1. Introduction
Near-inertial waves (NIWs), caused by the restoring force from Earth’s rotation, are one of the two types of energetic internal waves widely observed in the ocean (the other type is internal tides). In the Northern Hemisphere, the currents associated with the inertial motions always exhibit clockwise polarization. Surface winds, including traveling storms (D’Asaro 1985), hurricanes (Firing et al. 1997), typhoons (Chen et al. 2010), and monsoons (Shu et al. 2016), are critical for the generation of NIWs. When a strong wind blows at the surface, the wind stress forces inertial motions in the mixed layer; subsequently, internal waves with a frequency close to the local inertial frequency (f = 2Ω sinφ, where Ω represents the angular velocity of Earth’s rotation and φ represents the latitude) are generated at the base of the mixed layer owing to horizontal convergences and divergences (Gill 1984).
Wind work on the ocean surface contributes substantial energy to oceanic near-inertial motions (0.3–1.5 × 1012 W), which is comparable to the energy involved in the conversion of barotropic tides to internal tides in the deep ocean (∼0.9 × 1012 W) (Alford 2001; Egbert and Ray 2000; Thomas and Zhai 2022). After their generation, energetic NIWs propagate downward and equatorward (Garrett 2001), thereby significantly contributing to turbulent mixing in the upper and deep ocean (e.g., Hebert and Moum 1994; Alford and Gregg 2001; Silverthorne and Toole 2009; Alford et al. 2012). Under the assumption of horizontal propagating periodic solutions, the governing equations of internal waves reduce to a single dimension with solutions in the form of vertical normal modes (Musgrave et al. 2022). Normal mode analysis has been widely used to identify the vertical modal content of NIWs (e.g., Alford 2010; Cao et al. 2021). Although high-mode NIWs with high wavenumbers are more important for mixing because of their high shear, more energy is contained in the low-mode NIWs, which move fast and can travel thousands of kilometers from their sources (Alford 2003, 2010; Simmons and Alford 2012).
The South China Sea (SCS) is the largest marginal sea in the western Pacific; it is affected by frequent tropical cyclones and Asian monsoons that often generate energetic NIWs. Previous observations have mainly focused on NIWs on the continental shelf and the upper ocean of the SCS. On the stratified continental shelf, typhoon-induced NIWs are dominated by the first baroclinic mode, and their oscillations vary from 15 to 60 cm s−1 for meridional and zonal current components (Z. Sun et al. 2011; Chen et al. 2015; Sun et al. 2015; Yang et al. 2015; Shen et al. 2020; Li et al. 2021); away from the continental shelf, typhoon-induced NIWs oscillate from 10 to 150 cm s−1 (L. Sun et al. 2011; Chen et al. 2013; Guan et al. 2014; Yang and Hou 2014; Zhang et al. 2016; Cao et al. 2018; Ma et al. 2019; Yang et al. 2021). In the upper ocean, typhoon-induced NIWs can persist from several days to half a month. NIWs in the subsurface layer are larger in autumn owing to the occurrence of typhoons in the SCS (Chen et al. 2013). Monsoons are another driver in NIW generation. Observations in the central SCS indicate that the oscillations of NIWs induced by the summer monsoon onset reach 25 cm s−1 in the upper ocean and are comparable to those of typhoon-induced NIWs (Shu et al. 2016). In addition, background relative vorticity (Chen et al. 2013; Sun et al. 2015; Le Boyer et al. 2020; Yang et al. 2021) and nonlinear interactions (Alford 2008; Guan et al. 2014; Liu et al. 2018; Shen et al. 2020) also contribute to the NIW evolution in the SCS.
Although there are several observational case studies of typhoon-induced NIWs, most of them utilized moorings in the upper ocean and focused on the upper 1000 m. Only a few studies have mentioned NIWs in the deep SCS (Yuan et al. 2002; Xiao et al. 2016; Ma et al. 2022), and their relationship with surface winds remains poorly understood. An array including 39 current- and pressure-recording inverted echo sounders (CPIESs) and two moorings were deployed within an area of approximately 6° × 6° in the northeastern SCS to clarify the circulations and dynamic processes in that region (Zheng et al. 2021a, b, 2022a,b; Zhao et al. 2023; Wang et al. 2023). Typhoon Mangkhut was the strongest tropical cyclone that occurred in the SCS during the monitoring period and traveled across the center of the array on 15 September 2018, with a wind speed of approximately 48 m s−1. Our observations provide an unprecedented opportunity to study the characteristics of typhoon-induced NIWs in the upper and deep SCS, and to compare conditions on the left and right sides of the typhoon track.
The remainder of this paper is organized as follows. The data and methods used in this study are described in section 2. The observations of NIWs in the upper and deep SCS after the crossing of Typhoon Mangkhut are described in section 3. The vertical modes of NIWs are analyzed in section 4. The discussion of the influence of an anticyclonic eddy is provided in sections 5 and 6 summarizes the study.
