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  • View in gallery
    Fig. 1.

    (a) Ship tracks (black) and stations (red) during the observations on 18–29 May 2018, overlapped on the map of time-averaged SSH distributed by AVISO. (b) Measurements of velocity using ADCP and TKE dissipation rate ε and T–S by MSS in the warm-core eddy (WE). The background map is the time-averaged SLA during the observation of the eddy. The 50 stations (red dots) and their station numbers are labeled. The six transects T1–T6 are marked by colored segments in the subgraph. The velocity vectors at a depth of 100 m are denoted by gray arrows. (c) As in (b), but for the cold-core eddy (CE).

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    Fig. 2.

    (a) Eastward velocity component u and (c) northward velocity component υ along the space–time varying ship tracks in the cold-core eddy (CE). (b),(d) As in (a) and (c), but for the warm-core eddy (WE). The transects and T–S stations in different directions corresponding to those in Fig. 1 are marked at the top of the horizontal axis. The T–S stations near the eddy center are highlighted with their station numbers labeled. Contours of the potential density anomaly σθ are plotted to aid in identifying the eddy structure.

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    Fig. 3.

    As in Fig. 2, but for the (top) stratification N2 and (bottom) normalized relative vorticity ζ/f. The local inertial frequency f is 8.0 × 10−5 s−1 (8.9 × 10−5 s−1) for the CE (WE).

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    Fig. 4.

    (a) Map of the depth-averaged (above 200 m) velocity on the 3 km × 3 km horizontal grids by linear interpolation for the cold-core eddy (CE). The depth-averaged eddy center estimated by the local minimum velocity is marked by the red dot. The regions of missing values are masked by gray dots. The ship tracks are overlaid by the gray dashed lines. (c) The depth-averaged velocity above 200 m (black dots) is fitted with the Gaussian profile (red line) to estimate the eddy radius r0 of the CE, using the location of the maximum velocity V0. Outliers (gray dots) at the eddy periphery are excluded from the fitting. (b),(d) As in (a) and (c), but for the warm-core eddy (WE).

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    Fig. 5.

    Schematic of extracting the balanced velocity (blue) from the SADCP velocity profiles (gray) by MRM. Positions of the T–S station pair and velocity profiles are denoted by red and black dots, respectively. The Vbp is the pth balanced velocity profile between the kth and (k + 1)th T–S station pair, Fn indicates the first two vertical modes decomposed from the T–S profiles at the station pair (n = 1, 2), and L is the distance of the velocity profile to the nearby station pair. The displayed velocity profiles are the SADCP velocity between the station pair 26–27 in the warm-core eddy.

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    Fig. 6.

    (a) T–S stations (black dots) and the station pairs selected for the calculation of geostrophic velocity (red dots) in the cold-core eddy (CE). (b) Comparison of the SADCP (gray), MRM-derived (blue), and geostrophic/cyclogeostrophic balanced (red) velocity profiles in the CE. GB and CGB are the abbreviations of geostrophic balance and cyclogeostrophic balance, respectively. Root-mean-square (RMS) bias between the diagnosed balanced velocity and the MRM-derived balanced velocity is marked in black text. (c),(d) As in (a) and (b), but for the warm-core eddy (WE). The cyclogeostrophic (geostrophic) balanced velocity of the CE (WE) is regarded as the reference for examining the MRM-derived balanced velocity.

  • View in gallery
    Fig. 7.

    Clockwise (CW) and counterclockwise (CCW) vertical wavenumber spectra of the (a) NIW velocity and (b) NIW shear in the cold-core eddy (CE). (c),(d) As in (a) and (b), but for the warm-core eddy (WE). The displayed spectra are the average spectra inside (r < r0/2, “In”) and outside (r > r0, “Out”) the eddy core, and r0 is the radius of the eddy core. The 95% confidence interval is marked by the error bar. The vertical wavelengths are shown at the top of the horizontal axis. The NIW shear is estimated using the 32-m vertical gradient of the NIW velocity smoothed over a 32-m interval to remove the noise at high wavenumbers. The GM spectra are calculated using the MATLAB toolbox downloaded from http://jklymak.github.io/GarrettMunkMatlab/.

  • View in gallery
    Fig. 8.

    As in Fig. 2, but for the NIW velocity; u′ and υ ′ are the eastward and northward velocity components.

  • View in gallery
    Fig. 9.

    As in Fig. 2, but for NIW phase θ (top) before and (bottom) after inertial back-rotation. The θ is calculated with the NIW velocity components horizontally smoothed over 30 km.

  • View in gallery
    Fig. 10.

    As in Fig. 2, but for the NIW velocity after inertial back-rotation; u′ and υ ′ are the eastward and northward velocity components.

  • View in gallery
    Fig. 11.

    Three-dimensional structure of the near-inertial kinetic energy (NIKE) in the warm-core eddy (WE). (a) Radial section of the NIKE averaged every 10 km in the radial direction. The contours of the potential density anomaly σθ are overlaid with dashed lines. (b) Radial distribution of the depth-averaged NIKE. Average profiles of the NIKE (full line) and relative vorticity (dashed line) inside (r < r0 /2) and outside (r > r0) the eddy core in the (c) σθ and (d) depth coordinate. (e) Clockwise (CW) and counterclockwise (CCW) NIKE inside the eddy core. The canonical value of 3 J m−3 (gray dashed line) in (b)–(e) is marked for reference. The NIKE is calculated by NIW velocity that is first WKB normalized and vertically smoothed over a 32-m interval. r is the distance from the eddy center, and r0 is the eddy radius of 56 km.

  • View in gallery
    Fig. 12.

    As in Fig. 11, but for the three-dimensional structure of the NIKE in the CE. The eddy radius r0 is 77 km.

  • View in gallery
    Fig. 13.

    Radial sections of the (a) NIW shear SNIW2, (b) eddy shear Seddy2, (c) TKE dissipation rate ε in the CE. (d)–(f) As in (a)–(c), but for the WE. The radial compositions of the shears take a 10-km average in the radial direction. The TKE dissipation rate ε profiles are plotted individually to avoid the discrepancy of magnitudes by average, and the larger values are overlaid on the smaller ones; r is the distance from the eddy center, and r0 is the eddy radius of 77 km (56 km) for the CE (WE).

  • View in gallery
    Fig. 14.

    Vertical structures of the (a) stratification N2, (b) total shear S2, (c) Richardson number Ri, (d) TKE dissipation rate ε, and (e) vertical diffusivity Kρ inside (red) and outside (blue) the core of the CE. (f)–(j) As in (a)–(e), but for the WE. The N2 and S2 are estimated by the 32-m vertical gradient of the density and total velocity that are smoothed over a 32-m interval. The S2 are calculated with velocity profiles at the T–S stations to match the observation of the TKE dissipation rate ε.

  • View in gallery
    Fig. 15.

    (a) Horizontal energy transform rate Fh between NIWs and mesoscale eddies and (b) the average Fh inside the core of the CE vs the balance-to-NIWs energy. (c),(d) As in (a) and (b), but for the WE. The positive and negative Fh indicate the increase and decrease of the NIW energy, respectively.

