1. Introduction
The global ocean hosts an estimated 40 000–55 000 seamounts rising from the ocean floor (Kim and Wessel 2011). It is widely recognized that sharp topographic features like seamounts can support the existence of subinertial topographically trapped waves (Rhines 1969, 1970; Mysak 1980; Eriksen 1991). The term “topographically trapped waves” encompasses a wide range of wave modes such as topographic Rossby waves and internal Kelvin waves, as well as some cross-slope wave modes like coastal-trapped waves and seamount-trapped waves (Huthnance 1978; Mysak 1980; Codiga 1997; Schlosser et al. 2019). These waves propagate in phase with shallower water to the right (left) in the Northern (Southern) Hemisphere. The restoring force is the potential vorticity gradient resulting from variations in water depth (Mysak 1980; White and Mohn 2004). They can induce robust near-bottom currents, largely contributing to deep-ocean subinertial variability and mixing (Garrett 2003; Lavelle and Mohn 2010). Consequently, seamounts have remained a research hotspot for physical oceanographers since the late nineteenth century (Pitcher et al. 2007).
Seamount-trapped waves are the most typical form of subinertial topographically trapped waves at a seamount (Brink 1989, 1990). They can be considered as the special form of coastal-trapped waves (Huthnance 1978) adapted to the unique geometry of submarine seamounts. Inviscid seamount-trapped waves propagate azimuthally with a standing wave structure in the radial and vertical directions, while frictionally damped seamount-trapped waves propagate phase downward and outward in addition to azimuthally (Codiga 1997). Notably, seamount-trapped waves can significantly amplify subinertial impinging oscillations (Chapman 1989). For example, diurnal seamount-trapped waves can amplify diurnal tidal currents by more than 10 times, reaching 20–40 cm s−1, over Fieberling Guyot in the eastern North Pacific (Eriksen 1991). Model studies, such as the one focused on a tanh-shaped seamount at 45°N with a Burger number of order 1 and a diurnal period barotropic impinging current (Beckmann 1995), have demonstrated that the most pronounced amplification occurs at symmetric intermediate and tall seamounts with a radius of 20 km and a slope of 0.24. Since the azimuthal wavelength is effectively fixed by the seamount perimeter, seamount-trapped waves exist only at discrete natural frequencies (Brink 1989). Among these, the radial–vertical wave mode 1 has a much higher natural frequency than other modes, with the frequency of each mode increasing with the Burger number (Huthnance 1978; Brink 1989). The radial–vertical wave mode 1 for azimuthal wavenumber 1 manifests as dipoles rotating anticyclonically around the seamount (Sansón 2010). When the frequency of subinertial impinging oscillations is sufficiently close to (not necessarily identical to) one of the natural frequencies, seamount-trapped waves can be resonantly excited (Brink 1990).
Another type of topographically trapped vorticity waves, known as topographic Rossby waves (TRWs), has also been identified as contributing to the subinertial variability of deep currents at the base of seamounts (Liao et al. 2016; Shu et al. 2016, 2022). These individual plane propagating TRWs are an extension of the classical Rossby waves, accounting for the influence of the topographic slope instead of the planetary beta effect (Rhines 1970). TRWs are generally excited by cross-isobathic motions linked to perturbations in the upper ocean (Pickart 1995; Hamilton 2009). Codiga (1997) proposed an idealized scenario where TRWs are confined within a re-entrant waveguide encircling the seamount, resonating to reinforce and evolve into seamount-trapped waves. Unlike seamount-trapped waves, TRWs are not exclusive to seamounts. Observations indicate that TRWs with periods ranging from a few days to over a hundred days are widely present over steep topography in global oceans, such as over the continental slope in the Gulf of Mexico and the South China Sea, and in the deep channel at the Pacific Yap–Mariana Junction (e.g., Pickart 1995; Hamilton 2007, 2009; Zhao and Timmermans 2018; Ma et al. 2019; Wang et al. 2019). Seamount-trapped waves encircle the seamount, indicating that energy appears simultaneously on opposite flanks of the seamount. In contrast, TRWs would typically be characterized by energy on an isolated portion of the seamount, and/or a significant time lag between the presence of energy on different flanks of the seamount.
Earlier studies of topographically trapped waves at seamounts primarily focused on seamount-trapped waves excited by diurnal tidal currents. Examples include studies over the Yermak Plateau (84°N) in the Arctic Ocean (Hunkins 1986), Cobb Seamount (46.8°N) (Codiga and Eriksen 1997), and Fieberling Guyot (32.5°N) in the North Pacific (Genin et al. 1989; Brink 1995; Lavelle 2006). Since diurnal tidal currents are superinertial at low latitudes and diurnal seamount-trapped waves would no longer exist, a knowledge gap regarding seamount-trapped waves at low latitudes exists. As for TRWs, observations have primarily concentrated on continental slopes and near the base of seamounts or islands. Seamount slopes, known for their steepness, theoretically can support higher-frequency TRWs (Rhines 1970). However, due to a scarcity of deep-sea observations, our understanding of TRWs around seamount slopes remains restricted.