2. Data and methods
a. CPIES observations
A total of 39 CPIESs (C13–C51) were deployed in the northeastern SCS for hundreds of days from west of the Luzon Strait to the interior SCS (Fig. 1) to elucidate the SCS circulation. All instruments were successfully recovered, except for C19. Of the recovered instruments, six (i.e., C41–C43, C46, C48, and C51) were deployed from July 2016 to April 2019; five (i.e., C44, C45, C47, C49, and C50) were deployed from October 2017 to April 2019; four (i.e., C21, C23, C29, and C30) were deployed from December 2017 to July 2019; and the rest were deployed from June 2018 to July 2019.
Map of the study region in the South China Sea. Blue stars and red triangles indicate current- and pressure-recording inverted echo sounder (CPIES) and mooring sites, respectively. The black line indicates the track of Typhoon Mangkhut (2018). White dots indicate the position of the typhoon along the track every 6 h; its maximum wind speed is also indicated. Arrows indicate the surface geostrophic currents recorded by satellite altimeter on 15 Sep.
Citation: Journal of Physical Oceanography 53, 10; 10.1175/JPO-D-22-0136.1
The CPIES consisted of a benthic pressure-recording inverted echo sounder (PIES) and an Aanderaa Doppler current sensor approximately 50 m above the seafloor. Near-bottom zonal and meridional currents (u, υ) were measured by current sensors with ±0.15 cm s−1 absolute accuracy, operating at hourly intervals. The PIES transmitted a 12.0-kHz pulse upward and recorded the round-trip acoustic travel time from the bottom to the surface (τ) 24 times each hour. All records were preprocessed as described by Zheng et al. (2021a, 2022a). High-quality current observations were collected at most sites; however, current sensors at C24, C32, C34, C41, and C42 stopped working in February 2019, October 2018, January 2019, June 2017, and January 2019, respectively. Nevertheless, the CPIES observations covered the period when Typhoon Mangkhut crossed the northern SCS in September 2018, except for C19 and C41. Although near-inertial motions are dominated by nearly horizontal currents, the tiny vertical displacements of isotherms of the first mode NIWs are expected to be detected by τ (Park and Watts 2005). Hence, τ after typhoon was used to quantify the first mode NIWs in the study.
b. Mooring observations
In addition to CPIESs, two tall moorings named M01 (21.5°N, 119.8°E) and M02 (19.1°N, 119.8°E) were deployed west of the Luzon Strait in December 2017 and June 2018, respectively, and both were recovered in July 2019 (Fig. 1). Upward- and downward-looking 75-kHz acoustic Doppler current profilers (ADCPs) with 8-m vertical resolution and a 1-h sampling interval were installed at approximately 400-m depth at each mooring. The observed current profiles spanned from ∼70 to ∼1000-m depths. Below the ADCPs, current meters (Aquadopp from Nortek) with 1 h sampling intervals were installed at 983-, 1999-, and 2912-m depths at M01, and at 2148- and 4151-m depths at M02. The deepest Aquadopps were approximately 220 and 120 m above the seafloor at M01 and M02, respectively.
c. Other data
Typhoon tracks and wind speeds were obtained from the China meteorological administration tropical cyclone data center (Lu et al. 2021). The topography was obtained from the Earth topography 1-min grid (ETOPO1), developed by the National Centers for Environmental Information (Amante and Eakins 2009). Surface geostrophic currents with a daily temporal resolution and a 0.25° × 0.25° spatial resolution from satellite altimetry were provided by the Copernicus Marine Environment Monitoring Service (CMEMS).
d. Dispersion relation and normal mode analysis
3. NIWs after Typhoon Mangkhut
a. NIWs in the upper ocean
Rotary frequency spectra (Gonella 1972) of upper-ocean currents captured by ADCPs at M01 and M02 during the observational periods reveal high-frequency variabilities with a period of several days (Figs. 2a,b,e,f). Diurnal and semidiurnal tides were identified in both clockwise and anticlockwise components in the upper ocean, with the clockwise component exhibiting a much higher amplitude. In addition to tides, fluctuations with frequencies close to the local f, which exhibited significant clockwise polarization, were identified at M01 and M02, consistent with the characteristics expected for NIWs in the Northern Hemisphere. Therefore, the high-frequency variability in the upper ocean was dominated by tides and NIWs.
Rotary frequency spectra during the observational periods for (a)–(d) M01 and (e)–(h) M02. Clockwise and anticlockwise components of upper currents are indicated in (a) and (e), and (b) and (f), respectively; those of deep currents are indicated by pink and green lines in (c), (d), (g), and (h). Black dashed lines indicate the tidal frequencies and local inertial frequency (f). Red dashed lines indicate the bandwidth of NIWs. Black solid lines indicate the 95% confidence intervals.
Citation: Journal of Physical Oceanography 53, 10; 10.1175/JPO-D-22-0136.1
The time series of currents associated with NIWs (uNIW, υNIW) were isolated using a third-order Butterworth filter with periods of 0.65–0.85 and 0.60–0.80 cycles per day (cpd) for M01 and M02, respectively, according to the clockwise spectra in Fig. 2. The near-inertial kinetic energy [i.e.,
Time series of (a) depth-averaged near-inertial kinetic energy (NIKE) in the upper 500 m and (b),(c) NIKE in the deep ocean. Black triangles indicate the time when Typhoon Mangkhut crossed the study region.