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Enhanced Near-Inertial Waves and Turbulent Diapycnal Mixing Observed in a Cold- and Warm-Core Eddy in the Kuroshio Extension Region

Qi LiaFrontier Science Center for Deep Ocean Multispheres and Earth System, and Physical Oceanography Laboratory, Ocean University of China, Qingdao, China
bQingdao National Laboratory for Marine Science and Technology, Qingdao, China

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Zhaohui ChenaFrontier Science Center for Deep Ocean Multispheres and Earth System, and Physical Oceanography Laboratory, Ocean University of China, Qingdao, China
bQingdao National Laboratory for Marine Science and Technology, Qingdao, China

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Shoude GuanaFrontier Science Center for Deep Ocean Multispheres and Earth System, and Physical Oceanography Laboratory, Ocean University of China, Qingdao, China
bQingdao National Laboratory for Marine Science and Technology, Qingdao, China

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Haiyuan YangaFrontier Science Center for Deep Ocean Multispheres and Earth System, and Physical Oceanography Laboratory, Ocean University of China, Qingdao, China
bQingdao National Laboratory for Marine Science and Technology, Qingdao, China

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Zhao JingaFrontier Science Center for Deep Ocean Multispheres and Earth System, and Physical Oceanography Laboratory, Ocean University of China, Qingdao, China
bQingdao National Laboratory for Marine Science and Technology, Qingdao, China

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Yongzheng LiuaFrontier Science Center for Deep Ocean Multispheres and Earth System, and Physical Oceanography Laboratory, Ocean University of China, Qingdao, China
bQingdao National Laboratory for Marine Science and Technology, Qingdao, China

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Bingrong SunaFrontier Science Center for Deep Ocean Multispheres and Earth System, and Physical Oceanography Laboratory, Ocean University of China, Qingdao, China
bQingdao National Laboratory for Marine Science and Technology, Qingdao, China

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Lixin WuaFrontier Science Center for Deep Ocean Multispheres and Earth System, and Physical Oceanography Laboratory, Ocean University of China, Qingdao, China
bQingdao National Laboratory for Marine Science and Technology, Qingdao, China

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Abstract

Shipboard observations of upper-ocean current, temperature–salinity, and turbulent dissipation rate were used to study near-inertial waves (NIWs) and turbulent diapycnal mixing in a cold-core eddy (CE) and warm-core eddy (WE) in the Kuroshio Extension (KE) region. The two eddies shed from the KE were energetic, with the maximum velocity exceeding 1 m s−1 and relative vorticity magnitude as high as 0.6f. The mode regression method was proposed to extract NIWs from the shipboard ADCP velocities. The NIW amplitudes were 0.15 and 0.3 m s−1 in the CE and WE, respectively, and their constant phase lines were nearly slanted along the heaving isopycnals. In the WE, the NIWs were trapped in the negative vorticity core and amplified at the eddy base (at 350–650 m), which was consistent with the “inertial chimney” effect documented in existing literature. Outstanding NIWs in the background wavefield were also observed inside the positive vorticity core of the CE, despite their lower strength and shallower residence (above 350 m) compared to the counterparts in the WE. Particularly, the near-inertial kinetic energy efficiently propagated downward and amplified below the surface layer in both eddies, leading to an elevated turbulent dissipation rate of up to 10−7 W kg−1. In addition, bidirectional energy exchanges between the NIWs and mesoscale balanced flow occurred during NIWs’ downward propagation. The present study provides observational evidence for the enhanced downward NIW propagation by mesoscale eddies, which has significant implications for parameterizing the wind-driven diapycnal mixing in the eddying ocean.

Significance Statement

We provide observational evidence for the downward propagation of near-inertial waves enhanced by mesoscale eddies. This is significant because the down-taking of wind energy by the near-inertial waves is an important energy source for turbulent mixing in the interior ocean, which is essential to the shaping of ocean circulation and climate. The anticyclonic eddies are widely regarded as a conduit for the downward near-inertial energy propagation, while the cyclonic eddies activity influencing the near-inertial waves propagation lacks clear cognition. In this study, enhanced near-inertial waves and turbulent dissipation were observed inside both cyclonic and anticyclonic eddies in the Kuroshio Extension region, which has significant implications for improving the parameterization of turbulent mixing in ocean circulation and climate models.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Zhaohui Chen, chenzhaohui@ouc.edu.cn

Abstract

Shipboard observations of upper-ocean current, temperature–salinity, and turbulent dissipation rate were used to study near-inertial waves (NIWs) and turbulent diapycnal mixing in a cold-core eddy (CE) and warm-core eddy (WE) in the Kuroshio Extension (KE) region. The two eddies shed from the KE were energetic, with the maximum velocity exceeding 1 m s−1 and relative vorticity magnitude as high as 0.6f. The mode regression method was proposed to extract NIWs from the shipboard ADCP velocities. The NIW amplitudes were 0.15 and 0.3 m s−1 in the CE and WE, respectively, and their constant phase lines were nearly slanted along the heaving isopycnals. In the WE, the NIWs were trapped in the negative vorticity core and amplified at the eddy base (at 350–650 m), which was consistent with the “inertial chimney” effect documented in existing literature. Outstanding NIWs in the background wavefield were also observed inside the positive vorticity core of the CE, despite their lower strength and shallower residence (above 350 m) compared to the counterparts in the WE. Particularly, the near-inertial kinetic energy efficiently propagated downward and amplified below the surface layer in both eddies, leading to an elevated turbulent dissipation rate of up to 10−7 W kg−1. In addition, bidirectional energy exchanges between the NIWs and mesoscale balanced flow occurred during NIWs’ downward propagation. The present study provides observational evidence for the enhanced downward NIW propagation by mesoscale eddies, which has significant implications for parameterizing the wind-driven diapycnal mixing in the eddying ocean.

Significance Statement

We provide observational evidence for the downward propagation of near-inertial waves enhanced by mesoscale eddies. This is significant because the down-taking of wind energy by the near-inertial waves is an important energy source for turbulent mixing in the interior ocean, which is essential to the shaping of ocean circulation and climate. The anticyclonic eddies are widely regarded as a conduit for the downward near-inertial energy propagation, while the cyclonic eddies activity influencing the near-inertial waves propagation lacks clear cognition. In this study, enhanced near-inertial waves and turbulent dissipation were observed inside both cyclonic and anticyclonic eddies in the Kuroshio Extension region, which has significant implications for improving the parameterization of turbulent mixing in ocean circulation and climate models.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Zhaohui Chen, chenzhaohui@ouc.edu.cn

1. Introduction

Mesoscale eddies are energetic circulations with spatial scales on the order of 100 km and lifetimes spanning from weeks to months (Chelton et al. 2007; Ferrari and Wunsch 2009). They are ubiquitous in global oceans and are mainly generated by instabilities of large-scale ocean circulation (Gill et al. 1974; Chelton et al. 2011). Near-inertial waves (NIWs) are internal gravity waves with a frequency close to the local inertial frequency f and are energetic motions at high frequencies (Garrett and Munk 1979; Ferrari and Wunsch 2009). NIWs are characterized by circularly polarized velocities and strong shears. The lateral spatial scales of NIWs range from tens to hundreds of kilometers, and are comparable to mesoscale eddies, but their vertical wavelengths are relatively short, typically 100–400 m (Alford et al. 2016). They are usually inspired by the resonant wind forcing and therefore commonly appear in the upper ocean (D’Asaro et al. 1995; Chen et al. 2013; Pallàs-Sanz et al. 2016). Once generated in the surface layer, NIWs propagate both equatorward and downward (Gill 1984; Garrett 2001). During propagation, NIWs transform energy to waves with smaller vertical scales and ultimately break, triggering turbulent mixing in the ocean interior (Alford 2003; Whalen et al. 2020). Therefore, NIWs are supposed to be one of the main drivers of the diapycnal mixing in the interior ocean (Munk and Wunsch 1998; MacKinnon et al. 2017).

