Introduction

Ocean mixing, mainly driven by wind and tides, is known to play a crucial role in maintaining oceanic stratification and the global-scale thermohaline circulation1. The ocean needs about 2.1 terawatt of energy for mixing, and NIWs are responsible for 0.4–0.7 terawatt1,2,3,4, approximately 25% of the total. NIWs exist everywhere in the ocean (except at the equator) from tropical to polar regions2,5. They redistribute energy through long-distance propagation in stratified waters and are dissipated eventually through turbulence due to their high shear3. Nevertheless, because of low spatial resolution (>1/4 degree) and low temporal resolution of the wind forcing (>6 hours), climate and Earth system models which are used for future climate prediction do not represent realistic NIWs and their mixing6,7,8.

NIWs travel over hundreds of kilometres toward the equator because of decreasing inertial frequency with latitude2,3,9,10,11. Negative relative vorticity induced by horizontal current shear can trap and amplify NIWs10,12 with enhancement of NIW energy transfer to the deep ocean12,13,14,15. Numerical simulation and observations have shown that the Gulf Stream and Kuroshio, the western boundary currents in the Atlantic and Pacific Oceans, can move the waves eastward away from their sources, and hence produce a NIW “desert” south of a western boundary current16,17. Nevertheless, our understanding of the behaviour of non-equatorward NIW propagation is insufficient, largely due to lack of observations, especially in strong current regions.

Wind is the best-known forcing capable of generating energetic NIWs in the ocean. A typhoon or hurricane generates energetic NIWs, especially on the right-hand side of its track because of the stronger wind energy18 and more favourable wind-direction change. The Joint Kuroshio-Ryukyu Current System Study (JKRYCSS), an international collaborative project to observe the Kuroshio and Ryukyu Current systems, began in June 2015, and tall current moorings were installed in the Okinawa Trough to monitor the Kuroshio where it flows northeastward. While the current moorings were in operation, four typhoons passed over or near the two mooring sites: CHAN-HOM in July, SOUDELOR in early August, GONI in late August, and DUJUAN in late September (Fig. 1a). Time series of current profiles from upward-looking 75-kHz acoustic Doppler current profilers (ADCP) reveal particularly energetic NIWs after the passage of SOUDELOR and of DUJUAN, which passed across a region of the Kuroshio upstream from the mooring sites (Fig. 1b,c). Amplitudes of the waves induced by the typhoons were stronger than those during the winter season. When passing through the region near the mooring sites the four typhoons had similar intensities, category 4 for CHAN-HOM, GONI, and DUJUAN and category 3 for SOUDELOR. Typhoons CHAN-HOM and GONI passed closest to the mooring sites, but the other two typhoons, SOUDELOR and DUJUAN, produced stronger NIW signals at the KCM1 and KCM2 mooring sites, particularly at KCM1 (Fig. 1b,c).

The strongest observed NIW events were responses to the two typhoons SOUDELOR and DUJUAN, which crossed the Kuroshio upstream, east of Taiwan, about 350 km southwest of the mooring sites on August 8th and September 28th, respectively (Fig. 1a); these events lasted 15 and 9 days, respectively. In both cases, the wave amplitude was stronger at KCM1 than at KCM2 (Fig. 1b,c). Energetic NIWs at KCM1 for SOUDELOR were observed from August 8th at 64 m to August 23rd at 448 m, exhibiting downward propagation (Fig. 1d,e). For DUJUAN, energetic NIWs were detected from September 29th at 64 m to October 7th at 448 m, again exhibiting downward propagation (Fig. 1g,h). The waves at about 1000- and 1500-m depths had amplitudes less than 0.04 m s–1, which is much weaker than in the upper layer. The clockwise component of the NIWs (solid lines in Fig. 1f,i) was stronger than the anticlockwise component (dotted lines), which is an obvious characteristic of NIWs in the Northern Hemisphere. Frequencies of the NIWs are smaller than the local inertial frequency (f) at all measurement depths, 64–448 m, during both typhoon passages (Fig. 1f,i). The local inertial period is 27.47 hours (f = 0.0364 cph) at KCM 1, but, with this so-called red-shift, the period of NIWs determined from the spectral analysis was 30.3 hours (=0.033 cph) (see Methods), corresponding to ~0.9 f.