Citation: Journal of Physical Oceanography 53, 10; 10.1175/JPO-D-22-0136.1
As shown in Fig. 4, after the crossing of Typhoon Mangkhut, uNIW (υNIW) reached 58 (52) cm s−1 at M02 and 39 (50) cm s−1 at M01 in the upper 100 m. A phase difference of ∼90° between uNIW and υNIW was identified, corresponding to the clockwise polarization of NIWs in the Northern Hemisphere. Weaker NIWs were evident at M01, likely because it was farther from the track of the typhoon than M02. Energetic NIWs were found between 60- and 1000-m depth at M01 and M02 after the crossing of the typhoon on 15 September 2018. Upward phase speed and downward energy propagation were identified in Fig. 4. NIWs were evident in the upper 400 m at M01 and M02 after 15 September; however, below 400 m depth, NIWs exhibited a time lag (Figs. 4c,f). Although NIWs in the upper layer were continuous and persisted for over one month, those below ∼400 m were intermittent. Energetic NIWs were evident on 20 September and 15 October at ∼600-m depth at M01 (Figs. 4a–c), and on 30 September and 20 October at ∼600-m depth at M02 (Figs. 4c–f). The intermittent bursts of NIWs below the mixed layer were possibly caused by refraction, scattering, or different NIW modes.
Time series of near-inertial wave (NIW) velocities and NIKE after the crossing of Typhoon Mangkhut in the upper 1000 m at (a)–(c) M01 and (d)–(f) M02. Black triangles indicate the time when Typhoon Mangkhut crossed the study region.
Citation: Journal of Physical Oceanography 53, 10; 10.1175/JPO-D-22-0136.1
According to previous observations in the SCS, the vertical group velocity of typhoon-induced NIWs in the upper ocean is 10–70 m day−1 (Guan et al. 2014; Ma et al. 2019; Yang et al. 2021), indicating a delay of 9–60 days at ∼600-m depth. Our observations corroborate these findings, except for the energetic NIWs on 20 September below 400-m depth at M01, which exhibited a much faster vertical group velocity of ∼120 m day−1 (Fig. 1). The enhanced vertical group velocity of NIWs at M01 was caused by the anticyclonic eddy southwest of Taiwan (Fig. 1), which will be discussed in section 5.
b. NIWs in the deep ocean
Energetic NIWs were also evident in the deep ocean, although they were weaker than those observed in the upper ocean, as shown in Figs. 2 and 3. The clockwise components were two orders of magnitude greater than the anticlockwise components (Figs. 2c,d,g,h), indicating a clockwise polarization. The contributions of uNIW (υNIW) to the variance of deep currents during the observation period were determined by the standard deviation ratios of uNIW (υNIW) to the hourly records and were 21% (28%) at 2912-m depth and 25% (36%) at 1999-m depth at M01. At M02, the uNIW (υNIW) fluctuation accounted for 26% (34%) of the variance at 4151-m depth and 28% (30%) of the variance at 2148-m depth. The contributions of NIWs in the deep ocean were comparable to those in the upper 1000 m (i.e., approximately 28%).
In contrast to the extremely energetic and persistent NIWs in the upper ocean in September (Fig. 3a), the NIWs in the deep ocean were characterized by multiple intermittent peaks after the crossing of Typhoon Mangkhut (Figs. 3b,c). At M02, several peaks with nearly equal temporal intervals were evident at 2148- and 4151-m depth between October 2018 and January 2019 (Fig. 3c); however, these NIWs conspicuously lagged the energetic NIWs in the upper ocean, indicating vertical energy propagation. At M01, energetic NIWs were found immediately at the bottom (i.e., 2912 m) after the crossing of the typhoon (Fig. 3b), but were absent at 1999 m. Such a bottom-enhanced fluctuation only occurred at a small region, according to observations from the CPIES array, which revealed similar fluctuations only at sites close to M01 (i.e., C21 and C30). However, the dynamics of this phenomenon remain unclear. In addition to this peak, NIWs were strong in the deep ocean at M01 between October 2018 and January 2019, similar to those at M02. The multiple intermittent bursts in the deep ocean were consistent with the characteristics of NIWs at 983-m depth (Fig. 3b), which likely resulted from the vertical energy propagation of different NIWs modes because the vertical group velocities of NIWs decrease with increasing mode number (Simmons and Alford 2012). Refraction and scattering are also considered potential causes of intermittent bursts.
Deep NIWs were evident at M01 and M02, and the CPIES observations revealed widespread near-inertial motions in the deep ocean (Fig. 5). The rotary frequency spectra for abyssal currents from the CPIES observations revealed similar dominant high-frequency variations with those of the upper currents, indicating the dominance of NIWs, diurnal and semidiurnal tides. Enhanced energy in the near-inertial band was observed in the clockwise spectra at most sites. Significant clockwise polarization was identified at frequencies slightly higher than the local f at sites not close to the continental slope (i.e., C17–C18, C21–C28, C30–C35, and C37–C51). However, the clockwise polarization was not evident at sites close to the northern continental slope (i.e., C13–C16, C20, C29, and C36).