Relatively slow group velocities allow NIWs likely to interact with mesoscale eddies (Weller 1982). Mesoscale vorticity could modify the propagation pathways of NIWs by changing their intrinsic frequencies. Using the ray tracing approach based on the WKB approximation, Kunze (1985) found that the relative vorticity ζ shifts the lower bound of internal wave band from f to an effective Coriolis frequency, feff = f + ζ/2, by which the negative vorticity [e.g., the anticyclonic warm-core eddies (WEs)] traps the incident NIWs while the positive vorticity [e.g., the cyclonic cold-core eddies (CEs)] expels them. The trapped NIWs are generally reflected off the turning points in the horizontal direction and stall at the critical layers in the vertical direction, where their amplitudes increase and vertical wavelengths shrink. The critical layer behaviors of NIWs lead to strong vertical shears and give rise to intense turbulence owing to shear instabilities (Kunze 1986). A lot of the trapped NIW energy was found to have been lost to turbulence at the base of the eddy core in the WE (Kunze et al. 1995). However, the WKB approximation assumes the NIW scales are smaller than the mesoscale eddies, which makes it inapplicable to the synoptic-scale NIWs initially generated by winds (D’Asaro et al. 1995; D’Asaro 1995). To overcome this limitation, Young and Ben Jelloul (1997) developed a framework that circumvented the scale separation assumption as a supplement to Kunze’s (1985) theory, which predicts that mesoscale vorticity effectively distorts the near-inertial motions at eddy scales and subsequently accelerate their downward dispersion.

Following the above theoretical studies, several numerical studies have focused on the modification of NIW propagation by mesoscale eddies (e.g., Lee and Niiler 1998; Zhai et al. 2005), which emphasize the trapping of NIWs by the WEs. The WEs efficiently drain near-inertial energy from the surface to the deep layer below the thermocline, a phenomenon referred to as the “inertial chimney” effect (Lee and Niiler 1998). This process is significant for the down-taking of wind-generated near-inertial energy to facilitate diapycnal mixing in the deep ocean (Wunsch and Ferrari 2004; Jing and Wu 2014). The inertial chimney effect of WEs has drawn a lot of attention and has been studied extensively using numerical models (Zhai et al. 2007; Whitt and Thomas 2013; Lelong et al. 2020) and observations (Alford and Whitmont 2007; Joyce et al. 2013; Martínez‐Marrero et al. 2019). The elevated turbulent dissipation driven by the trapped NIWs in the WEs was also observed in different regions across the global ocean (Lueck and Osborn 1986; Cuypers et al. 2012; Kawaguchi et al. 2016; Fer et al. 2018; Cyriac et al. 2021).

Previous studies have significantly elucidated the inertial chimney effect and the accompanying diapycnal mixing in the WEs. According to Young and Ben Jelloul’s (1997) theory, the presence of CEs could also enhance the downward propagation of NIWs. However, the modification of NIW propagation by the CEs has been rarely reported. In numerical models, downward near-inertial energy propagation appeared in the CEs but with low strength and shallow depth (Lee and Niiler 1998; Danioux et al. 2008). Jaimes and Shay (2010) observed that NIWs stalled in the upper layers of CEs and strengthened the vertical shears and turbulence. Kawaguchi et al. (2021) observed that weak NIWs generated by the local wind forcing were trapped in the upper 300 m of a CE. Based on the limited studies mentioned above, the CEs aid in accelerating the downward NIW propagation despite lower strength and shallower residence compared to the inertial chimney effect of the WEs, which eventually leads to elevated diapycnal mixing in the interior ocean. Furthermore, the down-taking of wind-generated near-inertial energy through the CEs has a significant impact on diapycnal mixing in the global ocean (Whalen et al. 2018). This necessitates additional efforts to elucidate the NIW propagation modified by the CEs.

The Kuroshio Extension (KE) in the northwestern Pacific is one of the most dynamically complex regions across the global ocean (Donohue et al. 2008). There are abundant energetic mesoscale eddies pinched off by the eastward jet and NIWs forced by the frequent storms (Qiu and Chen 2010; Rimac et al. 2013). In this study, we compared the NIWs modified by a CE and WE as well as the concurrent turbulent dissipation based on shipboard observations in the KE region, with particular focus on the downward near-inertial energy propagation in the CE. This study begins with an introduction section comprising field observations, data collection, and a brief description of the eddy characteristics in section 2. Section 3 presents a method for separating the balanced motions and waves from the shipboard acoustic Doppler current profiler (SADCP) measurement. Results of the NIW characteristics and downward near-inertial energy propagation modified by the eddies are shown in section 4, followed by an analysis of locations of turbulent dissipation in the eddies in section 5. The energy exchange between the NIWs and eddies, and the implications for the parameterizations of turbulent mixing are discussed in section 6. Section 7 presents the conclusions drawn from the study findings.

2. Data

a. Observations of two mesoscale eddies

A spring cruise in 2018 was conducted to maintain the Kuroshio Extension Mooring System (KEMS), constructed by Ocean University of China, in the KE region in the northwestern Pacific [see Zhu et al. (2021) for details about KEMS]. To explore the dynamics in the mesoscale eddies, we designed a comparative experiment in a CE and WE shed from the KE during 18–29 May (Fig. 1a). Locations of the two eddies were tracked by the near-real-time sea level anomaly (SLA) fields distributed by AVISO (https://www.aviso.altimetry.fr/). Finally, 2 (6) transects and 10 (50) temperature–salinity (T–S) stations were deployed in the CE (WE) (Figs. 1b,c).

Fig. 1.
Fig. 1.

(a) Ship tracks (black) and stations (red) during the observations on 18–29 May 2018, overlapped on the map of time-averaged SSH distributed by AVISO. (b) Measurements of velocity using ADCP and TKE dissipation rate ε and T–S by MSS in the warm-core eddy (WE). The background map is the time-averaged SLA during the observation of the eddy. The 50 stations (red dots) and their station numbers are labeled. The six transects T1–T6 are marked by colored segments in the subgraph. The velocity vectors at a depth of 100 m are denoted by gray arrows. (c) As in (b), but for the cold-core eddy (CE).

