In the northern South China Sea, the world's most energetic nonlinear internal waves originate as baroclinic tides at the Luzon Strait ridge system and then steepen into rank-ordered solitary-wave packets while crossing the deep basin. Long-term records show pronounced seasonal-to-interannual amplitude variability, yet two observed five-day segments with nearly identical tidal forcing (August 2005 and August 2007) exhibited mean wave heights differing by roughly 60%, implicating nontidal background processes. The source study (Li et al., 2016) traced this discrepancy to the Kuroshio intrusion and mesoscale eddies using a composite chain of simplified models, but the quantitative attribution problem remains unresolved: the baroclinic vertical structure of the intrusion was represented only in a linearized, depth-averaged way; the weakly nonlinear evolution model and two-dimensional front tracing omitted three-dimensional processes; and generation, nonlinear evolution, and lateral refraction were not combined in a single self-consistent computation. This problem asks for a quantitative, validated attribution of observed amplitude variability to specific large-scale background states.

Background

Internal waves propagate in the stratified ocean interior; when tides push stratified water over steep topography, the baroclinic response is an internal tide, whose steepening can produce large-amplitude internal solitary waves (ISWs). The Luzon Strait between Taiwan and Luzon has two parallel ridges that generate the world's largest ISWs, which then travel westward across the South China Sea (SCS). Two rank-ordered wave types arrive there on a diurnal cycle: larger 'a-waves', generated by the stronger semidiurnal barotropic tidal pulse within each diurnal cycle, and smaller 'b-waves' from the intervening weaker pulse. The principal lunar semidiurnal constituent, M2M_2, dominates the tidal forcing. The background through which these waves travel is not static: the Kuroshio, the western boundary current of the North Pacific, either leaps directly past Luzon Strait or loops into the SCS, supplying an intrusion flow and tilting the thermocline (the pycnocline layer separating upper and deep ocean); and mesoscale eddies — rotating vortices roughly 100 km wide lasting weeks to months — frequently drift across the wave corridor. Both alter the stratification and background currents that control internal-tide generation and ISW evolution.

Li, Wang, Chen, Chen and Park (2016, J. Geophys. Res. Oceans 121:2098–2118) documented the attribution puzzle at the core of this problem. Inverted echo sounders (instruments inferring thermocline displacement from round-trip acoustic travel time) recorded mean a-wave heights of 88±3 m during 5–9 August 2005 but 143±25 m during 12–16 August 2007, despite nearly identical barotropic tidal forcing (the depth-uniform tide itself) at the generating ridges. A nonhydrostatic numerical model (one that solves the full pressure field rather than assuming vertical hydrostatic balance, as required to resolve steep internal waves) with horizontally uniform stratification (SUNTANS) reproduced only about 7–8% inter-segment differences, so the observed discrepancy had to come from the background state. Reanalysis fields from the HYCOM (Hybrid Coordinate Ocean Model) data-assimilative ocean model showed a strong Kuroshio intrusion plus a cold eddy in 2005 and a weaker intrusion plus a warm eddy in 2007. Using a chain of simplified tools — a two-layer linear generation model, a Hibiya-type elementary-wave interference model with a steady, depth-averaged intrusion superimposed, a generalized Korteweg–de Vries (KdV) equation (the standard weakly nonlinear long-wave evolution equation, here with horizontally varying nonlinear coefficient α\alpha, inhomogeneity coefficient QQ, and phase speed cc derived from the reanalysis), and two-dimensional ray-type wave-front tracing — they concluded that intrusion-modulated generation (~11% difference in generated M2M_2 amplitude), eddy-modified KdV coefficients, and above all eddy-induced lateral steering of the wave fronts (so that fixed sensors sample the low-amplitude front edge rather than the center) jointly explain much of the difference.

This composite chain leaves the mechanism attribution quantitatively incomplete. The linearized, depth-averaged intrusion treatment cannot represent the baroclinic vertical structure of the Kuroshio and its role in internal-tide generation. The generalized KdV and two-dimensional front tracing omit three-dimensional processes: along-front gradients of the type described by the Kadomtsev–Petviashvili (KP) extension of KdV, scattering of wave energy to higher vertical modes by eddies, and near-field interactions with the western Luzon ridge. Horizontal steering was assessed separately from nonlinear evolution rather than in a single self-consistent computation. And attribution of long-term variability is constrained by observational coverage: existing records rarely resolve the mesoscale geostrophic fields (the rotation-dominated large-scale currents) and the high-frequency internal waves simultaneously.

Problem Statement

To what extent can the observed seasonal-to-interannual variability of nonlinear internal wave amplitudes in the northern South China Sea — including cases such as the August 2005 versus August 2007 segments, where tidal forcing at the Luzon Strait ridges was nearly identical but recorded mean wave heights differed by tens of percent — be quantitatively attributed to specific large-scale background processes, namely the Kuroshio intrusion (its path, its steady intrusion flow, and its baroclinic vertical structure) and mesoscale eddies, acting separately and jointly on (i) M2M_2 internal-tide generation at the ridge system, (ii) the nonlinear evolution of the generated internal tides into solitary waves, and (iii) the lateral refraction and steering of the wave fronts that determines whether a fixed sensor intercepts the front's center or its edge? For the two recorded segments, August 2005 versus August 2007, resolving this attribution requires the self-consistent decomposition of the observed amplitude difference into the separate and joint contributions of the Kuroshio intrusion and the mesoscale eddies at each of stages (i)–(iii). Because the question is open-ended, a contribution that is negligible, bounded only, or not isolable is resolved by quantifying it or bounding it explicitly. The decomposition must be consistent with the available observational record (the reported in-situ amplitude estimates and the observationally constrained background states, as documented in the source study) and with the quantitative effects reported in the cited literature, and its inferred contributions should be reconcilable with the reported segment heights (88±3 m and 143±25 m) within their stated uncertainties.

References

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