Instabilities of Finite‐Amplitude Internal Wave Beams

• Published in: Geophysical research letters Vol. 46; no. 13; pp. 7527 - 7535
• Main Authors: Onuki, Y., Tanaka, Y.
• Format: Journal Article
• Language: English
• Published: Washington John Wiley & Sons, Inc 16.07.2019
• Subjects: Amplitude; Amplitudes; Beams (radiation); Bottom topography; Computer simulation; Coriolis force; Coriolis parameters; Dependence; Doppler sonar; Earth; Earth rotation; Energy spectra; Growth rate; Instability; internal tides; Internal waves; Latitude; Ocean circulation; Ocean currents; ocean mixing; Oceans; Parameters; Photosystem I; Stability; Stability analysis; Surveying; Tidal currents; Tidal flow; Tides; Topography (geology); Vertical mixing; Water circulation; Water mixing; Wave dissipation
• ISSN: 0094-8276; 1944-8007
• DOI: 10.1029/2019GL082570

Beam‐like internal waves are commonly generated by tides in the ocean, but their dissipation processes that cause vertical mixing remain poorly understood. Previous studies examined small‐amplitude beams to find that parametric subharmonic instability (PSI) induces latitude‐dependent wave dissipation. Using a novel approach based on Floquet theory, this study analyzes the stability of finite‐amplitude beams over a wide range of parameters. If beam amplitude is small, PSI is indeed the principal mode under the condition f/σ ≤ 0.5, where f is the Coriolis parameter and σ is the beam frequency, and the growth rate is maximum when equality holds. However, as beam amplitude is increased, instability arises even when f/σ>0.5, but the location of maximum instability shifts toward lower f/σ; thus, the latitudinal dependence of instability is significantly altered. Furthermore, the resulting energy spectrum is strongly Doppler shifted to higher frequencies, which therefore distinguishes this configuration from the common cases of PSI. Plain Language Summary When a tidal flow in the ocean passes over bottom topography, energy is radiated away in the form of a locally confined beam wave. Dissipation of this beam wave causes vertical water mixing that drives the ocean's overturning circulation, but the actual dissipation process remains poorly understood. Recent studies have shown that tide‐generated beam waves are dissipated by parametric instability, a phenomenon similar to pumping a playground swing, whose efficiency is controlled by the effect of the Earth's rotation, which varies depending on the latitude. This study introduces a new calculation method that enables the survey of beam wave instability over a wide range of parameters. The results show that the efficiency of instability is highly dependent on beam amplitude and that the conventional explanation of parametric instability is no longer applicable to cases of large beam amplitude. These findings should be incorporated into computer simulation systems of global ocean circulation. Key Points Stability of finite‐amplitude internal wave beams is numerically analyzed over a wide range of parameters based on Floquet theory Increasing the beam amplitude significantly changes the latitudinal dependence of the disturbance growth rate The frequency spectrum generated in a large‐amplitude beam is broad, unlike that produced by parametric subharmonic instability