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0160.1

The research vessel (R/V DFH2) was equipped with a 75-kHz SADCP to record the underway velocity in the upper 650 m, with a typical ship speed of ∼10 kt (1 kt ≈ 0.51 m s−1). It stopped after every several tens of kilometers to conduct an 800-m cast of turbulent kinetic energy (TKE) dissipation rate ε and T–S using the Microstructure profiler (MSS90, Sea and Sun Technology GmbH). The single ping SADCP velocity was first processed by CODAS (https://currents.soest.hawaii.edu/docs/adcp_doc/index.html) and then averaged into 10-min ensembles. Velocity profiles acquired during the ship stopping at T–S stations (usually 1–2 h) and under slow navigation were discarded because of unacceptable errors for the SADCP measurement. The velocity profiles range from 20 to 650 m and comprise 80 bins, each with a bin size of 8 m. Velocity in the first bin was disregarded owing to numerous disqualified values flagged in CODAS. Finally, we obtained a set of velocity profiles with a spacing of approximately 3 km (navigating speed of ∼10 kt and average ensembles of 10 min). The ε and T–S profiles have an original vertical interval of 1 m. To match the vertical resolution of the SADCP velocity, they were averaged into 8-m bins.

b. Characteristics of the two eddies

As shown in Fig. 1, the two eddies are close to deformed ellipses with scales of ∼200 km in the horizontal direction. Their three-dimensional structures are visible from the velocities along transects in different directions (Fig. 2). The meridional squeezing and zonal stretching of the WE lead to a greater eastward velocity u than the northward velocity υ (Figs. 1b, 2b, and 2d), while the CE is meridionally stretched and zonally squeezed so that u is smaller than υ (Figs. 1c, 2a, and 2c). According to the vertical structure of the velocity, both eddies are surface intensified with the maximum velocity exceeding 1 m s−1, are attenuated with increasing depth, and remain energetic at the maximum observation depth of 650 m. Usually, mesoscale eddies in the KE region can penetrate a 1000-m depth (Dong et al. 2017). The eddy center can be clearly distinguished by the zero line of velocity. Unlike mesoscale eddies that have distinct vertical tilts of their axes in the marginal seas of complicated topography (Zhang et al. 2016), the two eddies’ axes show nearly no tilt in the open ocean. The up-heaving (down-heaving) isopycnals of the CE (WE) reach their maximum heaves around the eddy center, thereby showing that the T–S structure is highly consistent with the velocity field.

Fig. 2.
Fig. 2.

(a) Eastward velocity component u and (c) northward velocity component υ along the space–time varying ship tracks in the cold-core eddy (CE). (b),(d) As in (a) and (c), but for the warm-core eddy (WE). The transects and T–S stations in different directions corresponding to those in Fig. 1 are marked at the top of the horizontal axis. The T–S stations near the eddy center are highlighted with their station numbers labeled. Contours of the potential density anomaly σθ are plotted to aid in identifying the eddy structure.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0160.1

Furthermore, we calculated the stratification N2 [N2=(g/ρ0)ρ/z, g = 9.8 N kg−1, ρ0 = 1025 kg m−3] and relative vorticity ζ [ζ=(dυ/dx)(du/dy)]. To remove high-wavenumber noise, N2 was estimated using the 32-m differencing of the density profile smoothed over a 32-m interval, and values N2 < 10−6 s−1 were replaced by 10−6 (Fer et al. 2018). The velocity components used to calculate the relative vorticity were first smoothed over 9 km horizontally and linearly interpolated to 3 km × 3 km horizontal grids layer by layer. Subsequently, the gridded relative vorticity was derived using the horizontal gradient of the velocity components, from which the along-track relative vorticity was finally extracted. Figure 3 shows a high (low) stratified region in 25.5–26.5 kg m−3 σθ (26.0–26.1 kg m−3 σθ) in the CE (WE) resulting from the up-heaving (down-heaving) isopycnals. The CE (WE) is characterized by positive (negative) vorticity. The relative vorticity is the strongest at the eddy center in the upper layer with a maximum magnitude up to 0.6f, and decays away from the eddy center horizontally and vertically.

Fig. 3.
Fig. 3.

As in Fig. 2, but for the (top) stratification N2 and (bottom) normalized relative vorticity ζ/f. The local inertial frequency f is 8.0 × 10−5 s−1 (8.9 × 10−5 s−1) for the CE (WE).

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0160.1

To compare the features of NIWs and turbulent dissipation inside and outside the eddy cores in the following sections, we estimated the radius of each eddy to distinguish the two regions. The location of the depth-averaged eddy center was first determined by the local minimum of the gridded velocity. As shown in Figs. 4a and 4b, the estimated eddy center of the CE (WE) is located at 33.14°N, 152.00°E (37.70°N, 147.00°E), close to that determined by the local minimum (maximum) of SLA as shown in Fig. 1. Usually, the eddy velocity increases away from the eddy center, reaches its maximum at the edge of the eddy core, and then decreases. The linear increase along with the exponential decay and the Gaussian profiles were commonly applied to the radial distribution of the velocity in mesoscale eddies (Olson 1980). Hence, we made a radial composition of the velocity with a 10-km average in the radial direction. The velocity increases first and then decreases as the radius increases, which is quite remarkable in the upper 200 m. The depth-averaged velocity above 200 m is therefore used to show the radial eddy structure, which displays an apparent Gaussian distribution for both eddies (Figs. 4c,d). Fitting the depth-averaged velocity with the Gaussian function, V(r)=V0(r/r0 )exp{[(r/r0)21]/2}, where V0 is the maximum velocity located at r0 away from the eddy center (Bosse et al. 2017), yields eddy radii r0 of 77 and 56 km for the CE and WE, respectively.

Fig. 4.
Fig. 4.

(a) Map of the depth-averaged (above 200 m) velocity on the 3 km × 3 km horizontal grids by linear interpolation for the cold-core eddy (CE). The depth-averaged eddy center estimated by the local minimum velocity is marked by the red dot. The regions of missing values are masked by gray dots. The ship tracks are overlaid by the gray dashed lines. (c) The depth-averaged velocity above 200 m (black dots) is fitted with the Gaussian profile (red line) to estimate the eddy radius r0 of the CE, using the location of the maximum velocity V0. Outliers (gray dots) at the eddy periphery are excluded from the fitting. (b),(d) As in (a) and (c), but for the warm-core eddy (WE).

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0160.1

3. Separating balanced motions and waves from shipboard ADCP measurement

a. Method

The SADCP velocity contains multifrequency signals contributed by different motions, including the geostrophic and cyclogeostrophic balanced flows at low frequencies and the unbalanced part dominated by internal gravity waves at high frequencies (Torres et al. 2018). Conventionally, a temporal or spatial filter is used to separate motions of different scales (Thomson and Emery 2014). However, the space–time aliasing of the SADCP velocity precludes the separation of the balanced motions and waves by the frequency-domain filter (Alford et al. 2013). Considering the mismatch between the vertical wavelengths of the balanced motions and waves, applying the vertical wavenumber filter to a single velocity profile to realize the separation is feasible. Wavenumber-domain filter (Karstensen et al. 2017; Martínez‐Marrero et al. 2019) and fit (Kunze 1986; Joyce et al. 2013) were commonly used for a velocity profile to separate the mesoscale balanced flow and NIWs by first obtaining the trend of the balanced flow and then subtracting the trend from the total velocity to derive the NIWs. However, the selection of vertical cutoff wavenumber and fitting functions mainly relies on subjective judgments, requiring sensitivity experiments to identify optimal practice.

