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A Growth Mechanism for Topographic Internal Waves Generated by an Oscillatory Flow

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  • 1 Department of Geophysics, Graduate School of Science, Kyoto University, Kyoto, Japan
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Abstract

On the basis of ray tracing of individual waves generated at various phases of the tidal flow, an amplification mechanism is presented for a new class of topographically generated internal waves identified by Nakamura et al., which develop across a broad latitude range and can exist even above the critical latitude where the tidal frequency equals the inertial frequency. The results show that unsteady lee waves are always amplified when the maximum frequency is much smaller than the buoyancy frequency because their phase speeds (amplitudes) are equal (proportional) to the tidal flow speed at their time of generation. Fast mixed tidal–lee waves are also effectively amplified, when the rotation effect is significant. Accordingly, amplification of unsteady lee and fast mixed tidal–lee waves can occur even if the requirements of previous theories (e.g., the critical slope and critical Froude number conditions) are not satisfied. Since the result here covers the generation and amplification processes of topographic internal waves across a broader parameter range than earlier theories, it should contribute to a better understanding of boundary mixing processes, especially in high-latitude regions.

Corresponding author address: Dr. Tomohiro Nakamura, Dept. of Geophysics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan. Email: nakamura@kugi.kyoto-u.ac.jp

Abstract

On the basis of ray tracing of individual waves generated at various phases of the tidal flow, an amplification mechanism is presented for a new class of topographically generated internal waves identified by Nakamura et al., which develop across a broad latitude range and can exist even above the critical latitude where the tidal frequency equals the inertial frequency. The results show that unsteady lee waves are always amplified when the maximum frequency is much smaller than the buoyancy frequency because their phase speeds (amplitudes) are equal (proportional) to the tidal flow speed at their time of generation. Fast mixed tidal–lee waves are also effectively amplified, when the rotation effect is significant. Accordingly, amplification of unsteady lee and fast mixed tidal–lee waves can occur even if the requirements of previous theories (e.g., the critical slope and critical Froude number conditions) are not satisfied. Since the result here covers the generation and amplification processes of topographic internal waves across a broader parameter range than earlier theories, it should contribute to a better understanding of boundary mixing processes, especially in high-latitude regions.

Corresponding author address: Dr. Tomohiro Nakamura, Dept. of Geophysics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan. Email: nakamura@kugi.kyoto-u.ac.jp

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