Fully nonlinear, nonhydrostatic simulations by Xie, He, Chen, Xu and Cai (2015) showed that an isolated mesoscale eddy in the northeastern South China Sea distorts the long front of an internal solitary wave (ISW), focusing wave energy onto concave front fragments and scattering it from convex ones, with amplitude modulation reaching a factor of about two, while linear ray tracing reproduces the eddy-crossing stages but not the subsequent stage-III behavior in which accumulated energy and distortion are gradually released as the ISW propagates away from the eddy. The open problem comprises three linked aspects: (1) the nonlinear dynamical mechanism of this post-eddy self-adjustment, which lies beyond ray-based diagnosis; (2) quantitative, data-constrained reproduction of the observed distortion magnitude and trailing wave packets, replacing the 2015 study's qualitative comparison with May 2001 satellite observations; and (3) the combined influence of eddies with the other simultaneously active regional factors — variable Luzon Strait generation, tides, Kuroshio intrusion, and bottom topography.

Background

Internal solitary waves (ISWs) are large-amplitude waves that propagate along the pycnocline — the stable density interface of the stratified ocean — balancing nonlinearity against internal dispersion, so that a wave of depression or elevation keeps its shape over long distances. The northern South China Sea (SCS) hosts the largest ISWs observed in the world ocean: barotropic tides oscillating over the two ridges of the Luzon Strait (the passage between Taiwan and Luzon through which the Kuroshio — the strong western boundary current of the North Pacific — intrudes into the sea) shed westward-propagating internal tide energy that steepens into ISWs; these cross the deep basin as rank-ordered packets (a succession of waves of decreasing amplitude and spacing) with crests hundreds of kilometers long, and are routinely imaged by synthetic aperture radar (SAR), which sees their slick-like signatures on the sea surface.

Mesoscale eddies are coherent ocean vortices of roughly 50–500 km radius that persist for weeks to months with swirl velocities up to order 1 m s−11\,\mathrm{m\,s^{-1}}; both cyclonic (counterclockwise in the Northern Hemisphere) and anticyclonic (clockwise) eddies are ubiquitous in the northern SCS, many spawned by Kuroshio-loop instability. Because the phase speed of a mode-1 internal wave (the gravest vertical baroclinic eigenmode, with no internal zero crossing in its vertical displacement structure) depends on the background current and stratification, an eddy's spatially varying velocity and density fields differentially accelerate and retard segments of a long ISW crest, refracting and distorting the front.

Motivated by SAR and satellite-altimeter observations from May 2001 showing a distorted ISW front northwest of an anticyclonic eddy together with an unexplained short-crested trailing packet, Xie et al. (2015) performed three-dimensional simulations with the MITgcm (a fully nonlinear, nonhydrostatic ocean model, i.e., one whose equations retain vertical accelerations so that steep internal waves are resolved rather than assumed hydrostatic) of a long-crested ISW crossing an idealized, stationary, isolated Gaussian eddy over a flat 1000 m bottom. They organized the interaction into three stages by the wave's position relative to the eddy center: during stage I the front first distorts under the eddy's lateral current shear; in stage II, past the eddy center, along-front energy and wave characteristics become strongly uneven; in stage III, after the ISW has propagated away from the eddy and direct eddy forcing has ended, the accumulated distortion and energy are gradually released through self-adjustment. Energy is focused onto concave front fragments and scattered from convex ones, so the modulated amplitude in the focusing region can reach about twice the incident amplitude while the scattering region loses more than half of it, and behind an anticyclonic focusing region an internal gravity wave steepens and breaks into a secondary rank-ordered trailing packet. A linear ray-tracing diagnosis — following wave crests with phase speeds obtained from the Taylor–Goldstein equation, the standard linear eigenvalue problem for waves in a sheared, stratified background current — reproduces the distortion during stages I and II (attributing roughly 83% of it to the eddy's current variations and 17% to its stratification anomalies in the representative case) but cannot reproduce the stage-III energy release, which is intrinsically nonlinear. Xie et al. (2015) concluded that models with eddies included, especially the energetic eddies, could further improve ISW amplitude predictions in the northeastern SCS. The comparison with the May 2001 observations was qualitative, and the deliberate idealization (isolated stationary eddy, flat bottom, no tides, Kuroshio, or generation-site variability) left the eddy's combined influence with those other regional factors untested. Observational capabilities have since improved — notably the SWOT (Surface Water and Ocean Topography) satellite mission, launched in late 2022, delivers high-resolution sea surface height fields from which ISW amplitudes can be inverted — making the open aspects below both tractable and increasingly urgent.

Problem Statement

Provide a dynamically complete and quantitatively validated account of how mesoscale eddies distort and modulate long-crested internal solitary waves in the northeastern South China Sea, closing the three linked gaps left by Xie et al. (2015) under one common objective — connecting the eddy-forcing stage, the nonlinear response, and the observable imprint:

  1. Mechanism of the nonlinear self-adjustment (stage III): explain, beyond linear ray tracing, how an ISW that has accumulated along-front energy and front distortion while crossing an eddy gradually releases and redistributes them after propagating away from the eddy — identifying the operative dynamics (e.g., along-front nonlinear wave–wave interaction, transverse dispersion or instability, radiation of secondary waves) in the fully nonlinear, nonhydrostatic regime appropriate to large-amplitude SCS waves.

  2. Quantitative, data-constrained reproduction: reproduce, in a realistic eddy-including configuration of the northeastern South China Sea constrained by observed eddy, stratification, and background fields, the observed magnitude of ISW front distortion and the characteristics of trailing wave packets — replacing the 2015 study's qualitative agreement with the satellite observations by quantitative agreement, within observational uncertainty, for interaction events that have contemporaneous observations of both the eddy and the wave, including the May 2001 SAR/altimeter event and further contemporaneous-observation events where available.

  3. Combined influence: quantify how eddies act together with the other factors simultaneously present in the northeastern SCS — variable generation conditions at the Luzon Strait, tides, Kuroshio intrusion and the large-scale circulation, and bottom topography — in producing the observed ISW distortion, amplitude modulation, and secondary trailing wave packets, treating the listed factors as the class of jointly acting background conditions rather than as a checklist of separate single-factor experiments; the 2015 study's idealized configuration of an isolated stationary eddy over a flat bottom, with no tides, Kuroshio, or generation-site variability, left this combined action untested.

Together these components connect the idealized eddy-only simulations with the observed phenomenon. All three aspects (1)–(3) are posed jointly, and quantitative agreement means agreement with the contemporaneous observations within observational uncertainty rather than qualitative resemblance.

References

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