Inspired by the vertical sine structure of mesoscale eddies in the stretched coordinate (Zhang et al. 2013), a SADCP velocity profile was projected on the first two “vertical modes” (F1 and F2) decomposed from the observed T–S profiles by linear regression. The trend of the mesoscale balanced velocity was obtained and then the waves can be derived by subtracting the balanced velocity from the total velocity. Therefore, we call the method above Mode Regression Method (MRM). MRM assumes that the first baroclinic mode is solely from the mesoscale eddy because the first mode component of the NIWs propagates fast and quickly leaves the observation area (Chen et al. 2013). In addition, the first two vertical modes differ from the barotropic and first baroclinic modes of Rossby waves in magnitude because the observed T–S profiles are not in full water depth, but their vertical trends are similar to the latter with F1 and F2 being constant and stretched sine, respectively. As shown in Fig. 5, the balanced velocity Vb can be calculated using the following equation:
Vbp=ck(b1kF1k+b2kF2k)+ck+1(b1k+1F1k+1+b2k+1F2k+1),
where Vbp is the pth balanced velocity profile between the kth and (k + 1)th T–S station pair, F1 and F2 are the first two vertical modes at the station pair, b is the regression coefficient, and c is the weighting coefficient of the balanced velocity profile at each station [ck = Lk+1/(Lk + Lk+1), ck+1 = Lk/(Lk + Lk+1), where L is the distance of the velocity profile to the nearby station pair]. Superscripts p and k indicate the positions of the velocity and T–S profiles, respectively. Subscripts 1 and 2 correspond to the first two vertical modes.
Fig. 5.
Fig. 5.

Schematic of extracting the balanced velocity (blue) from the SADCP velocity profiles (gray) by MRM. Positions of the T–S station pair and velocity profiles are denoted by red and black dots, respectively. The Vbp is the pth balanced velocity profile between the kth and (k + 1)th T–S station pair, Fn indicates the first two vertical modes decomposed from the T–S profiles at the station pair (n = 1, 2), and L is the distance of the velocity profile to the nearby station pair. The displayed velocity profiles are the SADCP velocity between the station pair 26–27 in the warm-core eddy.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0160.1

b. Validation of mode regression method

We validated MRM by comparing the balanced velocity extracted by MRM with the geostrophic/cyclogeostrophic balanced velocity diagnosed from T–S. The T–S station pairs that were nearly aligned in the meridional or zonal directions were selected for the diagnosis of the balanced velocity (e.g., station pairs 18–19 in the CE and 25–26 in the WE, Figs. 6a,c). To draw close to the trend of the SADCP velocity profile, the balanced velocity was regarded as the cyclogeostrophic velocity Vc for the CE and geostrophic velocity Vg for the WE. The cyclogeostrophic velocity Vc was calculated using the following equation:
Vc2fR+Vc=Vg,
where Vg is the geostrophic velocity diagnosed from T–S, and R is the distance from the eddy center to the position of Vc. The reference geostrophic velocity took the MRM-derived balanced velocity at a depth of 650 m and was averaged between the station pairs.
Fig. 6.
Fig. 6.

(a) T–S stations (black dots) and the station pairs selected for the calculation of geostrophic velocity (red dots) in the cold-core eddy (CE). (b) Comparison of the SADCP (gray), MRM-derived (blue), and geostrophic/cyclogeostrophic balanced (red) velocity profiles in the CE. GB and CGB are the abbreviations of geostrophic balance and cyclogeostrophic balance, respectively. Root-mean-square (RMS) bias between the diagnosed balanced velocity and the MRM-derived balanced velocity is marked in black text. (c),(d) As in (a) and (b), but for the warm-core eddy (WE). The cyclogeostrophic (geostrophic) balanced velocity of the CE (WE) is regarded as the reference for examining the MRM-derived balanced velocity.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0160.1

As shown in Fig. 6, although the diagnosed balanced velocity shows a trend that is similar to that of the SADCP velocity, the two velocities exhibit large shifts at certain station pairs, which probably results from the fast-varying flow compared to the slow-varying T–S owing to the eddy deformation and/or movement, like station pairs 1–2 and 19–20 (1–2 and 26–27) at the eddy periphery of the CE (WE), and station pairs 3–4 and 16–17 (21–22 and 22–23) at the eddy center of the CE (WE). At other station pairs, the diagnosed balanced velocity is consistent with the SADCP velocity trend and can therefore be regarded as a reference for examining the accuracy of the balanced velocity derived by MRM. The root-mean-square bias between the diagnosed balanced velocity and the MRM-derived balanced velocity does not exceed 5 (6) cm s−1 in the CE (WE), significantly lower than the balanced velocity and also lower than the wave amplitude (i.e., residual velocity), accounting for approximately one-third (one-fifth) of the typical wave amplitude (shown in the subsequent section). Therefore, MRM was confirmed to be valid for separating the balanced motions and waves from the SADCP velocity.

MRM is a fit that is similar to the smooth spline fit used by Joyce et al. (2013). We found that the residual velocities derived by MRM and the smooth spline fit differed slightly (figures not shown). The smooth spline fit was performed using the curve fitting toolbox in MATLAB, with the smoothing parameters artificially selected as 0.1 to better fit the trend of the SADCP velocity. In addition, the 350-m lowpass Butterworth filter used by Martínez‐Marrero et al. (2019) was also applied to the SADCP velocity to separate the balanced motions and waves, but it failed to completely extract the waves owing to the relatively long vertical wavelengths we observed. Therefore, MRM has the advantage of objectivity compared to the vertical wavenumber filter and fit. Theoretically, MRM is applicable for regions dominated by geostrophic/cyclogeostrophic dynamics, such as in the mesoscale eddies as well as western boundary currents and their jet-like extensions.

4. Enhanced NIWs observed in the two eddies

The waves separated from the SADCP velocity are mainly composed of internal waves, like NIWs and internal tides (Torres et al. 2018). Internal tides are weak in the upper 1000 m in this region (Zhao et al. 2016). Therefore, the waves are speculated to be dominated by NIWs. We estimated the vertical wavenumber spectra of the velocity and shear of the waves, and compared them with the GM spectra. The WKB normalization was applied to the waves to remove the effect of stratification. As shown in Fig. 7, the observed spectra are consistent with the GM spectra, and the spectral peak is located at a vertical wavelength ranging between 200 and 400 m, indicative of the dominance of NIWs.

Fig. 7.
Fig. 7.

Clockwise (CW) and counterclockwise (CCW) vertical wavenumber spectra of the (a) NIW velocity and (b) NIW shear in the cold-core eddy (CE). (c),(d) As in (a) and (b), but for the warm-core eddy (WE). The displayed spectra are the average spectra inside (r < r0/2, “In”) and outside (r > r0, “Out”) the eddy core, and r0 is the radius of the eddy core. The 95% confidence interval is marked by the error bar. The vertical wavelengths are shown at the top of the horizontal axis. The NIW shear is estimated using the 32-m vertical gradient of the NIW velocity smoothed over a 32-m interval to remove the noise at high wavenumbers. The GM spectra are calculated using the MATLAB toolbox downloaded from http://jklymak.github.io/GarrettMunkMatlab/.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0160.1

a. Eddy-modified NIW characteristics

Figure 8 shows the NIW structure along the transects in different directions. NIWs are enhanced inside the eddy cores of both eddies. The typical NIW amplitude in the CE is approximately 0.15 m s−1, half of that of the WE, which is 0.3 m s−1. In the CE, the strong NIWs are mainly concentrated around the eddy center at a depth exceeding 350 m. On the contrary, the NIWs are amplified at the base of the eddy core at depths below 350 m in the WE, which is the feature of the trapped NIWs encountering the critical layers (Kunze 1986; Martínez‐Marrero et al. 2019). The NIW structure in the CE has been rarely observed and compared with that in the WE. Kawaguchi et al. (2021) observed attenuated NIWs across the inner core of a CE, but the most energetic waves were packed at a depth above 150 m, probably because the CE was weaker (<0.3 m s−1) and shallower (above 200-m depth) compared to the CE shed from the KE in this study.