Rotary frequency spectra during the observational periods for near-bottom currents measured by CPIESs. Upper and lower patterns indicate the clockwise and anticlockwise components, respectively. Vertical red lines indicate the local f. Pink lines are a frequency band of [f − 0.05, f + 0.15] cpd. Subplots are arranged according to the spatial distribution of CPIESs shown in the map.
Citation: Journal of Physical Oceanography 53, 10; 10.1175/JPO-D-22-0136.1
NIWs in the deep ocean exhibited frequency higher than local f, possibly owing to equatorward propagation; however, NIW peaks at the southern sites (C41–C51) showed clearer shifts from local f compared with those at the northern sites (C21–C27 and C30–C35) due to two possible reasons. First, the higher water depth to the south required a longer time for the downward energy propagation, which also caused a larger meridional distance from the NIWs source. Second, NIWs in the north, where upper relative vorticity was negative (Fig. 1), had faster vertical group velocity, which reduced the horizontal propagation distance before reaching the bottom.
Near-inertial currents were isolated using a third-order Butterworth filter with frequencies of [f − 0.05, f + 0.15] cpd as indicated in Fig. 5. The NIW currents 40 days after the crossing of Typhoon Mangkhut (i.e., 15 September–25 October) are shown in Fig. 6, revealing clockwise rotation at most sites, which is consistent with the clockwise polarized characteristic of NIWs. North of the typhoon track, the amplitudes of polarized NIWs were decreased close to the boundary (i.e., C14, C16–C18, C28, C37–C39) compared with those away from the boundary (i.e., C21–C27, C30–C34). In addition, the ellipses were round in regions with gentle topography and oblate in regions close to steep boundaries. Motions at C13–C15 were disordered compared to those at other sites. In particular, C20, C29, and C36 in the north, which recorded weak polarization (the spectra in Fig. 5), showed extremely oblate ellipses (Fig. 6), suggesting nearly rectilinear motions. Such phenomena have been previously reported by Zhang et al. (2022). Mangkhut-induced NIWs were clockwise polarized in the upper ocean but near-rectilinear polarized in the deep ocean, according to their observations on the continental slope of the SCS. The possible mechanism could be inertio-gravity waves occurring in nearly homogeneous water where N < f (Gascard 1973; van Haren and Millot 2004; Gerkema and Shrira 2005). However, the dynamical interpretation is speculative, and it is beyond the scope of this study.
Hodographs of currents associated with NIWs in the deep ocean based on the CPIES observations 40 days after the crossing of Typhoon Mangkhut (15 Sep–25 Oct). Black “X” marks indicate the starting points, i.e., the currents on 15 Sep 2018. Subplots are arranged according to the spatial distribution of CPIESs shown in the map.
Citation: Journal of Physical Oceanography 53, 10; 10.1175/JPO-D-22-0136.1
The contribution of uNIW (υNIW) to the variance of abyssal currents increased to 35% (41%) 40 days after the crossing of Typhoon Mangkhut, which was significantly higher than the average value of 23% (30%) during the entire observational period. The largest uNIW (υNIW) reached ∼10 (∼10) cm s−1 at C32, and over half of the sites reported NIW currents larger than 5 cm s−1 in either u or υ. Compared with NIWs in the center of the array north of the typhoon track (i.e., C21–C27, C30–C33), NIWs in the south (i.e., C35, C40, C42–C51) generally exhibited lower amplitudes. Possible reasons for this include the enhanced oceanic near-inertial response on the right side of the typhoon track in the Northern Hemisphere (Price et al. 1994), and less energy dissipation before reaching bottom in the north due to the shallower depth.
Near-bottom NIWs at different sites exhibited slightly different frequencies 40 days after the crossing of Typhoon Mangkhut (15 September–25 October). It indicates that they have different origin latitudes because the frequency of NIWs follows the inertial frequency at their origins. NIWs in the north (i.e., C13–C39) had a frequency of ∼5.60 × 10−5 s−1, while those in the south and over a gentle topography (i.e., C40–C51) had a frequency of ∼5.10 × 10−5 s−1 (Fig. 7). Frequencies of 5.60 × 10−5 s−1 and 5.10 × 10−5 s−1 corresponded to origins at 22.6° and 20.5°N, respectively, without considering the influence of background currents. It indicates that the energy of NIWs in the upper ocean was transferred equatorward for hundreds of kilometers during downward propagation.
Clockwise rotary frequency spectra after the crossing of Typhoon Mangkhut (15 Sep–25 Oct) of (a) C13–C39 and (b) C40–C51. Dashed vertical lines indicate near-inertial frequency.
Citation: Journal of Physical Oceanography 53, 10; 10.1175/JPO-D-22-0136.1
4. Vertical normal modes
a. Vertical normal modes from mooring observations
To identify the dominant vertical normal modes of NIWs, normal mode analysis was applied based on the historical averaged Brunt–Väisälä frequency profile as introduced in section 2d. The horizontal near-inertial velocities in the upper ocean from ADCPs and deep ocean from current meters at M01 and M02 after the crossing of Typhoon Mangkhut were projected onto the vertical normal modes (Figs. 8a,d). The feasibility of normal mode decomposition without full-depth measurements is shown in the appendix (Fig. A1).