Caiwei Guyot (15.71°N, 155.19°E) is a flat-topped seamount in the western equatorial Pacific (Fig. 1a). Caiwei Guyot is covered by an anticyclonic cap, with mean currents reaching approximately 2.5 cm s−1 at the summit, ∼1.0 cm s−1 at the slope, and 4.9 cm s−1 at the foot (Guo et al. 2020; Xie et al. 2022). The anticyclonic cap dynamics play a significant role in shaping the distribution of sediments and cobalt-rich crusts on the summit (Zhao et al. 2019; Guo et al. 2020). The presence of a deep current with strong subinertial variability at the slope of Caiwei implies the possibility of topographically trapped wave generation (Guo et al. 2020). These waves are generally considered to carry more energy than the anticyclonic cap and could also have a substantial impact on the local geological distribution. This motivated our investigation into topographically trapped waves at Caiwei Guyot. Notably, the Pacific Prime Crust Zone (PPCZ; Fig. 1a) in the central and western equatorial Pacific, extending from near the equator to around 20°N, consists of many low-latitude deep guyots similar to Caiwei. The PPCZ is currently of the greatest economic interest in the world for mining mineral-rich crusts (Hein and Koschinsky 2014). Therefore, enhancing our understanding of topographically trapped wave dynamics at Caiwei Guyot would contribute to predicting the distribution of cobalt-rich crusts on deep guyots within the PPCZ (Turnewitsch et al. 2013).
Observation map of Caiwei Guyot. (a) Boundary of the Pacific Prime Crust Zone (yellow dashed line) and general location of Caiwei Guyot (red rectangle); (b) shaded-relief image of Caiwei Guyot (color shaded), isobaths (solid black line), and mooring positions (purple triangle). Note that the topography and isobaths in (b) have not been smoothed. The subplot at the bottom right corner of (b) explains how the velocity vectors are projected for radial (u) and azimuthal (υ) components, and the thick black line is a schematic isobath along the slope.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0121.1
This paper is organized as follows: section 2 briefly describes the observation data, the idealized seamount-trapped wave solutions, and the TRW dispersion relation. In section 3, we describe the main signatures of observed seamount-trapped waves and TRWs. In section 4, we employ numerical calculations to further explain the seamount-trapped waves observations and discuss the excitation of seamount-trapped waves and TRWs. In section 5, we summarize the findings of this study.
2. Data and methods
a. Seamount geometry
Caiwei Guyot lies in the north central region of the Magellan Seamount Trail and to the east of the Mariana Trench in the western Pacific Ocean (Fig. 1a). Rising steeply from 5600 to 1405 m (Fig. 1b), it is an isolated high seamount according to the definition by Chapman and Haidvogel (1992). The summit is an elliptically shaped plain of 2421 km2, with a long axis of 72 km and a short axis of 40 km. The area with depths between 1500 and 4500 m is the slope region. For analyzing topographically trapped waves, the field bathymetric data (Figs. 1b and 2a) were smoothed to determine the isobath and topographic gradient at the slope (Fig. 5). The data were collected in the Chinese Da‐Yang Survey 32 (July 2014) and Survey 36 (June–July 2015) by the R/V Hai Yang Liu Hao, using a 12-kHz Kongsberg EM122 multibeam echo sounder (Yang et al. 2020). A 19-point (∼10-km spatial scale) smoothing filter was applied to remove short-scale topographic irregularities. Along the 2500-m isobath, the perimeter of the slope is approximately 227 km, and the topographic gradient ranges from 0.07 to 0.18 with an average of 0.13.
(a) A scatterplot of measured bathymetric data (gray points) projected onto the radial–vertical plane centered at 15.71°N, 155.19°E. The solid curve represents the mean bathymetric profile used to derive idealized seamount-trapped wave solutions. (b) Buoyancy frequency N profile (black line) observed at station E2 in July 2012. A 2200–2500-m averaged N is shown with a red line and used to derive idealized wave solutions.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0121.1
b. Observation data
The primary observation data were obtained from four moorings deployed around the slope of Caiwei at a depth of 2527–3033 m (Fig. 1b). Moorings E2 and W2 were deployed in July 2012 and recovered in June 2013. Mooring N2 was deployed from July 2013 to 2014, while mooring S2 was deployed from July 2014 to 2015. It is worth noting that a few instruments on these moorings experienced power depletion prior to their scheduled recovery, as detailed in Table 1. For instance, the available current data at mooring W2 just lasted until late March 2013.
Setup of the moorings at the slope of Caiwei Guyot. Note: mab = meters above bottom.
Each mooring consisted of a downward-looking Teledyne RD Instruments Workhorse Long Ranger 75‐kHz acoustic Doppler current profiler (ADCP) at ∼410 m above bottom (mab), two Aanderaa Model 9 recording current meters (RCM, except at stations W2 and E2), multiple Seabird-16 conductivity‐temperature‐depth loggers (SBE16 CTD, except at stations W2 and E2), and Seabird-39 temperature‐depth loggers (SBE39 TD) within ∼590 mab. The vertical resolution (i.e., the bin size) of the ADCP was 16 m. The sampling time interval was 1 h for ADCP and SBE16 CTD, 30 min for RCM, and 10 min for SBE39 TD. All instruments were calibrated before deployment. More details of the mooring observations are given in Table 1.
The mooring data were quality‐checked using the procedure recommended by Karstensen (2005) and averaged to hourly intervals. Deep ADCP bins within ∼210 mab were not used in this study because of the relatively poor quality due to the low backscatter environment, while RCMs at 15–111 mab still worked well. The velocity vector was projected for radial (cross-slope u) and azimuthal (along-slope υ) components, where u and υ were positive in the downslope and counterclockwise directions, respectively (Fig. 1b). Given an inertial period of ∼45 h at Caiwei, the time series of the current, temperature, and pressure were low‐pass filtered with a 52‐h fourth-order Butterworth low‐pass filter to remove the effects of tides and inertial oscillations. Additionally, the tidal current was derived by a harmonic tidal analysis utilizing the t_tide program (Pawlowicz et al. 2002). To examine the dominant frequencies of the observations, the variance-preserving kinetic energy spectra of the current and the power spectra of the temperature were calculated (Emery and Thomson 2001). The period band (i.e., 13–24-day and 3.3–4.7-day) and the central period (i.e., 14.5, 3.9 days, etc.) used for extracting the topographically trapped wave signals were determined based on the kinetic energy spectra. Subsequently, a frequency domain empirical orthogonal function (FDEOF) decomposition was performed on the subset of current records corresponding to each selected wave case to further extract the topographically trapped wave signals (Wallace and Dickinson 1972). Unlike the covariance matrix for EOF in the time domain, FDEOF was performed with cross-spectrum matrix averaged within the selected frequency band of interest.