Comparisons of NIWs from observations and numerical simulations reveal good agreements in both amplitude and frequency-shift, and the characteristic that the NIWs were stronger at KCM1 than at KCM2 in the observations is well represented in the simulations (Supplementary Figs S13). Numerical simulation results (see Methods) show typhoon-SOUDELOR-induced energetic NIWs distributed widely near the sea surface (4-m depth) in the Kuroshio upstream about 100 km southwest from the mooring sites. The simulated waves are weak (<0.25 m s−1) at the mooring sites at 00 h GMT on August 8th when the most intense NIWs are generated by typhoon SOUDELOR, and the waves in the Kuroshio downstream and on the northern side of the mooring sites are weaker still (Fig. 2a, Supplementary Video 1). The waves at 100-m depth become energetic ~3 days later along the Kuroshio downstream (over about 300 km including the mooring sites), suggesting poleward energy propagation (Fig. 2b, Supplementary Video 2). Depth-integrated kinetic energy greater than 3000 J m−2 exists along the right-hand side of the Kuroshio path from 25°N to 27.6°N (Fig. 2c), resulting from energy propagation downstream along the Kuroshio. During typhoon DUJUAN, generation of NIWs in the surface layer (4 m) is weak (<0.2 m s−1) at the mooring sites, while strong (>0.4 m s−1) in the Kuroshio upstream, roughly 2 times farther from observation sites than during typhoon SOUDELOR (Fig. 2d, Supplementary Video 3). After ~5.5 days, prominent NIWs exist at and around mooring sites along the Kuroshio at 100-m depth (Fig. 2e, Supplementary Video 4). Depth-integrated kinetic energy shows the same spatial distribution along the right-hand side of the Kuroshio path in the case of DUJUAN from about 25°N to 28°N (Fig. 2f), similar to that of typhoon SOUDELOR. The NIWs were stronger at KCM1 than at KCM2 from both observations and simulations due to the location of KCM1 which is close to the center of the right-hand side of the Kuroshio, where the NIW energy was more concentrated.

The Kuroshio path and its perpendicular lines (Fig. 3a; see Methods) and Hovmöller diagrams of NIW kinetic energy density averaged over the right-hand side of the Kuroshio from the centre to 80 km away from the centre during typhoons SOUDELOR and DUJUAN (Fig. 3b–e), show the detailed behaviour of NIWs along that side of the Kuroshio (Supplementary Videos 5 and 6). The NIW kinetic energy density at the sea surface are weak (<40 J m−3) around the mooring sites when SOUDELOR and DUJUAN go through, however they become strong 1–2 days and 2–3 days later at the sea surface (Fig. 3b,d) and ~3 days and 5.5 days later at 100-m depth (Fig. 3c,e), respectively. The kinetic energy density at the sea surface shows energy movement from upstream to downstream with speed of 1.5 m s−1 for SOUDELOR and 0.93 m s−1 for DUJUAN on average, almost the same speed of the Kuroshio near the axis. The advection of NIWs at the sea surface shows similar patterns (Supplementary Videos 1 and 3) as that in the Gulf Stream17. The energy movement at 100-m depth exhibits 0.58 m s−1 for SOUDELOR and 0.43 m s−1 for DUJUAN on average, about 85% of the Kuroshio speed on its right-hand side for both cases.

Numerical simulation results reveal a negative relative vorticity (see Methods) region with 80–90 km width on the right-hand side of the Kuroshio path during the passage of SOUDELOR and of DUJUAN (Fig. 4a,d). Due to this negative relative vorticity, the effective inertial period 1/feff, where feff is effective Coriolis frequency (see Methods), is longer than 30 hours (approximately 10% longer than the local inertial period 1/f) along the right-hand side of the Kuroshio up to about 27.5°N (Fig. 4b,e). This implies that NIWs generated in the upstream region of the Kuroshio can be trapped and their energy propagated in a band along the right-hand side of the Kuroshio. This is supported by the fact that NIWs in this band reveal periods similar to 1/feff (Fig. 4c,f). In other words, the negative relative vorticity region works like a waveguide for NIWs. Moreover, the Kuroshio itself advects these NIWs northeastward (poleward) more than 300 km.

The Hovmöller diagram of NIWs along the right-hand side of the Kuroshio shows slight upstream directional phase propagation, the speed of which is faster than 4.5 m s−1 (Fig. 3b–e). This unrealistic propagation speed can be explained with spatially different phase of NIWs along the Kuroshio. The Hovmöller diagram of NIWs shows temporally fixed NIWs along the Kuroshio at the sea surface and 100-m depth over hundreds of kilometres. Because the NIWs move downstream over time with a speed of >50 km day−1 and with downward propagation of their energy with O(10) m day−1, the NIWs at 100-m depth can have different phase at a fixed time (Figs 1, S1). If the NIW phase in the downstream is earlier than in the upstream, there could be an upstream directional phase propagation. The spatially different NIW phase can also happen by different frequency of NIWs along the Kuroshio (Fig. 4c,f).

Typhoons CHAN-HOM and GONI passed close to the mooring sites (Fig. 1a), generating strong NIWs in the surface layer around the sites. Nevertheless, the observations show no distinguishable NIWs spreading from the 64 to 448 m depths at KCM1 since they are advected to downstream regions by the Kuroshio (Figs 1b,c, S4 and Supplementary Videos 710). This advection removes NIW energy from the source region in the upper layer, which accounts for the observed weak deep-layer NIWs, <0.04 m s−1, at 1000- and 1500-m depths (Fig. 1d,e,g,h). The energetic NIWs are found at KCM2 during typhoon GONI due to its position on the right-hand side of the typhoon track. The relatively slow Kuroshio current at KCM2 enables to sustain the locally generated NIWs.

