Direct measurements reveal instabilities and turbulence within large amplitude internal solitary waves beneath the ocean

Internal solitary waves (ISWs) commonly arise from nonlinear steepening of internal tides generated over abrupt topography and can travel long distances before shoaling on continental slopes. During shoaling, ISWs can fission, reverse polarity, and break, producing strong turbulent dissipation that mediates tidal energy to smaller scales and mixes water masses, impacting global energy budgets and climate models. In the South China Sea (SCS), among the most energetic ISWs globally, waves generated by Luzon Strait ridges evolve into bore-like structures and are amplified by the continental slope, leading to strong packets above the Dongsha plateau. Prior observations showed elevated dissipation during shoaling, but the detailed physical mechanisms initiating turbulence inside ISWs (convective breaking within the core versus shear-driven Kelvin-Helmholtz instabilities near the rear/lower periphery) are difficult to observe in situ due to intermittency and rapid evolution. This study aims to directly observe and quantify these instabilities and associated turbulence in shoaling ISWs east of Dongsha Atoll, to clarify the conditions and dynamics governing mixing.

Field studies on the Oregon Shelf and Dongsha Plateau identified trains of ISWs with prominent shear instabilities as primary turbulence sources. Subsequent laboratory and numerical studies examined mechanisms and occurrence criteria for instability, including Ri thresholds and spatial extent of unstable regions. Observations in the SCS documented convective breaking and trapped-core formation in shoaling ISWs of depression. However, many prior ocean observations relied on echo sounders and limited-resolution CTD data, with detailed dynamics inferred via models and tanks. Criteria from Miles-Howard (Ri < 0.25) are necessary but not sufficient in curved stratified shear; more stringent criteria (e.g., Ri < 0.1 and sufficient unstable region relative to wave half-width) have been suggested for KH billow formation within ISWs. Evidence for simultaneous convective and KH processes within oceanic ISWs has been scarce.

Study area and timing: East of Dongsha Atoll, South China Sea, along 20°42′N across a gently shoaling slope (mean slope ~0.013; local slope at 300 m ~0.025). Observations spanned 14–22 May 2019 (moored) and 18–23 May 2019 (shipboard), capturing 15 ISW packets. Moorings: Two moorings ~10 km east of Dongsha Atoll, separated by 252 m: A1 (bottom-mounted 75 kHz ADCP at 321 m; 8 m vertical bins; sampling every 6 s; effective velocity error 0.024 m s−1 after 1-min averaging; current profiles ~40–300 m), and T1 (thermistor chain at 323 m with 58 sensors, 4–5 m vertical spacing from 26–270 m depth; accuracy 0.002 °C; sampled at 0.1 Hz). Overlap period 14–22 May provided coincident temperature and velocity at high temporal resolution (10 s temperature, 6 s velocity). Shipboard systems: 75 kHz ADCP (8 m bins; 1-min ensembles over ~20 pings), 120 kHz echo sounder (0.5 Hz; 0.1–2 m vertical resolution), and an Underway Vertical Microstructure Profiler (UVMP) using a Rockland VMP-250 slack-tethered to a UCTD winch for tow-yo profiling. VMP-250 sensors: two shear probes and one fast thermistor (FP07) at 512 Hz to estimate turbulent kinetic energy (TKE) dissipation rate ε using ε = 7.5 ν ⟨(du/dz)²⟩. A CT sensor sampled conductivity and temperature at 16 Hz. ODAS software processed microstructure. Wave tracking: ISW #11 was surveyed three times. First survey: ship drifted westward with ISW-induced surface currents while profiling; second survey: ship transited across the wave; third: drift tow-yo as the wave shoaled across an abrupt ~100 m rise. A moving wave coordinate x(t) = xs(t) − C t was applied to first two surveys using GPS xs and assumed wave speeds (C ≈ 1.35 m s−1 first; 0.92 m s−1 second; mean between encounters ~1.22 m s−1) to align spatial scales. Seven VMP casts were obtained before/during passage in the first survey; eleven during the third. Event alignment and wave speed: Arrival times at A1 (from depth-averaged zonal velocity 150–250 m, Um) and T1 (from temperature averaged 150–250 m, θ) defined per-event centers, accounting for 1–3 min lag due to 252 m separation. Wave speed C estimated via (i) iterative ADCP-based method correcting for beam spreading and (ii) inter-mooring arrival time; both consistent (mostly 1.0–1.5 m s−1; mean 1.3 m s−1). The maximum observed C was 2.1 m s−1 (ISW #10). Derived quantities: Fields interpolated to 4 m vertical by 10 s temporal grids. Shear squared S² = (∂u/∂z)² + (∂v/∂z)² using 1-min averaged velocities; buoyancy frequency squared N² = −(g/ρ0)(∂ρ/∂z) with ρ from temperature (and constant salinity 34.5 psu), g = 9.81 m s−2, ρ0 = 1025 kg m−3. Richardson number Ri = N²/S². Half-amplitude full width λ1/2 measured at half of wave amplitude from isotherm displacements. Unstable region length Lx measured where Ri < 0.25; criteria tested: Ri < 0.1 and Lx/λ1/2 > 0.86 (or 0.8) for KH growth. Eddy diffusivity estimated as Ke = 0.2 ε N−2. Echo sounder images used to identify KH billow trains and breaking structures. Bathymetry from cross-section provided local slope context.