AVISO (Archiving, Validation, and Interpretation of Satellite Oceanographic) gridded sea level anomaly (SLA) and surface geostrophic current data during the observation period were used to discuss the energy source of topographically trapped waves. The AVISO data have a horizontal resolution of 1/4° and a temporal resolution of 1 day. The power spectra of surface geostrophic current over the center of Caiwei Guyot were calculated, in which the chi-square test was used to calculate the 95% confidence level.
c. Idealized seamount-trapped wave solutions
We used the Brink code (Brink 2018) to derive the idealized seamount-trapped wave solutions at Caiwei Guyot. The 2D numerical code can simulate the free wave solutions in linearized seamount-trapped waves at an axisymmetric circular seamount (Brink 1989, 1990). The setup of the Brink code can be found in the appendix. A mean bathymetric profile estimated from the field bathymetric data of Caiwei Guyot was set in the code (Fig. 2a), and a small ancillary seamount located south of Caiwei Guyot (Fig. 1b) was pre-eliminated. For simplicity, a constant buoyancy frequency of N = 4.6 × 10−4 rad s−1, a 2200–2500-m average derived from the CTD profile observed at station E2 with a Seabird-917 plus CTD in July 2012 (Fig. 2b), was used to represent the deep ocean stratification at the slope. A Coriolis parameter of 3.9 × 10−5 rad s−1 was applied. The numbers of numerical grid points in the radial and vertical directions were set to 120 and 60, respectively. The corresponding radial resolution of the model was 517 m, and the vertical resolution ranged from 45 m at the summit center to 96 m at the foot (with radial distance from the summit center, r = 61 km). For simplicity, the mean flow and bottom friction were first neglected in section 4a. To discuss the damping of the seamount-trapped waves in section 4b, a bottom friction parameter of 0.01–0.05 cm s−1 was then used to run the Brink code.
d. Topographic Rossby wave dispersion relation
3. Results
a. Subinertial, bottom-intensified oscillations around the slope
The kinetic energy spectra of the velocity records were calculated to examine the subinertial frequency peaks (Fig. 3). The most significant phenomenon observed was the emergence of the bottom-intensified oscillations with the periods of 13–24 days and 3.3–4.7 days at all four slope stations. At stations N2, W2, and S2, the 13–24-day oscillations with central periods of ∼14.5 or 18.4 days had the strongest subinertial energy, which increased from 359–590 to 220–261 mab (Figs. 3a,c,d). The bottom intensification of the 13–24-day oscillations was most significant at station S2 (Fig. 3d). At station W2, the 3.3–4.7-day oscillations with a central period of ∼3.9 days have a comparable energy to the 13–24-day oscillations (Fig. 3c). At station E2, the 3.3–4.7-day oscillations become much stronger than the 13–24-day oscillations (Fig. 3b). The observations at the four stations indicate that the energy at the 3.3–4.7-day band increased from 359–590 mab to 220–261 mab. For the 13–24- and 3.3–4.7-day oscillations, a slight energy falloff from 220 to 111 mab and a significant energy falloff from 111 to 15 mab was observed at station S2 (Fig. 3d), which might have occurred due to the bottom friction weakening the topographically trapped waves in the bottom boundary layer (Hallock et al. 2009). Note that when we used harmonic analysis to remove all tidal components, the peaks in the 13–24-day band (Fig. 3) did not change, indicating that the 13–24-day oscillations did not represent the spring and neap tides. The kinetic energy spectra also showed peaks at other periods such as 32–100- and 8–13-day bands (Fig. 3). However, the 32–100-day oscillations weakened downward at the four stations, and the 8–13-day oscillations clearly weaken downward at stations N2 and W2, which does not conform to the characteristic of topographically trapped waves (Rhines 1970; Mysak 1980). Hence, this work focused only on the 13–24- and 3.3–4.7-day oscillations over the slope.
Variance-preserving kinetic energy spectra of 52-h low-pass-filtered current at mooring stations. The station labels and seabed depths are displayed in the upper left corner. Every acoustic Doppler current profiler (ADCP; solid line) and recording current meter (RCM; dashed line) observation covers approximately 1 year. Observations above 200 mab are indicated by red, blue, or green colors, while those below 111 mab are depicted by black or cyan colors. In the legend, “mab” means meters above bottom.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0121.1
The subinertial oscillations were seen not only in the observed currents at the four slope mooring stations but also in the observed temperatures (Figs. 4a–d). The deep temperature spectra showed peaks at similar periods with the kinetic energy spectra, such as the ∼8–13-day period, as well as the ∼13–24- and ∼3.3–4.7-day periods that this work focused on (Figs. 4e–h). Since the density variation at the deep slope of Caiwei Guyot is mainly produced by the temperature, the vertical displacements of an isotherm represent isopycnal variations (i.e., stretching or compression of the water column) (Zhao and Timmermans 2018).