Fig. 8.
Fig. 8.

As in Fig. 2, but for the NIW velocity; u′ and υ ′ are the eastward and northward velocity components.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0160.1

The NIWs have constant phase lines almost slanting along the heaving isopycnals, which is consistent with the NIW characteristics shown in previous studies (Alford 2010; Joyce et al. 2013). The heaving NIW phase along with the isopycnals was found to be the manifestation of water parcels oscillating along the isopycnals under the strong baroclinicity of mesoscale eddies (Whitt and Thomas 2013). NIW phase θ can be identified by combining the signs of the velocity components, u′ and υ ′, of the NIW velocity (i.e., the direction of the velocity) in Fig. 8 or calculated by the equation, θ=tan1(υ/u), as shown in Fig. 9.

Fig. 9.
Fig. 9.

As in Fig. 2, but for NIW phase θ (top) before and (bottom) after inertial back-rotation. The θ is calculated with the NIW velocity components horizontally smoothed over 30 km.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0160.1

To better show the spatial structure (snapshot) of the NIWs, the inertial back-rotation was used to remove the temporal evolution of the NIWs (Alford et al. 2013). As the NIWs are dominated by the clockwise component (recall Fig. 7), the NIW velocity was rotated counterclockwise to a time point before the observation:
w^(x,y,z,τ)=w(x,y,z,t)exp[iω(ttref)],
where w(x, y, z, t) is the complex NIW velocity at a given time t (w = u′ + ′, the eastward component u′ and northward component υ′), w^(x,y,z,τ) is the back-rotated velocity that varies slowly with a “slow time” τ relative to an inertial period, ω is the NIW frequency usually approximated by the local inertial frequency, f. Here, ω is approximated by f for the CE but is 0.8f for the WE to reduce the frequency error amplified by the 6-day-long duration in the WE. The tref is the reference time and is set to the initial observation time of each eddy, respectively.

After inertial back-rotation, most of the discontinued NIW phase along the ship tracks resulting from the stops at T–S stations and slow navigation is removed (Figs. 810; Shcherbina et al. 2003). Upon examining the phase change in transect 3 of the WE, discontinuities are observed to vanish. This transect has opposing NIW phases on the two sides owing to the intrinsic long and slow navigation that is sufficient for the NIWs to rotate half a circle (Figs. 8b, 8d, and 9b), whereas the phases become consistent across the transect after inertial back-rotation (Figs. 9d, 10b, and 10d). Generally, the NIW phases in both eddies become more coherent along the isopycnals across the entire eddy after inertial back-rotation (Fig. 9). For example, most of the NIW phase in 25.5–26.0 kg m−3 σθ (26.0–26.1 kg m−3 σθ) in the CE (WE) is positive along the transects in different directions, indicating that the observed NIWs in each eddy are all part of the same wave packet.

Fig. 10.
Fig. 10.

As in Fig. 2, but for the NIW velocity after inertial back-rotation; u′ and υ ′ are the eastward and northward velocity components.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0160.1

According to the vertical and horizontal variations of the NIW phase after inertial back-rotation (Figs. 9c,d), the wavelengths can be determined by the NIW phase spanning a complete cycle (changing from −180° to 180°). The vertical wavelengths of the NIWs are approximately 300 m in the CE and 400 m in the WE. In the horizontal direction, the NIW phase is almost consistent throughout the eddy for both eddies; therefore, the horizontal NIW scales are comparable to the eddy size.

b. Downward propagation of NIW energy

The vertical NIW propagation is visible from the changing of the NIW phase versus depth (Fig. 9). The NIWs are of clockwise rotation by the dominance of clockwise energy (recall Fig. 7) and a 90° phase lead for u′ versus υ′ through a downward view in Figs. 8 and 10. Generally, clockwise rotating NIWs (in the Northern Hemisphere) have a downward group speed (Leaman and Sanford 1975). Such energetic NIWs of downward propagation are usually generated by the wind. Because NIW energy is dominated by the near-inertial kinetic energy (NIKE), we calculated the NIKE with the NIW velocity that was first processed by WKB normalization to remove the stratification effect and then smoothed over a 32-m interval to eliminate noise at high vertical wavenumbers. In addition, we made a radial composition to the NIKE to show its distribution in the eddy. As shown in Figs. 11 and 12, the enhanced NIKE more than the canonical value of 3 J m−3 (Munk 1981) appears inside the inner core (r < r0/2) of the WE and CE. The enhancement of NIKE inside the inner core is thought to result from the inward and downward energy propagation (Fig. 9). For this reason, we considered the average of the NIW profiles inside the inner cores when comparing the NIW spectra inside and outside the eddy cores in Fig. 7. Then, we would separately analyze the three-dimensional structures of the NIKE in the two eddies.

Fig. 11.
Fig. 11.

Three-dimensional structure of the near-inertial kinetic energy (NIKE) in the warm-core eddy (WE). (a) Radial section of the NIKE averaged every 10 km in the radial direction. The contours of the potential density anomaly σθ are overlaid with dashed lines. (b) Radial distribution of the depth-averaged NIKE. Average profiles of the NIKE (full line) and relative vorticity (dashed line) inside (r < r0 /2) and outside (r > r0) the eddy core in the (c) σθ and (d) depth coordinate. (e) Clockwise (CW) and counterclockwise (CCW) NIKE inside the eddy core. The canonical value of 3 J m−3 (gray dashed line) in (b)–(e) is marked for reference. The NIKE is calculated by NIW velocity that is first WKB normalized and vertically smoothed over a 32-m interval. r is the distance from the eddy center, and r0 is the eddy radius of 56 km.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0160.1

Fig. 12.
Fig. 12.

As in Fig. 11, but for the three-dimensional structure of the NIKE in the CE. The eddy radius r0 is 77 km.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0160.1

In the WE, the enhanced NIKE appears in regions of negative vorticity, which is known as the inertial chimney effect (Lee and Niiler 1998; Fig. 11). Generally, the NIKE is amplified at the base of the eddy core at depths ranging from 350 to 650 m with the maxima exceeding 40 J m−3 (Fig. 11a), which results from the stall of the NIWs that have their vertical wavelengths shrunk and amplitudes enlarged at the critical layers. Radially, the depth-averaged NIKE reaches 19 J m−3 at the eddy center and decreases away from the center (Fig. 11b). This radial structure of the NIKE is consistent with the azimuthal-mode-one eddy-trapped NIWs (Kunze and Boss 1998). Vertically, approximately 67% of the NIKE propagates downward via the inertial chimney effect. The average NIKE inside the inner core peaks at ∼18 J m−3 and a depth of ∼450 m, which is approximately 6 times larger than that at the same depth outside the eddy core (Figs. 11c–e).

