Oceanic internal tides: do they get phased at the Equator?

TL;DR

This study addresses the observed loss of phase coherence of the lunar semidiurnal M2 internal tide near the Equator by developing a linear, modal-decomposition model on an equatorial beta plane that includes equatorial jets. The authors employ vertical mode decomposition and ray tracing to analyze how a zonal jet, whether vertically uniform or vertically sheared, interacts with a mode-1 M2 wavepacket, using Dedalus for numerical solutions. They find that a vertically uniform jet can strongly redirect or reflect the wavepacket, while a vertically sheared jet excites higher vertical modes (e.g., mode 3) with slower phase and group speeds, causing energy transfer and later return to mode 1 but with a phase shift that can produce incoherence in the surface signal. These results offer a plausible mechanism for the observed M2 altimetry incoherence and highlight the role of wave-mean flow interactions in modulating energy distribution and coherence, with implications for interpreting equatorial ocean dynamics and guiding future studies with realistic stratification and jet profiles.

Abstract

Low-mode baroclinic tides play a major role in ocean dynamics, especially for energy redistribution and deep ocean mixing. These internal waves, generated by tidal flow over submarine topography, can propagate for thousands of kilometres across ocean basins, and become unstable through wave-mean flow or wave-wave interactions. Satellite observations of internal tides have shown that part of their lunar semidiurnal (M2) altimetry signal loses phase coherence in equatorial regions, thus affecting how we interpret their dynamics and energy distribution (Buijsman et al. 2017). We investigate the interaction of a baroclinic M2 internal tide wavepacket with an equatorial zonal jet, possibly of any horizontal or vertical structure. The dynamics of the low modes are explored as well as the potential excitation of higher vertical modes and how these interactions can generate incoherences in the baroclinic tide signal. We develop an idealized linear model using modal decomposition (Kelly et al. 2016), which is solved using Dedalus, to study the dynamics of a mode 1 M2 internal wavepacket on an equatorial beta plane. A zonal jet, with a uniform or a sheared vertical structure, is added at the equator to investigate potential wave-mean flow interaction. We find that a vertically uniform zonal jet affects the propagation of the mode 1 wavepacket. Depending on the strength of the jet, this can cause total reflection or strong distortion of the wavepacket. In contrast, a wavepacket entering a vertically sheared jet shows energy scattering into higher modes, which have lower phase and group speeds, shorter wavelengths, and are thus more susceptible to dissipation (and critical layers for non-uniform stratification). As the wavepacket exits the jet, reverse energy transfer occurs and the phase speed difference between the modes may explain part of the phase incoherence observed in altimetry data.

Figures (20)

• Figure 1: Vertical structure of the zonal equatorial current, computed using the LLC4320 configuration of the Massachusetts Institute of Technology general circulation model (MITgcm, Marshalletal1997)
• Figure 2: Three first vertical structure functions, $\Phi_{n}$, for $\overline{N_0}^{2}=1\times10^{-4}$ s$^{-2}$ and H$=5000$m.
• Figure 3: Schematics of the evolution of the wavepacket when interacting with a uniform jet ignoring the $\beta$ effect. Initial situation is displayed in the center, with wavenumbers drawn in grey arrows. In the upper part, the wavepacket is incident upon a positive horizontal shear so that $k_y$ increases while $k_x$ stays fixed (black arrows), ultimately reacting to a critical layer where $k_{y}\rightarrow\infty$. In the lower part, the wavepacket is incident upon a negative horizontal shear and $k_y$ decreases while $k_x$ stays fixed (black arrows), ultimately leading to a total reflection of the wavepacket where $k_{y}\rightarrow 0$.
• Figure 4: Initial condition in a typical simulation: the wavepacket is launched from the position $(x_0, y_0)$ in the southern hemisphere at an angle $\theta$ from north. Jet limits at $y\pm2$W are shown by orange lines, sponge layers limits are shown by red dashed lines.
• Figure 5: Zonal velocity (m$\cdot$s$^{-1}$) of vertical mode 1 M2 internal tide. The wavepacket is launched from $(x_0, y_0)=(-0.5\,L_x, -0.5\,L_y)$ with $\theta=\pi/4$.