Subinertial oscillations in the temperature at the slope. Time–depth variations of 52-h low-pass filtered temperature at stations (a) E2, (b) W2, (c) N2, and (d) S2. In (a)–(d), the depths of the Seabird-16 conductivity–temperature–depth (SBE16 CTD) and the Seabird-39 temperature–depth (SBE39 TD) loggers are indicated by black stars. (e)–(h) Power spectra density (black lines) of deep temperature. In spectra plots, red lines denote a significance level of 95%, and the observation depths are shown in the upper right corner.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0121.1
The current ellipses of the 13–24- and 3.3–4.7-day bandpassed bottom velocities near 230 mab were narrow (Fig. 5), with their principal axis magnitudes reaching maxima of 1.1 cm s−1 (station S2, 2331 m) and 0.5 cm s−1 (station E2, 2310 m), respectively. Comparing the smoothed (over an ∼10-km spatial scale) topography with the principal axis at each station, we found that the principal axes of oscillations in the two frequency bands were nearly aligned with the isobaths (Fig. 5).
Variance ellipse of the 13–24-day (blue lines) and 3.3–4.7-day (red lines) bandpass-filtered bottom (near 230 mab) velocities at slope stations (magenta points). The black lines are the isobaths smoothed over a ∼10-km spatial scale.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0121.1
b. Intermittent seamount-trapped waves
The 13–24- and 3.3–4.7-day oscillations observed around the slope of Caiwei Guyot were subinertial and bottom-intensified with elongated current ellipses nearly aligned with the isobaths. These signatures suggested the potential formation of seamount-trapped waves, in which the energy would encircle the seamount and form an azimuthal mode (Brink 1989; Codiga 1997). To further confirm the presence of seamount-trapped waves, we utilized the observations from stations W2 and E2, covering the same period.
When the strong 13–24-day oscillation occurred simultaneously on opposite flanks of Caiwei Guyot, as in case 2 (8 October–27 November 2012) and case 3 (26 December 2012–24 January 2013), alternating converging (i.e., crossing each other) and diverging (i.e., spreading out) current vectors (i.e., at 2250 m) dominated at both stations (Fig. 6c). Foldvik et al. (1988) showed that converging current vectors correspond to counterclockwise (CCW) eddies passing a moored instrument, and diverging vectors correspond to clockwise (CW) eddies. The observed pattern can thus be explained by the movements of a wave that contains alternating CW and CCW rotating zones (Jensen et al. 2013), and current vectors at the opposite flanks were rotating in the opposite sense (CW or CCW) simultaneously (Fig. 6c). In cases 2 and 3, the deep (2182–2310 m) azimuthal velocity at station E2 were in the nearly opposite phase to that at station W2 (Figs. 6a,b), as were the deep (2232 m) temperature fluctuations at station E2 in comparison to that (2239 m) at station W2 (Fig. 6d). These features aligned with characteristics of 13–24-day seamount-trapped waves with an odd azimuthal wavenumber (i.e., 1, 3, etc.) (Brink 1989, 1990; Sansón 2010). The 13–24-day seamount-trapped waves could induce temperature fluctuations up to 0.014°C at 1985 m (586 mab) at station E2, and the temperature fluctuations at 2097 m (474 mab) were weaker than those at 1985 and 2232 m (Fig. 6d).
Time–depth variations of 13–24-day bandpass-filtered (a)–(c) velocity and (d) temperature at stations E2 and W2. The azimuthal velocity (υ) is shown in (a) and (b). In (c), the y axis points to the north. In (a)–(c), the center segments of cases 1, 2 and 3 are marked in black dashed rectangles. A 13–24-day bandpass filter was applied to all variables.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0121.1
In the observed periods outside of cases 2 and 3, such as December 2012 and February–March 2013, several of the above characteristics (i.e., two counterrotating cells of horizontal currents, nearly opposite phase of azimuthal velocity and temperature at the opposite flanks) disappeared and the 13–24-day bandpass-filtered deep current much weakened in at least one station (Fig. 6). For example, the 13–24-day energy existed only at station W2 but not at station E2 in the period between cases 2 and 3 (i.e., December 2012), indicating that the 13–24-day seamount-trapped waves encircling the seamount may break apart into a more localized type of topographically trapped wave propagating along part of the slope. Notably, although the 13–24-day energy occurred simultaneously at two stations in August–September 2012, the energy at station W2 was a lot weaker than that in cases 2 and 3 and not comparably strong as that at station E2 (Figs. 6a,b). In addition, the signature of two counterrotating cells of horizontal currents on the opposite flanks was not clearly established in case 1 (21 August–24 September 2012; Fig. 6c). These two points indicate that the seamount-trapped waves encircling the seamount had not fully formed in case 1. Hence, the 13–24-day seamount-trapped waves were intermittent.
The comparably energetic 3.3–4.7-day oscillations appeared simultaneously on opposite flanks of Caiwei Guyot in case 4 (27 September–8 October 2012) and case 8 (5–17 March 2013), which may be interpreted as the intermittent 3.3–4.7-day seamount-trapped waves (Fig. 7). However, case 6 (9–26 December 2012) and case 7 (15 January–15 February 2013) showed 3.3–4.7-day oscillations on opposite flanks without comparable energy levels at station W2 (Fig. 7), suggesting that these cases cannot be interpreted as seamount-trapped waves.