Similar to the WE, the enhanced NIKE appears in regions of positive vorticity inside the inner core of the CE, but with lower strength and shallower residence (Fig. 12). There is an energetic wave packet between 150 and 350 m with the maxima exceeding 10 J m−3 (Fig. 12a), only one-quarter of that in the WE. The depth-averaged NIKE shows a decreasing radial structure, similar to that in the WE (Fig. 12b). The average NIKE inside the inner core peaks at ∼6 J m−3 at a depth of ∼250 m, which is approximately 3 times larger than that at the same depth outside the eddy core (Fig. 12d). Jaimes and Shay (2010) have observed the vertical structure of NIW amplitude in a CE that is similar to Fig. 12d, which is intensified in the upper 250 m and reaches the maximum at ∼125-m depth, shallower than the 250-m depth in our observation. The difference is the NIWs are dominated by the upward propagation component in their study (Jaimes and Shay 2010).

The enhanced NIKE in the inner core of the CE is thought to result from the vertical dispersion of the NIWs accelerated by the existence of relative vorticity in mesoscale eddy fields (Young and Ben Jelloul 1997). Unlike the negative vorticity in the WE, which can trap the NIWs and drain the NIW energy deep into the eddy base through the inertial chimney effect, the positive vorticity seems to have less influence on the downward NIW propagation so that the enhancement of the NIKE is relatively weak and shallow (Figs. 12d,e).

5. Enhanced turbulent dissipation observed in the two eddies

As shown in Figs. 13c and 13f, the TKE dissipation rate ε is as high as 10−7 W kg−1 in both eddies, accompanied by an elevated diapycnal mixing with the vertical diffusivity Kρ (Kρ = 0.2ε/N2, Osborn 1980) up to 5 × 10−4 m2 s−1, which is 50 times larger than the average value in the upper 1000 m (10−5 m2 s−1, Waterhouse et al. 2014). To explain the mechanisms of the turbulence generation, the vertical shears of the NIWs and mesoscale balanced flow were calculated (Figs. 13a,b,d, e). The NIW shear is one order of magnitude larger than the mesoscale shear and is mainly responsible for turbulence production. The gradient Richardson number, Ri, was estimated as follows: Ri = N2/S2. Similar to the estimation of N2, the total shear S2 was calculated using the 32-m vertical gradient of the total velocity that was first smoothed over a 32-m interval, and the values below 10−6 s−1 were replaced by 10−6 to remove noise at high wavenumbers (Fer et al. 2018). As shown in Figs. 14c and 14h, the average Ri significantly exceeds its critical value of 0.25 for the production of turbulence because of the 32-m average and the difficulty in detecting the patchy and intermittent turbulence by a velocity of 8-m vertical space and 10-min average. The average Ri is below 15 with the increasing ε, which might suggest the production of turbulence by shear instability.

Fig. 13.
Fig. 13.

Radial sections of the (a) NIW shear SNIW2, (b) eddy shear Seddy2, (c) TKE dissipation rate ε in the CE. (d)–(f) As in (a)–(c), but for the WE. The radial compositions of the shears take a 10-km average in the radial direction. The TKE dissipation rate ε profiles are plotted individually to avoid the discrepancy of magnitudes by average, and the larger values are overlaid on the smaller ones; r is the distance from the eddy center, and r0 is the eddy radius of 77 km (56 km) for the CE (WE).

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0160.1

Fig. 14.
Fig. 14.

Vertical structures of the (a) stratification N2, (b) total shear S2, (c) Richardson number Ri, (d) TKE dissipation rate ε, and (e) vertical diffusivity Kρ inside (red) and outside (blue) the core of the CE. (f)–(j) As in (a)–(e), but for the WE. The N2 and S2 are estimated by the 32-m vertical gradient of the density and total velocity that are smoothed over a 32-m interval. The S2 are calculated with velocity profiles at the T–S stations to match the observation of the TKE dissipation rate ε.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0160.1

In the WE (Figs. 13d,f), the elevated turbulent dissipation shows good consistency with the strong NIW shear, implying the efficient turbulence production driven by the NIWs. The turbulent dissipation is enhanced in two regions. One is in the surface layer of high stratification, which is in funnel shape following the down-heaving isopycnals that extend to depths of 200 and 100 m in the eddy center and periphery, respectively. Another is at the base of the eddy core at a depth ranging from 350 to 650 m, which results from the shrinking of the vertical NIW wavelengths at the critical layers. Between the two regions, a reduced turbulent dissipation following the suppression of the NIW shear is a common feature of these structures because of the increase in vertical wavelength caused by reduced stratification and negative vorticity (Fernández-Castro et al. 2020). In other words, the NIWs generated in the surface layer are radially trapped in the WE, propagate downward through the region of negative vorticity inside the eddy core, and finally break to drive the elevated turbulent dissipation and vertical diffusivity inside the eddy core, which are 3–4 times larger than those on the outside (Figs. 14g–j). The high–low–high sandwiched structure of the turbulent dissipation associated with trapped NIWs in the WE is generally consistent with observations made in other oceans (e.g., Lueck and Osborn 1986; Cuypers et al. 2012; Fer et al. 2018).

Turbulent dissipation following the NIW shear is also expected in the CE. Figures 13a and 13c show that the elevated turbulent dissipation mainly occurs in the sloping region above the 26.0 kg m−3 σθ, which is similar to the enhanced thermocline mixing due to eddy-induced geostrophic shear in a permanent CE, the Mindanao Eddy (Liu et al. 2017). The eddy shear is smaller than the NIW shear in our observation (Figs. 13a,b), and thus is unlikely to induce such strong turbulent dissipation. Therefore, we attempt to partly explain the turbulence production by the shear instability of NIWs. Locally, the turbulent dissipation enhanced in the high-stratified surface layer above a depth of 100 m is consistent with the strong NIW shear there, and that sporadically appears in regions below the surface layer inside the eddy core might result from the strong NIW shear as well. However, the turbulent dissipation is significantly higher and more concentrated in the eddy periphery (25.0–26.0 kg m−3 σθ, deep to 400-m depth), where the NIW shear is weaker than that inside the eddy core but the eddy kinetic energy is higher. We speculate there are other mechanisms of producing turbulence by cascading the eddy energy forward. For example, the submesoscale motions commonly generated in the eddy periphery (Yang et al. 2017) can penetrate far beneath the mixed layer through the presence of a weakly stratified transitional layer (e.g., the layer in 25.0–25.5 kg m−3 σθ in the CE in Figs. 3a) between the mixed layer and the thermocline, and eventually transfer the eddy energy to the turbulence through symmetric instability (Zhang et al. 2021).

In this study, we focus on the turbulent dissipation and diapycnal mixing driven by NIWs. Therefore, the enhancement of turbulent dissipation and diapycnal mixing inside the core of CE is relative to the global-averaged values in the upper ocean, rather than those outside the CE. In fact, the average turbulent dissipation and diapycnal mixing inside the CE are comparable with those driven by the trapped NIWs inside the WE (Figs. 14d,e,i,j). This indicates enhanced turbulent dissipation and diapycnal mixing driven by the downward propagating NIWs inside the CE.