• Fifteen ISW packets were observed arriving primarily at semidiurnal intervals. Leading waves had vertical velocities of 0.3–0.5 m s−1.
• Propagation speeds C ranged 1.0–1.5 m s−1 (mean 1.3 m s−1); a maximum C of 2.1 m s−1 occurred for ISW #10.
• Maximum particle velocities within leading ISWs (Umax) exceeded propagation speeds for all events (Umax > C), indicating convective breaking. Mean Umax was 1.7 m s−1 (~30% greater than mean C).
• Thermistor observations showed mode-1 depression waves. Maximum vertical displacement of the 18 °C isotherm lmax ranged 76–125 m (mean 103 m). Half-amplitude full width λ1/2 ranged 0.53–1.16 km (mean 0.79 km). Most waves had gentle front slopes and steep trailing edges.
• Kelvin-Helmholtz (KH) billows and waveform breaking were prevalent near the trailing edge and along/above the strong stratification. Clear KH roll-ups (~10–15 m vertical scale) and subsequent breaking were documented in several waves (notably #4, #7, #8, #11). Largest KH billows occurred in ISW #14.
• Shear-stratification analysis showed S² enhanced along the lower periphery of the wave core, N² strongest below the periphery. Regions with Ri < 0.25 occurred predominantly along the lower core periphery. For most waves, criteria favoring KH growth were met (Ri minimum < 0.1 and Lx/λ1/2 > 0.86); exceptions with smoother waveforms (#1, #2, #3, #5) did not satisfy these criteria.
• Convective instability features: Stages 2–3 (overturning and plunging) were observed in #1, #7, #13; a fully developed convective overturn/trapped-core-like region (Stage 4) was observed in #11, including warm near-surface water plunging to ~100 m and mixed rear regions; concurrent KH billows were present at the rear.
• Turbulence measurements (ε): Pre-wave background ε was O(10−9–10−7) W kg−1. Within the plunging tongue: ε ≈ 2.2×10−6 W kg−1; within KH billows: ε ≈ 4.5×10−6 to 3×10−5 W kg−1; well-mixed rear (casts 6–7): mean ε ≈ 2.3×10−5 W kg−1, peak 1.7×10−4 W kg−1. During shoaling over an abrupt ~100 m rise, KH billows of 20–30 m amplitude formed ~20 m above bottom with ε ~10−5–10−4 W kg−1; maximum ε reached 1.4×10−3 W kg−1 (Cast 8).
• Eddy diffusivity Ke = 0.2 ε N−2: Elevated Ke correlated with shear-instability conditions. About 18% of measurements had S²/N² > 4 (Miles-Howard threshold) with generally higher Ke. A stricter ISW criterion S²/N² ≥ 10 further concentrated Ke in the 10−2–100 m² s−1 range. Mean Ke in the high-ε band was ~10−1 m² s−1, about four orders of magnitude above typical open-ocean values (~10−5 m² s−1), and exceeding common parameterization maxima (e.g., KPP) by 3–4 orders in places.
• Interplay of instabilities: Convective instability (enabled by Umax > C) can enhance shear instability by compressing isopycnals between the core and thermocline, increasing S² more strongly than N² and favoring KH. Observations suggest KH-induced breaking at the rear may, in turn, hinder formation of trapped cores by stirring interfaces.