Time–depth variations of 3.3–4.7-day bandpass-filtered azimuthal velocity (υ) at (a) stations E2 and (b) W2. The center segments of cases 4, 5, 6, 7, and 8 are marked in black dashed rectangles.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0121.1
In case 4, the 3.3–4.7-day bandpass-filtered deep (2182–2310 m) azimuthal velocity at stations E2 and W2 were in the nearly opposite phase (Figs. 8a,b), and the signature of two counterrotating cells of horizontal currents dominated the two stations (Fig. 8c). Similarly, the temperature fluctuations at station E2 (2141 m) were also in a nearly opposite phase to those at station W2 (2141 m, Fig. 8d). These characteristics aligned with the behavior of 3.3–4.7-day seamount-trapped waves with an odd azimuthal wavenumber (Brink 1989, 1990; Sansón 2010). It is worth noting that the 3.3–4.7-day energy vanished at 2300 m at station W2 in 9–14 October 2012 (Fig. 8b), and the temperature fluctuations at 2141 m of both stations were no longer in the nearly opposite phase (Fig. 8d). Hence, we can more confidently identify the 3.3–4.7-day seamount-trapped wave case during 27 September–8 October 2012. The 3.3–4.7-day seamount-trapped wave in case 4 induced temperature fluctuations of up to 0.007°C (i.e., at 2141 m at station W2). In general, temperature fluctuations weakened upward from 2232 m (339 mab) to 1985 m (586 mab) at station E2 (Fig. 8d).
Time–depth variations of 3.3–4.7-day bandpass-filtered (a)–(c) velocity and (d) temperature at stations E2 and W2 in case 4; the azimuthal velocity (υ) is shown in (a) and (b). In (c), the y axis points to the north. In (a)–(c), the center segment of case 4 is marked in a black dashed rectangle. A 3.3–4.7-day bandpass filter was applied to all variables.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0121.1
In case 8, alternating converging and diverging current vectors dominated at stations E2 and W2 (i.e., at 2250 m, Fig. 9c). The phase difference of 3.3–4.7-day bandpass-filtered deep (2182–2310 m) azimuthal velocity at two stations was ∼107° (Figs. 9a,b), while that of the deep (2141 m) temperature fluctuations at two stations was 60°–85° (Fig. 9d). This phase difference of about π/2 on opposite flanks differed from the typical mode of seamount-trapped waves, where an odd azimuthal wavenumber mode corresponds to a phase difference of about π and an even azimuthal wavenumber mode corresponds to a phase difference of about 0 (Sansón 2010). One possibility is that the 3.3–4.7-day oscillations in case 8 could result from the superposition of different seamount-trapped wave modes.
As in Fig. 8, but for case 8. A 3.3–4.7-day bandpass filter was applied to all variables.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0121.1
c. Topographic Rossby waves
In addition to the seamount-trapped waves, another type of topographically trapped waves also contributed to the deep 13–24- and 3.3–4.7-day oscillations around the slope. In case 1 (21 August–24 September 2012; see Fig. 6), case 5 (19 November–5 December 2012; Fig. 7), case 6 (9–26 December 2012; see Fig. 7), and case 7 (15 January–15 February 2013; Fig. 7), the 13–24- or 3.3–4.7-day energy was strong on one flank of the seamount but was absent or very weak on its opposite flank, indicating the generation of topographically trapped waves propagating along part of the slope rather than seamount-trapped waves encircling the seamount. For convenience narration, they are referred to as “localized topographically trapped waves” here.
These localized topographically trapped waves over a deep seamount may take the form of topographic Rossby waves (TRWs) or internal Kelvin waves (Huthnance 1978; Vangriesheim et al. 2005; Hallock et al. 2009; Arzeno 2020). Only when the Burger number Bu = (NH/fD)2 ≫ 1 do topographically trapped waves tend to approximate internal Kelvin waves and see the seamount as a vertical wall (Huthnance 1978; Schlosser et al. 2019; Arzeno 2020). Here, N is the buoyancy frequency, H is the water depth, f is the Coriolis parameter, and D is the radius of the seamount. For the observed localized topographically trapped waves, with a 2200–2500-m average N = 4.6 × 10−4 rad s−1 (Fig. 2b), H = ∼2500 m, f0 = 3.9 × 10−5 rad s−1, and D = ∼36 km, we obtained a Bu of ∼0.67. This suggests that the observed localized topographically trapped waves tend to approximate TRWs.
To validate that the observed localized topographically trapped waves were indeed TRWs, we compared the observed orientation angle (φobs) of the group velocity vector from the isobath with the theorical angle (φt) predicted by the TRW dispersion relation (Rhines 1970; Pickart 1995). It should be noted that the TRW dispersion relation is derived under the assumption of inviscid, individual TRWs. However, in the real ocean, factors such as the frictional effects, the formation of cross-slope modes, and the superposition of multiple individual TRWs can introduce certain deviations between the observations and the TRW dispersion relation (Hamilton 1984; Codiga 1997; Vangriesheim et al. 2005). For instance, in a study on TRWs in the Bay of Campeche, Kolodziejczyk et al. (2011) reported that friction deviated the group velocity vector within the bottom boundary layer to the left. Nevertheless, based on extensive previous research (e.g., Uehara and Miyake 2000; Hamilton 2007; Kolodziejczyk et al. 2011; Münchow et al. 2020), utilizing the TRW dispersion relation to examine motions in the ocean interior is considered relatively dependable.