(a) Normalized vertical structures of modes 1–5 for horizontal velocity. Gray shadows indicate the depths covered by observations. Five-day low-pass-filtered depth-averaged NIKE of (b) vertical normal modes 1–5 and (c) raw (solid line) and reconstructed (dashed line) NIWs from modes 0 to5 at the upper 1000 m at M01 after the crossing of Typhoon Mangkhut. (d)–(f) As in (a)–(c), but at M02.
Citation: Journal of Physical Oceanography 53, 10; 10.1175/JPO-D-22-0136.1
The contribution of each vertical normal mode in the upper 1000 m covered by observations was evaluated based on the proportions of depth-averaged NIKE. As most energy is contained in the low-mode NIWs, a total of six modes (modes 0–5) were considered as described in the appendix. The signal reconstructed from modes 0 to 5 accounted for 80% (86%) of the raw NIWs’ variance and 71% (79%) of the raw NIKE at M01 (M02) (Figs. 8c,f), which indicates that modes 0–5 reconstruct the NIWs well. For the first 5 baroclinic modes, modes 2 and 3 were most important at either M01 or M02. The combined contributions of these two modes reached over 60%. Modes 2 and 3 contributed to 44% and 27% (24% and 36%) of NIKE in the upper 1000 m at M01 (M02), respectively, while the contributions of other modes were all less than 20% (Figs. 8b,e). NIKE of most modes peaked within 10 days of Typhoon Mangkhut, corresponding to the energetic NIWs in the upper ocean, as shown in Fig. 4.
The contributions of the vertical normal modes follow the energy distribution of NIWs where low modes contain most of the energy (Simmons and Alford 2012). Modes 2 and 3 dominated the NIWs after the crossing of Typhoon Mangkhut; this result is in accordance with the results of a modeling study of NIWs in the northeastern SCS after the crossing of Typhoon Megi (2010) (Cao et al. 2021, their Fig. 12).
b. Complex empirical orthogonal function analysis
(a) Spatial amplitude (dot size), phase (dot color), and (d) temporal amplitude of complex empirical orthogonal function (CEOF) MODE 1 of υNIW after the crossing of Typhoon Mangkhut (15 Sep–25 Oct) for sites in the north. (b),(e) As in (a) and (d), but for CEOF MODE 2. (c),(f) As in (a) and (d), but for CEOF MODE 3. Black lines in (a)–(c) indicate the typhoon track.
Citation: Journal of Physical Oceanography 53, 10; 10.1175/JPO-D-22-0136.1
(a) Spatial amplitude (dot size) and phase (dot color), and (b) temporal amplitude of the CEOF MODE 1 of υNIW after the crossing of Typhoon Mangkhut (15 Sep–25 Oct) for sites in the south. (c),(d) As in (a) and (b), but for CEOF MODE 2. Black lines in (a) and (c) indicate the typhoon track.
Citation: Journal of Physical Oceanography 53, 10; 10.1175/JPO-D-22-0136.1
Characteristics of CEOF MODEs in the north and south.
Because NIWs at sites close to the boundary showed insignificant clockwise polarization (Figs. 5 and 6), C13, C15, C20, C29, and C36 were not used in the CEOF analysis; C32 was excluded because its operation was interrupted; and C27, C28 and C35 were excluded because they were located in the Manila Trench and exhibited a discontinuous phase with the surrounding sites. The CEOF results in the north exhibited scattered variance distribution among CEOF MODEs compared with those in the south, as the contributions of the first three CEOF MODEs all exceeded 10% (i.e., 45%, 18%, and 12%). CEOF MODE 1 exhibited lower amplitude at deeper sites (Fig. 9a), which was possibly due to the dissipation of NIKE during the downward propagation. Southward phase propagation was clearly identified from CEOF MODE 1 of υNIW (uNIW) with a wavelength and phase speed of 453 (422) km and 4.04 (3.76) m s−1, respectively. The wavelength of CEOF MODE 2 of υNIW (uNIW) was 153 (148) km, and the phase speed was 1.36 (1.32) m s−1 with a direction of south by east 20° (18°). CEOF MODE 3 of υNIW (uNIW) exhibited a wavelength of 240 (227) km and a phase speed of 2.14 (2.02) m s−1 with a direction of south by east 9° (14°). The ratio between vertical and horizontal distances between the measurements is less than 0.02. Therefore, the wavenumbers obtained from Fig. 9 can be regarded as horizontal wavenumbers with little error, although their depth differences exceeded 2000 m.
Although we applied CEOF analysis to near-bottom near-inertial currents at C42–C51 in our previous study (Zheng et al. 2021a), in which the first CEOF MODE with a southwestward horizontal phase speed of 2.4 m s−1 contributed 25% of the total NIW variance over one year, the NIWs after the crossing of Typhoon Mangkhut were not selected for detailed analysis. The region south of the typhoon track was characterized by a gentle topography slope, and the contributions of the first two CEOF MODEs after the crossing of the typhoon (15 September–25 October) reached 80% (Fig. 10), in which CEOF MODE 1 contributed the most to abyssal near-inertial currents (i.e., 61%).