6. Discussion

a. NIWs-eddy energy exchange

Energy exchange between NIWs and mesoscale eddies occurs when the NIWs are captured by the mesoscale strain (Bühler and McIntyre 2005). There are many theoretical and numerical studies focusing on NIWs–eddy energy exchange (e.g., Jing et al. 2017; Thomas and Arun 2020), while observational evidence is still quite limited. With the separated mesoscale balanced flow and the NIWs, we calculated the horizontal energy transform rate using the following equation:
Fh=(uuυυ)Sn2uυSs,
where u and υ are the velocity components of the NIWs. The terms Sn = Ux − Vy and Ss = Uy + Vx are the normal and shear components of the balanced flow. The U and V are the velocity components of the balanced flow (Polzin 2010). The calculation of Sn and Ss is similar to the estimation of the relative vorticity (section 2).

As shown in Figs. 15a and 15c, the NIWs both extract energy from (positive Fh) and transfer energy to (negative Fh) the mesoscale balanced flow, indicating the lack of a unique direction for the NIWs–balanced flow energy exchange (Thomas and Daniel 2020). The instantaneous energy transform rate is as high as 10−7 W kg−1, the same as that calculated in numerical model for the NIWs trapped by the WE (Lelong et al. 2020), but is two to three orders larger than the time-averaged values (Jing et al. 2018; Cusack et al. 2020).

Fig. 15.
Fig. 15.

(a) Horizontal energy transform rate Fh between NIWs and mesoscale eddies and (b) the average Fh inside the core of the CE vs the balance-to-NIWs energy. (c),(d) As in (a) and (b), but for the WE. The positive and negative Fh indicate the increase and decrease of the NIW energy, respectively.

Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0160.1

By comparing the average energy transform rate and the balance-to-NIWs energy inside the eddy, there appears to be a positive relation between them (Figs. 15b,d). In addition, there appears to be a critical value for the balance-to-NIWs energy to separate the positive and negative energy transform rate. When the balance-to-NIWs energy is high, the NIWs mainly draw energy from the balanced flow; however, when this ratio drops below the critical value, the NIWs transform energy to the balanced flow. The finding likely supports the numerical result that the NIWs transfer energy to balanced flows in regimes where balance-to-wave energy is low (Thomas and Daniel 2020).

b. Implication for parameterizing the wind-driven diapycnal mixing

Theoretical and numerical studies showed downward NIW energy propagation enhanced by the presence of mesoscale eddies (Kunze 1985; Young and Ben Jelloul (1997); Zhai et al. 2005; Danioux et al. 2008). In this study, the enhanced downward NIW energy propagation was observed inside the eddy cores of a CE and WE, which led to an elevated turbulent dissipation and diapycnal mixing in the interior ocean. The down-taking of wind-generated near-inertial energy through the inertial chimney effect of the WEs plays an important role in furnishing turbulent diapycnal mixing in the deep ocean (Kunze et al. 1995; Jing and Wu 2014; Fer et al. 2018). However, the downward NIW energy propagation enhanced by the CEs is somewhat debatable and lacks observation evidence. In our observations, the NIKE was enhanced inside the eddy core of the CE and facilitated an elevated turbulent dissipation below the surface layer, albeit with lower strength and shallower residence than those in the WE. From a global perspective, the wind-generated near-inertial energy propagating downward through the CEs might be nonnegligible in the eddying ocean, which has significant implications for the parameterization of wind-driven diapycnal mixing in climate models (Wunsch and Ferrari 2004; Whalen et al. 2020).

7. Conclusions

Shipboard observations of the upper-ocean current, temperature–salinity, and turbulent dissipation rate were conducted in a cold-core eddy (CE) and warm-core eddy (WE) in the Kuroshio Extension (KE) region in May 2018. The maximum velocities of the two eddies shed by the KE exceeded 1 m s−1 and the relative vorticity magnitude was as high as 0.6f. They were close to deformed ellipses with a scale of ∼200 km in the horizontal direction, and eddy core radii of 77 and 56 km for the CE and WE, respectively. Both eddies were surface intensified and remained energetic at the maximum observation depth of 650 m. The mode regression method (MRM) was proposed to separate the balanced motions and waves from the space–time aliasing shipboard ADCP velocities, and was confirmed to be valid and objective. In this study, the waves extracted by MRM were dominated by near-inertial waves (NIWs).

The enhanced NIWs were found inside the eddy cores of both eddies, with typical NIW amplitudes reaching up to 0.15 and 0.3 m s−1 in the CE and WE, respectively. The NIWs had their constant phase lines slanting along the heaving isopycnals under the modification of the strong baroclinic eddy flow, with the vertical wavelengths being approximately 300–400 m and the horizontal scale being comparable to the eddy size. They were dominated by clockwise rotation and efficiently propagated downward in regions of strong relative vorticity inside the eddy cores, leading to enhancement of the near-inertial kinetic energy (NIKE) far beneath the surface layer. In the WE, the NIKE was enhanced at the base of the eddy core at depths ranging between 350 and 650 m owing to the amplification of the downward propagating NIWs at the critical layers. The maximum NIKE was as high as 40 J m−3 and its average value inside the eddy core reached up to ∼18 J m−3 at a depth of ∼450 m, which is approximately 6 times larger than that at the same depth outside the eddy. In the CE, the enhanced NIKE was located at depths ranging between 150 and 350 inside the inner core of the eddy, with the maxima exceeding 10 J m−3 and an average of ∼6 J m−3 at a depth of ∼250 m, which is approximately 3 times larger than that at the same depth outside the eddy core. Compared to the deep propagation of the NIKE through the inertial chimney effect in the WE, the enhanced NIKE with lower strength and shallower residence in the CE was speculated to result from the enhanced downward dispersion of the NIWs by the existence of strong relative vorticity.

The downward propagating NIWs had strong shears and drove an elevated turbulent dissipation rate ε (10−7 W kg−1) and a vertical diffusivity Kρ (5 × 10−4 m2 s−1), below the surface layer in both eddies. In the WE, the elevated turbulent dissipation followed the strong NIW shear, which was enhanced in the high-stratified surface layer above the upper 200 m, weak in the low-stratified midlayer, and strongest at the base of the eddy core of the WE because of the variation of NIW vertical wavelengths with the changing stratification and relative vorticity versus depth. In the CE, the strong NIW shear also induced an enhanced turbulent dissipation that was concentrated in the surface layer above 100 m and patchily appeared in regions of strong NIW shear inside the eddy core.

The results in the present study show clear images of the eddy-modified NIW structures and turbulent dissipation in a CE and WE in the KE region and provide observational evidence for the downward NIW propagation accelerated by the presence of mesoscale eddies, which has significant implications for parameterizing the wind-driven diapycnal mixing in the eddying ocean. In the future, it is necessary to estimate the global diapycnal mixing based on high-resolution ocean circulation and climate models that take the downward NIW propagation modified by the CEs into account.

Acknowledgments.

We thank the three reviewers for their detailed and constructive comments that helped us greatly improve our manuscript. We also thank all crew of the R/V DFH2 for their great efforts. This study was funded by the National Natural Science Foundation of China (42076009, 41822601, 41806008 and 41776006), Qingdao Pilot National Laboratory for Marine Science and Technology (2017ASTCP-ES05), and Fundamental Research Funds for the Central Universities (201762013 and 202072001). Z. C. is partially supported by Taishan Scholar Funds (tsqn201812022).

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