The φobs can be estimated based on the angle of the principal axis of the bandpassed current ellipses with respect to the isobath. This is because TRWs propagate energy anticyclonically around the slope, with a group velocity vector parallel to the principal axis of the current ellipses (Rhines 1970; Hamilton 2007). The value of φ is taken within (0, π/2) and (π/2, π) when the group velocity vector points upslope and downslope, respectively. Employing a FDEOF decomposition on the subset of current records corresponding to each selected wave case, topographically trapped wave signals were extracted to compute the current ellipses (Figs. 10a,b). For the 13–24-day oscillation in case 1 and the 3.3–4.7-day oscillation in cases 5, 6, and 7, FDEOF mode 1 accounted for more than 78% of the total variance. The orientations of the principal axis of mode-1 oscillations in these four cases were almost vertically uniform. By comparing the principal axis of mode-1 oscillations with the smoothed topography (i.e., the along-slope direction; see Figs. 10a,b), the φobs of 13–24-day waves in case 1 was estimated to be ∼176.6° at near-bottom (i.e., 2310 m) of station E2. Similarly, the φobs of 3.3–4.7-day waves in cases 5, 6, and 7 was estimated to be ∼13.4°–17.1° (Table 2). It is evident that the group velocity vector of the 13–24-day waves (i.e., in a lower frequency) was more parallel to the isobath compared to the 3.3–4.7-day waves, which is consistent with the characteristic of TRWs (Ma et al. 2019). In Fig. 10, the arrows on the ellipses obtained from FDEOF analysis indicate the relative phases. For the 13–24-day waves (3.3–4.7-day waves) at station E2 in case 1 (cases 5, 6, and 7), the oscillations below 325 mab (389 mab) were almost vertically in phase. It was also consistent with the characteristic of TRWs (Hamilton 2007, 2009). However, in case 1, the phase of 13–24-day oscillations at 325 mab at station E2 differed by about 84° from that at 389 mab (Fig. 10a). This was due to the significant weakening of the 13–24-day waves at 340 mab (i.e., 2231 m) at station E2 (Fig. 6a). Likewise, in cases 5, 6, and 7, the phase of 3.3–4.7-day oscillations at 389 mab at station E2 differed by about 70°–81° from that at 590 mab (Fig. 10b), indicating there could be a vertical phase propagation (Hallock et al. 2009).
Current ellipses at station E2 calculated from observations of (a) 13–24-day oscillation cases and (b) 3.3–4.7-day oscillation cases, and idealized seamount-trapped wave model solutions in the (c) 13–24-day frequency band and (d) 3.3–4.7-day frequency band. In (a) and (b), frequency domain empirical orthogonal function (FDEOF) analysis was performed on all observation levels, with only FDEOF mode 1 at some selected levels shown here. The observation levels are labeled on the left and right of subplots, where “mab” means meters above bottom. Arrows within ellipses denote relative phase and rotation direction. Analysis interval and explained variances as percentages are provided at the bottom. “STWs” are seamount-trapped wave cases, while “TRWs” are topographic Rossby wave cases. In (c) and (d), the azimuthal wavenumber m, radial–vertical mode n, and period of model solutions are indicated at the bottom. These model solutions correspond to the black points in the gray shaded area in Fig. 12. Velocity from the model solution has a normalized unit (Brink 2018). To facilitate comparison with observations, the modeled principal axis amplitudes in (c) and (d) were scaled to match the observed amplitude at 2310 m in cases 2 and 4, respectively.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0121.1
TRW parameters at station E2. Note that φobs is the observed angle of the group velocity vector at 2310 m from the isobath, and φt is the angle predicted by the TRW dispersion relation; 1/λ is the vertical trapping scale and L is the wavelength.
Theoretical φt can be predicted by the TRW dispersion relation [Eq. (4)]. For a given ω, N, and |∇H|, two roots of φt can be easily obtained, that is, one within (0, π/2) and the other within (π/2, π). For comparison, we took the root within the same quadrant as the φobs (Figs. 10a,b, Table 2). For the 13–24-day oscillation in case 1, given the local parameters [N = 4.6 × 10−4 rad s−1; central frequency ω = 5.0 × 10−6 rad s−1 (i.e., central period = 14.5 days), |∇H| = 0.13], φt was estimated as 175.2°. For the 3.3–4.7-day oscillation in cases 5, 6, and 7, with an ω value of 1.9 × 10−5 rad s−1–2.0 × 10−5 rad s−1 (i.e., central period = 3.7–3.9 days), φt was estimated as 18.2°–19.2°. Note that φt compared reasonably well with φobs (Table 2). Therefore, the observations at station E2 in cases 1, 5, 6, and 7 satisfied the dispersion relation of TRWs and can be explained as TRWs.
Least squares fitting of the frequency domain empirical orthogonal function (FDEOF) mode-1 amplitude to A(z) = A0 cosh(λz) at station E2. (a) The 13–24-day oscillations in case 1; (b)–(d) 3.3–4.7-day oscillations in cases 5, 6, and 7, respectively. The FDEOF analysis was performed on the subset of current records at 1981–2310 m (black squares) corresponding to each selected wave case. The fitting equation and the coefficient of determination R2 are labeled near fitting curves (black dashed lines).
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0121.1
4. Discussion
a. Numerical calculations of idealized seamount-trapped waves
To explain the structure of the observed seamount-trapped waves, the numerical code developed by Brink (2018) was run to calculate the dispersion relations and modal structures for idealized seamount-trapped waves at Caiwei Guyot. The 2D code varies only in the across-slope direction, so an average bathymetric profile of Caiwei Guyot was used (Fig. 2a). The bottom friction was assumed to be negligible, and the resulting dispersion relations for the first five radial–vertical modes of idealized seamount-trapped waves are presented in Fig. 12 with the black points. According to the idealized wave solution in the 13–24-day frequency band, a circularly symmetric seamount with features similar to Caiwei Guyot can support the radial–vertical mode 4 (5) of an azimuthal wavenumber-1 seamount-trapped wave with a period of 13.9 (17.8) days. According to that in the 3.3–4.7-day frequency band, the radial–vertical mode 2 (n = 2) of an azimuthal wavenumber-2 (m = 2) seamount-trapped wave with a period of 3.7 days, radial–vertical mode 3 (n = 3) of an azimuthal wavenumber-3 (m = 3) seamount-trapped wave with a period of 4.0 days, and radial–vertical mode 4 (n = 4) of an azimuthal wavenumber-4 (m = 4) seamount-trapped wave with a period of 4.1 days can be also supported. The radial–vertical mode number n was estimated as the number of radial zero crossings in the azimuthal velocity υ (Figs. 13 and 14; Brink 2018).