The spatial amplitude of CEOF MODE 1 decreased from north to south, and phase differences among the sites indicated a mainly southward wave vector because k was significantly smaller than l (Table 1). The wavelength and horizontal phase speed of CEOF MODE 1 of υNIW (uNIW) were 305 (310) km and 2.47 (2.52) m s−1, respectively. We note that the spatial pattern of CEOF MODE 1 from near-inertial currents 40 days after the crossing of Typhoon Mangkhut was similar to that from 1-yr near-inertial currents (Zheng et al. 2021a), which indicates that the energetic NIWs induced by Typhoon Mangkhut can be easily identified in the entire observational periods. CEOF MODE 2 only contributed 19% of the total NIW variance; however, it also showed a clear phase propagation from north to south. Compared with CEOF MODE 1, CEOF MODE 2 of υNIW (uNIW) had shorter a wavelength and smaller phase speed, which were 204 (205) km and 1.66 (1.66) m s−1, respectively. Although both CEOF MODEs exhibited southward propagation, CEOF MODE 2 veered more to the west than CEOF MODE 1 by ∼25°, as shown in Table 1.
c. Vertical normal modes from near-bottom currents
As CEOF analysis is a statistical method that extracts the main features of the signal, the dynamical meaning of each CEOF MODE of near-bottom near-inertial currents remains unclear. In this section, phase speeds from CEOF MODEs are compared with those from normal mode analysis, which indicates that different CEOF MODEs can be explained by different vertical normal modes.
Considering that ω = 5.60 × 10−5 s−1 (vertical dashed line in Fig. 7a) and f = 5.11 × 10−5 s−1 (i.e., the value at the average latitude of the sites in the north), the phase speeds of the first five modes of NIWs were 6.31, 3.48, 2.22, 1.65, and 1.32 m s−1 according to Eq. (5). The phase speeds of CEOF MODE 1, 2, and 3 in the north corresponded to those of mode-2, mode-5, and mode-3 NIWs, which were similar to those in the upper ocean (Fig. 8). The amplitudes of CEOF MODE 1, 2, and 3 increased before 5 October, after 15 October, and around 5 October, respectively, indicating a lower vertical group velocity of the higher-mode NIWs.
The shallowest sites close to the boundary were excluded, and the depths of the CPIESs observations used in the CEOF analysis varied from ∼2000 to ∼4000 m. However, the vertical group velocity was slow in the upper ocean but was fast in the deep ocean due to stratification differences. The time for energy propagation from ∼2000 to ∼4000 m was less than five days for mode-5 NIWs, and the time delay was even smaller for the lower-mode NIWs, indicating that the surface low-mode NIKE reached near-bottom sites with different depths at almost the same time.
The frequency of NIWs in the south was considered as 5.10 × 10−5 s−1 according to Fig. 7b, f = 4.32 × 10−5 s−1 was based on the average latitude of C40 and C42–C51, and the horizontal phase speeds of the first four modes of NIWs were 5.10, 2.76, 1.76, and 1.32 m s−1 according to Eq. (5). The southward phase speed of CEOF MODE 1 corresponded to that of mode-2 NIWs. The temporal amplitude of CEOF MODE 1 was high between 21 September and 5 October (Fig. 10b), 6–20 days after the crossing of Typhoon Mangkhut, indicating the time spent during vertical energy propagation. CEOF MODE 2 exhibited a phase speed close to that of mode 3 NIWs. It indicated that only low-mode NIWs propagate to the bottom and the south compared with those in the upper ocean (Fig. 8), as high-mode NIWs are easily dissipated.
In conclusion, modes 2 and 3 were the most important two components of NIWs in the deep ocean, especially in the deep basin of the SCS. Higher-mode NIWs exhibited lower phase speeds and shorter wavelengths, and the wavelengths of different modes were similar to those from Simmons and Alford (2012).
5. Discussion
An anticyclonic eddy dominated the region southwest of Taiwan after the crossing of the typhoon, possibly related to the Kuroshio intrusion (Fig. 11). The center of the eddy was located at M01 on 15 September, coinciding with the passage of Typhoon Mangkhut through the northern SCS. Subsequently, the eddy moved westward, and its western edge reached C36 after 20 September. Finally, the eddy lost its structure on 25 September.
Daily maps of surface currents from 15 to 25 Sep.
Citation: Journal of Physical Oceanography 53, 10; 10.1175/JPO-D-22-0136.1
Variation of background mesoscale currents shifts the intrinsic frequency of NIWs to
Anticyclonic eddies create an advantageous environment for the vertical propagation of NIWs known as “inertial chimney” (Lee and Niiler 1998; Park and Watts 2005; Zhai et al. 2005; Vic et al. 2021; Yu et al. 2022), which could be the mechanism of the large vertical group velocity before 20 September at M01 as shown in Fig. 4. According to surface geostrophic currents from altimetry, ζ was ∼−1.00 × 10−5 s−1 at the surface around M01 during the period dominated by the eddy, which decreased the intrinsic frequency of NIWs generated there. The theoretical vertical group velocity of mode-1 NIWs was calculated according to Eq. (8) with the assumption that ζ in the upper 400 m is the same as that at the surface. Averaged theoretical vertical group velocities of mode-1 NIWs in the upper 400 m were 127 m day−1, close to the observed 120 m day−1.