Direct, co-located high-resolution observations of temperature, velocity, echo intensity, and microstructure within shoaling ISWs demonstrate that both convective breaking (in the weakly stratified core when Umax > C) and shear-driven KH billows (along the lower periphery and rear) are key pathways for energy transfer to turbulence. The spatial organization of enhanced S² above strong N² yields Ri minima primarily along the lower core periphery, consistent with prior theories and experiments for KH development in curved stratified shear flows. The data confirm that convective processes can intensify shear and stratification gradients, promoting KH instabilities, while the resulting waveform collapse and billow breakdown at the rear may disrupt plunging and trapped-core formation, suggesting a two-way interplay. Shoaling topography appears to focus shear and stratification near the bottom, enhancing KH billows and turbulence during upslope propagation. The resulting turbulent dissipation and mixing substantially exceed open-ocean background, facilitating transport of cool, nutrient-rich subthermocline waters toward shallow reefs at Dongsha, with implications for ecosystem metabolism, temperature moderation, and resilience. The observed diffusivities challenge limits in commonly used ocean mixing parameterizations, indicating a need for improved representations of ISW-driven mixing in models.

This study provides direct, fine-scale ocean measurements that reveal and quantify concurrent convective overturning and Kelvin-Helmholtz instabilities within large-amplitude internal solitary waves shoaling east of Dongsha Atoll. All observed leading ISWs satisfied the convective breaking condition (Umax > C). KH billows formed predominantly along the lower periphery of the wave core under conditions of low Ri and sufficient spatial extent, leading to intense waveform breaking and turbulence. Measured dissipation rates reached up to 1.4×10−3 W kg−1 and inferred eddy diffusivities up to 10−2–100 m² s−1, approximately four orders above open-ocean background. These findings validate laboratory and numerical criteria for instability onset within ISWs, illuminate the interplay between convective and shear processes, and demonstrate topographic enhancement of instability and mixing. Implications include significant contributions of ISWs to coastal and shelf mixing and potential impacts on coral reef environments. Future work should (i) directly resolve bottom boundary layer processes concurrently with interior instabilities, (ii) further test the hypothesized suppression of convective trapped-core formation by rear-edge KH breaking, (iii) improve joint density-velocity measurements at finer scales, and (iv) assess generality across diverse bathymetries and seasons to inform and improve turbulence parameterizations in ocean models.

• Bottom boundary layer processes were not directly observed, as moored instruments sampled above the BBL; thus, near-bottom instability and turbulence contributions are underresolved.
• Instabilities are intermittent and rapidly evolving; despite high cadence, the 4–5 m vertical spacing of thermistors may underresolve smaller billows or sharp gradients.
• Salinity was assumed constant (34.5 psu) for density and N² estimates from thermistor data, introducing uncertainty where salinity stratification is non-negligible.
• The two moorings were separated by 252 m; alignment assumes minimal evolution between sites and relies on arrival-time definitions.
• Wave speed during one ship survey (first pass) was inferred to match spatial scales; rapid spatial-temporal variability during shoaling (third survey) precluded wave-coordinate transformation.
• Trapped-core structure in ISW #11 was partially obscured by concurrent KH activity, complicating clear identification.
• Observations cover a 9-day window and a specific gentle-slope region; results may differ over steeper slopes or different seasons/stratification regimes.