Dispersion diagram for the first five radial-vertical modes of idealized seamount-trapped waves at Caiwei Guyot. Black points (red crosses) are solutions assuming a bottom friction parameter of 0 cm s−1 (0.01 cm s−1). Waves exist only at discrete black points or red crosses, and the dashed lines are only for clarity. The radial–vertical mode number n is labeled below every dashed line. The 3.3–4.7- and 13–24-day frequency bands are shaded in gray.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0121.1
(a),(d) Radial (u) and (b),(e) azimuthal (υ) velocity, and (c),(f) density (ρ) modal structures of idealized inviscid seamount-trapped wave modes in the 13–24-day band shown in Fig. 12. The azimuthal wavenumber m, radial–vertical mode n, and period of model solutions are indicated at the top of each column. Velocity and density have a normalized unit (Brink 2018). For clarity, the contour values of velocity and density are magnified 104 and 1011 times, respectively. A solid (dashed) contour indicates positive (negative) values. The contour range and intervals are labeled at the bottom left of each subplot. The mooring E2 is indicated with a red thick line.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0121.1
As in Fig. 13, but for the idealized inviscid seamount-trapped wave modes in 3.3–4.7-day band shown in Fig. 12.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0121.1
These selected inviscid seamount-trapped wave modes (depicted as black points within the shaded area in Fig. 12) were compared with the observed seamount-trapped waves at Caiwei Guyot. This comparison was conducted in two ways: first, current ellipses from modeled velocity structures at station E2 were compared with observed current ellipses (Figs. 10, 13, and 14); second, modeled density structures were compared with observed temperature structures (Figs. 13 and 14), as the density fluctuations at the deep slope were primarily driven by temperature variations. For instances in cases 2 and 3 when the 13–24-day seamount-trapped waves had an odd azimuthal wavenumber (Fig. 8), the observed velocity slightly decreased from 2182 to 2310 m (261–389 mab) to 1981 m (590 mab, Fig. 10a). It aligned with the simulated 17.8-day (mode for m = 1, n = 5) idealized seamount-trapped waves (Fig. 10c), where mooring E2 resided amid the velocity core and the nodal line (Fig. 13e). In contrast, the simulated 13.9-day (mode for m = 1, n = 4) idealized seamount-trapped waves predicted a significant velocity reduction from 2310 to 1981 m (Fig. 10c), as mooring E2 did lie within the velocity core (Fig. 13b). In these two cases, the observed temperature fluctuations at 2097 m were smaller than those at 1985 and 2232 m (Fig. 6d). It also aligned more closely with the simulated 17.8-day (mode for m = 1, n = 5) idealized seamount-trapped waves, which exhibited a nodal line of density fluctuations at 2134 m at station E2 (Fig. 13f). Consequently, the 13–24-day oscillations in cases 2 and 3 can be mainly attributed to radial–vertical mode 5 of an azimuthal wavenumber-1 seamount-trapped wave with a period of 17.8 days. Given an azimuthal wavenumber of 1 and a seamount perimeter of 227 km at ∼2500 m, the wavelength of the 17.8-day seamount-trapped waves in cases 2 and 3 was estimated to be ∼227 km. This leads to a calculated phase speed for the wave traveling around Caiwei Guyot of ∼0.15 m s−1. Note that these two estimates are localized and apply only along the 2500-m isobath, since the wavelength of seamount-trapped waves increases with distance radially from the seamount center.
With an odd azimuthal wavenumber (Fig. 8), the observed 3.3–4.7-day seamount-trapped waves in case 4 compared well with the simulated 4.0-day (mode for m = 3, n = 3) idealized seamount-trapped waves. Specifically, the observed current ellipses at 1981–2310 m were narrow with a principal axis nearly parallel to the slope isobaths (Fig. 10b), which aligned well with the simulated 4.0-day idealized seamount-trapped waves (Fig. 10d). Notably, the observed velocity at 2182 m slightly exceeded that at 1981 and 2310 m (Fig. 10b), and the temperature fluctuations weakened upward from 2232 to 1985 m (Fig. 8d). Correspondingly, mooring E2 was situated near a nodal line of azimuthal velocity but close to a density core (Figs. 14e,f). Consequently, it is reasonable to attribute the 3.3–4.7-day oscillations observed in case 4 predominantly to the radial–vertical mode 3 of an azimuthal wavenumber-3 seamount-trapped wave with a period of 4.0 days. Given an azimuthal wavenumber of 3 and a seamount perimeter of 227 km, the wavelength of the 4.0-day seamount-trapped waves in case 4 was estimated to be one-third of the seamount perimeter, approximately 76 km. This leads to a calculated phase speed for the wave traveling around Caiwei Guyot of ∼0.22 m s−1. Note that these two estimates apply only along the 2500-m isobath.
b. Damping of seamount-trapped waves
In contrast to the previously reported persistent diurnal seamount-trapped waves over most seamounts at middle and high latitudes (Hunkins 1986; Genin et al. 1989; Brink 1995; Codiga and Eriksen 1997), intermittent low-frequency (13–24-day and 3.3–4.7-day) seamount-trapped waves were observed at Caiwei Guyot. The low-frequency seamount-trapped waves are generally in a higher mode and have stronger damping, so they were thought not easy to observe in nature (Brink 1989). The influence of damping on the behavior of these seamount-trapped waves at Caiwei Guyot was evident in several aspects. First, in lack of persistent energetic ambient perturbations, the generated seamount-trapped waves would break apart into a more localized type of topographically trapped wave and be damped out by the rough topography in a period of time (Fig. 6). The observed 13–24-day seamount-trapped waves persisted for about 4–6 weeks (Fig. 6), while the 3.3–4.7-day seamount-trapped waves endured for around 1–2 weeks (Fig. 7). Second, the energy of 13–24-day and 3.3–4.7-day seamount-trapped waves at station E2 was comparable to but somewhat stronger than that at station W2 (Figs. 6 and 7). This energy asymmetry on opposite flanks of the seamount was a characteristic often associated with frictionally damped seamount-trapped waves (Haidvogel et al. 1993). Third, the friction made the current ellipse axes oriented at an angle to isobaths (Figs. 10a,b). For inviscid seamount-trapped waves, the current ellipse axes can be only parallel or perpendicular to isobaths (Figs. 10c,d; Codiga 1997).
