Poleward-propagating near-inertial waves enabled by the western boundary current

Near-inertial waves (NIWs), which have clockwise (anticlockwise) rotational motion in the Northern (Southern) Hemisphere, exist everywhere in the ocean except at the equator; their frequencies are largely determined by the local inertial frequency, f. It is thought that they supply about 25% of the energy for global ocean mixing through turbulence resulting from their strong current shear and breaking; this contributes mainly to upper-ocean mixing which is related to air-sea interaction, typhoon genesis, marine ecosystem, carbon cycle, and climate change. Observations and numerical simulations have shown that the low-mode NIWs can travel many hundreds of kilometres from a source region toward the equator because the lower inertial frequency at lower latitudes allows their free propagation. Here, using observations and a numerical simulation, we demonstrate poleward propagation of typhoon-induced NIWs by a western boundary current, the Kuroshio. Negative relative vorticity, meaning anticyclonic rotational tendency opposite to the Earth’s spin, existing along the right-hand side of the Kuroshio path, makes the local inertial frequency shift to a lower value, thereby trapping the waves. This negative vorticity region works like a waveguide for NIW propagation, and the strong Kuroshio current advects the waves poleward with a speed ~85% of the local current. This finding emphasizes that background currents such as the Kuroshio and the Gulf Stream play a significant role in redistribution of the NIW energy available for global ocean mixing.

www.nature.com/scientificreports www.nature.com/scientificreports/ 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).  www.nature.com/scientificreports www.nature.com/scientificreports/ 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 7-10). 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 evidence 3,5,10,19 . 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 breaking 2,3,6,15,20,21 , and as a result can influence pollutant dispersal, the marine ecosystem, carbon cycle, and climate 22 . 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  www.nature.com/scientificreports www.nature.com/scientificreports/ 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 tides 25 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
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 and ′ v are baroclinic zonal and meridional velocities filtered to the near-inertial frequency band [26][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 analysis 29 , 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 5 th and on September 26 th 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.  www.nature.com/scientificreports www.nature.com/scientificreports/ Effective Coriolis frequency. The effective Coriolis frequency is given by where ζ is the relative vorticity, ζ = ∂ ∂ − ∂ ∂ v x u y / / 10 . Negative (positive) ζ denotes anticyclonic (cyclonic) circulation.