Vertical NIKE profiles inside (M01) and outside (M02) of the anticyclonic eddy ten days before and after the crossing of Typhoon Mangkhut are compared in Fig. 12a to highlight the characteristic of NIWs in an anticyclonic eddy. NIKE at M01 was significantly enhanced after Typhoon Mangkhut in the upper 900 m, while that at M02 was enhanced only at the upper 500 m, suggesting the influence of the anticyclonic eddy present at M01. Compared with M02, which was not influenced by the eddy, M01 showed a lower value above 250 m and a larger value below 250 m. This indicates that more NIKE was transferred to the deeper ocean due to the effect of the anticyclonic eddy. In particular, NIKE was significantly concentrated at 250–350 m at M01, which was not observed at M02. This is consistent with the trapped depth of NIKE in an anticyclonic eddy observed by the mooring array at a similar location in winter 2013 (Xu et al. 2022).
(a) Average NIKE post-Mangkhut (from 15 to 25 Sep) and pre-Mangkhut (from 5 to 15 Sep) for M01 and M02. (b) Relative vorticity (background color) from surface geostrophic current and standard deviation (STD; dots) of near-inertial τ (τNIW) from 15 to 25 Sep.
Citation: Journal of Physical Oceanography 53, 10; 10.1175/JPO-D-22-0136.1
Although mode-1 NIWs did not dominate after the typhoon, according to Fig. 8, their vertical displacements of isotherms are expected to be detected by τ (Park and Watts 2005). Near-inertial τ was isolated using a third-order Butterworth filter with frequencies of [f − 0.05, f + 0.15] cpd. As mode 1 NIWs were enhanced 10 days after Typhoon Mangkhut (Fig. 8), the standard deviation (STD) of near-inertial τ from 15 to 25 September is shown in Fig. 12b. Mode-1 NIWs showed a larger STD on the north, indicating the enhanced NIWs on the right side of the typhoon track (Price et al. 1994). Surface relative vorticity showed an enhanced negative value southwest of Taiwan (Fig. 12b) following the anticyclonic eddy there (Fig. 11). STD of mode-1 NIWs was significant around the eddy (e.g., C20, C21, and C36) (Fig. 12b) because NIWs could be trapped by an anticyclonic eddy. As the negative vorticity decreases from the center to the boundary of the eddy, the eddy center shows lower feff. NIWs could not propagate to regions with feff higher than their own frequency; therefore, the boundary of eddy forms a “wall” where NIWs cannot escape.
NIWs were not significant in frequency spectra of τ after Typhoon Mangkhut’s passage at most sites (not shown), indicating that typhoon-induced mode-1 NIWs were not significant in the study region. However, τ from CPIESs southwest of Taiwan covered by the eddy (i.e., C20, C21, C30, and C36) showed spectrum peaks higher than the 95% confidence level at the near-inertial band within 10 days after the typhoon’s passage, as shown in Figs. 13a–c, hinting the eddy trapping of NIWs, which corresponds to the STD distribution of near-inertial τ in Fig. 12b. The time series of near-inertial τ showed large amplitude between 15 and 20 September (Figs. 13d–f), corresponding to the energy peak of mode 1 at M01 as shown in Fig. 8a. However, near-inertial motion in τ at C30 and C36 lasted to 25 September (Figs. 13e,f), which is longer than that at C21 (Fig. 13d).
(a)–(c) Variance-preserving spectra for τ from 15 to 25 Sep measured by CPIESs. Black dashed lines show the 95% confidence level of red noise. Vertical dashed lines indicate the local f. (d)–(f) Time series of near-inertial τ. Gray shaded areas indicate the period C30 and C36 with higher near-inertial motion than C21. (g)–(i) Surface relative vorticity at CPIES sites.
Citation: Journal of Physical Oceanography 53, 10; 10.1175/JPO-D-22-0136.1
NIWs trapped by anticyclonic eddies could be transported for hundreds of kilometers following the propagation of eddies over several months (Xu et al. 2022). NIWs before 20 September were induced by Typhoon Mangkhut directly; however, those after 20 September might have been carried by the westward propagating anticyclonic eddy from M01 to C21 (Fig. 11). Significant NIWs after 20 September at C30 and C36 (shadows in Figs. 13e,f) correspond to the negative relative vorticity in the upper layer (Figs. 13h,i), indicating the arrival of the eddy. The eddy left M01 and C21 after 20 September (Fig. 11). NIWs trapped by anticyclonic eddy moved westward following the propagation of the eddy and were observed at C30 and C36 after 20 September. After 25 September, the eddy lost its structure, indicating that the trapped NIWs could escape.
6. Summary
The NIWs induced by Typhoon Mangkhut, one of the strongest recorded typhoons in the SCS, were captured by an array of 38 CPIESs and two moorings. Mangkhut-induced NIWs traveled hundreds of kilometers in the SCS and were widely captured by the array, providing an unprecedented opportunity to elucidate the energy and phase propagation of typhoon-induced NIWs in the upper and deep oceans based on in situ observations. Although several tropical cyclones traveled across the study region, Typhoon Mangkhut induced extremely energetic NIWs in the upper ocean, with amplitudes as high as 58 cm s−1.