Following generation, the distribution of NIWs is traditionally thought to be governed by equatorward propagation, though the potential impact of background currents on propagation has been noted without supporting evidence3,5,10,19. The observations and simulations presented in this study provide a new paradigm suggesting that NIWs can be advected northward over hundreds of kilometres along a western boundary current. NIWs can mix waters through turbulence by their current shear and breaking2,3,6,15,20,21, and as a result can influence pollutant dispersal, the marine ecosystem, carbon cycle, and climate22. Our results suggest that proper incorporation of NIW effects in climate and Earth system models will require consideration of the impact of background currents on wave energy redistribution, resulting in further improvements of future climate predictions.

Data and Methods

In-situ moored measurements

Two sets of current measuring mooring systems were deployed in the Kuroshio from June 2015 to June 2016. Each system consisted of an upward-looking 75-kHz Acoustic Doppler Current Profilers (ADCP) at about 500-m depth, and single-level-measuring current metres at 1000-m and 1500-m depths with sampling interval of 30 minutes. The uncertainty of the 30-minute-interval ADCP data in configuration of 16-m bin size and 10 pings ensemble from Workhorse Long Ranger 75-kHz ADCP (20° beam angle) is 1.23 cm s−1. The two stations, KCM1 and KCM2, were positioned on the right-hand side of the Kuroshio path, with KCM1 close to the Kuroshio path (core) and KCM2 near its edge. The two stations were separated by about 34 km distance (Fig. 1a). Ocean depths at KCM1 and KCM2 are 2004 m and 2051 m, respectively.

Numerical model

Data-assimilative three-dimensional high-resolution numerical ocean model outputs (hourly) from the real-time forecast system covering the East Asian marginal seas were analyzed [https://dreams-c.riam.kyushu-u.ac.jp/vwp/]23. This system has horizontal resolutions of 1/12° in longitude and 1/15° in latitude, based on the RIAM Ocean Model (RIAMOM)24, a free-surface primitive general circulation model developed by the Research Institute for Applied Mechanics (RIAM) of Kyushu University. It is a three-dimensional, 38-layer, z-coordinate model that assumes hydrostatic balance and Boussinesq approximation. 32 of these 38 layers covers from the surface to 2250 m. The model includes tides25 and ocean general circulation and is forced by 6-hourly atmospheric forcings (GPV/GSM meteorological data) with 3rd-order Lagrange polynomial interpolation. Sea surface temperature data (MGDSST) of the Japan Meteorological Agency were utilized for the surface relaxation with a time scale of 3 days, and the along-track AVISO sea surface height data were assimilated by a reduced-order Kalman filter.

Horizontal energy

Time-mean depth-integrated horizontal kinetic energy of NIWs was calculated by $$HKE=\frac{1}{2T}{\int }_{-H}^{0}({\int }_{0}^{T}\rho (z,t)[\,{|{u}^{\text{'}}(z,t)|}^{2}+{|{v}^{\text{'}}(z,t)|}^{2}]dt)dz,$$ where t is time, z is the vertical Cartesian coordinate (positive upward), ρ is water density, T ( = 20 days) is an averaging period, and $${u}^{\text{'}}$$ and $${v}^{\text{'}}$$ are baroclinic zonal and meridional velocities filtered to the near-inertial frequency band26,27,28. This filter was a third-order Butterworth phase-preserving band-pass filter applied with cutoffs at −2 and +10 hours from the local inertial period. These cutoff periods, based on rotary spectral analysis, were chosen to prevent diurnal tide (D1) interference and took into consideration frequency shifts of the NIWs (Fig. 1f,i). The variance-preserving rotary spectral analysis29, which provides clockwise and anticlockwise rotating components, was conducted with 20-day-long current data during each typhoon passage. The duration of 20 days was necessary to separate the diurnal tides and NIWs. The start date of the duration of 20 days for horizontal energy and spectral analysis is 00 h GMT on August 5th and on September 26th during SOUDELOR and DUJUAN, respectively.

Kuroshio path and perpendicular lines

The Kuroshio path and its perpendicular lines were estimated. The Kuroshio path was determined as follows. First, the current field was 4-day lowpass filtered and the maximum surface velocity points were identified in these currents averaged over 20 days, corresponding to the duration of the spectral analysis. Points along the Kuroshio path were determined every 10-km and numbered 1 to 90 ranging from 23°N to about 28.5°N.

Effective Coriolis frequency

The effective Coriolis frequency is given by $${f}_{eff}=f+\zeta /2$$, where ζ is the relative vorticity, $$\zeta =\partial v/\partial x-\partial u/\partial y$$10. Negative (positive) ζ denotes anticyclonic (cyclonic) circulation.