

Efficiency of mixing, resulting from the reflection of an internal wave field imposed on the oscillatory background flow with a three-dimensional bottom topography, is investigated using a linear approximation. The radiating wave field is associated with the spectrum of the linear model, which consists of those mode numbers n and slope values α, for which the solution represents the internal waves of frequencies ω = nω₀ radiating upwrad of the topography, where ω₀ is the fundamental frequency at which internal waves are generated at the topography. The effects of the bottom topography and the earth’s rotation on the spectrum is analyzed analytically and numerically in the vicinity of the critical slope

α_n,θ^c = arcsin (n ²ω₀²-f ² / N ²-f ²) ^1/2

which is a slope with the same angle to the horizontal as the internal wave characteristic. In this notation, θ is latitude, f is the Coriolis parameter and N is the buoyancy frequency, which is assumed to be a constant, which corresponds to the uniform stratification.