Modes 2 and 3 were the most important two components of NIWs in both the upper and deep ocean. All NIWs modes exhibited southward propagation in the north and south of the Typhoon Mangkhut track based on CEOF analysis; however, higher modes NIWs exhibited lower phase speeds and shorter wavelengths. North of the typhoon track, mode-2 NIWs propagated southward with a horizontal phase speed of ∼3.9 m s−1 and a wavelength of over 400 km; mode-3 NIWs exhibited a horizontal phase speed of ∼2.1 m s−1 in the southwestward direction and a wavelength of ∼230 km. The horizontal phase speed and wavelength of mode-5 NIWs identified in the north were ∼1.34 m s−1 and ∼150 km, respectively. NIWs south of the track exhibited lower phase speed and shorter wavelength than those on the north; they were ∼2.5 m s−1 and ∼310 km for mode-2 NIWs and ∼1.7 m s−1 and ∼205 km for mode-3 NIWs, respectively. The energy of mode-2 NIWs reached the bottom 20 days after the crossing of the typhoon, while energetic mode-3 NIWs appeared in the deep ocean later because low-mode NIWs had high vertical group velocity. A westward propagating anticyclonic eddy dominated the region southwest of Taiwan after the crossing of the typhoon, which trapped NIWs and carried them westward.
Although several cases of NIWs after typhoons have been reported in the SCS, most have been based on a few moorings and focused on the upper ocean. Knowledge regarding the contribution of typhoon-induced NIWs to the abyssal currents, as well as their vertical modes and propagations in the SCS, remains limited. This study utilized a unique monitoring array, spanning an unprecedented ∼6° in latitude and longitude, and found that NIWs were widely present in the deep SCS after the crossing of Typhoon Mangkhut and significantly contributed to abyssal currents. The generation, propagation, and vertical modes of typhoon-induced NIWs in the upper and deep oceans were revealed in the study. As NIWs are a mechanism of energy transfer from the surface to the deep ocean. Therefore, this study contributes to advancing the knowledge of dynamic responses of abyssal processes to typhoons in the upper ocean.
Acknowledgments.
This study was sponsored by the National Natural Science Foundation of China (41920104006), the Scientific Research Fund of Second Institute of Oceanography, MNR (Grants JZ2001 and QNYC2102), the Project of State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography (SOEDZZ2106 and SOEDZZ2207), the Oceanic Interdisciplinary Program of Shanghai Jiao Tong University (Project SL2021MS021), the Innovation Group Project of Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai) (311020004), and the Global Climate Changes and Air-sea Interaction Program (GASI-02-PAC-ST-Wwin).
Data availability statement.
Bathymetry data were obtained from ETOPO1 (https://doi.org/10.7289/V5C8276M). For accessing the analyzed mooring data, please contact the corresponding author. Typhoon tracks and wind speeds were obtained from tcdata.typhoon.org.cn. Surface geostrophic currents were obtained from CMEMS (http://marine.copernicus.eu/).
APPENDIX
Feasibility of Normal Mode Decomposition
The synthetic currents at observational depths were picked out and further projected onto the different vertical normal modes to simulate the process of normal mode analysis from observations. For each mode, the fraction of variance not captured by the projected records is
As M01 showed lower values of r than M02, only the analysis for M02 is shown in Fig. A1. A total mode number of 5 (modes 0–4), 6 (modes 0–5), 7 (modes 0–6), and 8 (modes 0–7) is further used for decomposition. Figs. A1a–d show the r from decomposition of synthetic currents in the upper layer (60–1000 m). Modes 1–4 are always reliable, whereas the r of higher modes increases with the increase in the total mode number used for decomposition. r reached 1 at modes 5–7 when modes 0–7 were considered (Fig. A1d), indicating that the projected records can hardly restructure the theoretical records. Therefore, normal mode analysis for near-inertial currents is inaccurate for high modes if the observations only cover the upper 1000 m.
The fraction of variance not captured by the projected records (r) when (a) modes 0–4, (b) modes 0–5, (c) modes 0–6, and (d) modes 0–7 are used for decomposition from records at 60–1000 m. (f)–(j) As in (a)–(e), but from records at 60–1000, 2150, and 4150 m. Dots and error bars indicated the averaged r and their standard deviation among 10 000 cases with random initial phases.
Citation: Journal of Physical Oceanography 53, 10; 10.1175/JPO-D-22-0136.1
Records at 2150 and 4150 m are further considered in the decomposition. The r is similar without and with records in the deep ocean when modes 0–4 are considered (Figs. A1a,e), and the r of mode 5 slightly decreases when records in the deep ocean are further used (Figs. A1b,f). Although r of modes 5–7 significantly decreased after considering the deep observations (Figs. A1d,h), most fraction of variance was not captured by the projected records. It indicates that observations from two current meters in the deep ocean could reduce the error of high modes in normal mode analysis; however, the results for high modes remain unreliable. Considering that most energy of NIWs is contained in lower modes, modes 0–5 are considered in the study, which is expected to obtain reliable records, especially for modes 1–4 (Fig. A1f).
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