To gain further insights, a rerun of the idealized seamount-trapped wave solution code was performed, incorporating a bottom friction parameter of 0.01–0.05 cm s−1, as proposed in the works of Brink (1989, 1990). Despite the inclusion of the bottom friction parameter, there were minimal changes in the frequency and modal structure of the seamount-trapped waves. However, the inclusion of bottom friction only supported radial–vertical modes 1 and 2 (represented by red crosses in Fig. 12), while failing to account for the observed 13–24-day seamount-trapped waves. This inconsistency between the idealized wave solutions and observations indicates that the idealized bottom friction mechanism assumed in the Brink code (Brink 1989, 1990, 2018) may be not active at Caiwei Guyot and there could be other friction mechanisms at work. Codiga (1997) explored a different, but also highly idealized friction mechanism (i.e., Rayleigh damping). In the real ocean, frictional processes are likely a lot more complex than those captured in the simplified wave solution code.
c. Generation of two types of topographically trapped waves
The literature on subinertial topographically trapped waves over deep slopes can be categorized into two main groups. The first group focuses on interpreting observations as TRWs, for example, ∼10-day TRWs at the Sigsbee Escarpment in the Gulf of Mexico (Hamilton 2007), and ∼9–20-day TRWs at the Yongshu Reef and the Xisha Islands of the South China Sea (Shu et al. 2016, 2022). The second group refers to the cross-slope modes of topographically trapped waves, such as coastal-trapped waves or seamount-trapped waves. These waves have been identified in various locations, including biweekly coastal-trapped waves on the continental slope of the Gulf of Guinea (Vangriesheim et al. 2005), 35-h and 3-day coastal-trapped waves on the continental slope of the southern Weddell Sea (Jensen et al. 2013), and diurnal seamount-trapped waves above Fieberling Guyot in the North Pacific (Brink 1995). Interestingly, these two groups of literature have not been well connected. However, observations around the deep slope of Caiwei Guyot have revealed the presence of both seamount-trapped waves and TRWs, which might bridge these perspectives and provide a window for comparing and relating them.
The generation of seamount-trapped waves or TRWs probably depends on whether the ambient perturbations influence the entire seamount or only one flank. When the ambient motions are much broader than the seamount and impact the entire seamount, they would force flow in the same direction on opposite flanks of the seamount, favoring the excitation of seamount-trapped waves with an odd azimuthal wavenumber (Brink 1990; Codiga 1997), for example, the 13–24-day azimuthal wavenumber 1 seamount-trapped waves in cases 2 and 3, and the 3.3–4.7-day azimuthal wavenumber 3 seamount-trapped waves in case 4. On the other hand, if the ambient motions affect just one flank, such as in scenarios where the ambient motions are narrower than the seamount, they may generate a response only on that specific flank, possibly leading to the excitation of TRWs that propagate along part of the slope. Another factor is the frequency of ambient perturbations. To resonantly excite seamount-trapped waves, the frequency of these perturbations must be sufficiently close to a natural frequency of free seamount-trapped wave modes (see the seamount-trapped wave modes in Fig. 12; Brink 1990). In contrast, exciting TRWs is generally easier, requiring only that ambient perturbations have a frequency lower than N|∇H|, where |∇H| and N are the topographic gradient and the buoyancy frequency, respectively (Rhines 1969, 1970).
At middle and high latitudes, the subinertial energetic diurnal tides can continuously excite diurnal seamount-trapped waves (Hunkins 1986; Genin et al. 1989; Brink 1995; Codiga and Eriksen 1997). However, at the slope of Caiwei Guyot, the diurnal tides are superinertial and are unable to trigger TRWs or seamount-trapped waves. Although the tides were modulated by the spring-neap cycle at Caiwei Guyot (Fig. 15), there is no clear correlation found between the occurrence of 13–24-day TRWs (or 13–24-day seamount-trapped waves) and the spring–neap cycle.
(a) Azimuthal and (b) radial tidal current (gray lines) at 2310 m at station E2. In (a) and (b), the blue lines indicate the 13–24-day bandpass-filtered azimuthal and radial velocities at 2310 m, respectively. The center segments of cases 1, 2 and 3 are marked in black dashed rectangles.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0121.1
Mesoscale perturbations in the upper layer have been identified as an important energy source for deep TRWs (Hamilton 2007; Shu et al. 2016; Wang et al. 2019; Wang et al. 2021; Zheng et al. 2021). In the two seamount-trapped wave cases (see Fig. 16b for cases 2 and 4) and four TRW cases (see Fig. 16a for case 1, Fig. 16c for cases 5 and 6, and Fig. 16d for case 7), the sea surface mesoscale perturbations were active at Caiwei Guyot. Many peaks within the 13–24-day period band were also found in the spectra of the surface geostrophic current over Caiwei Guyot during the mooring observations between June 2012 and July 2015 (Figs. 16e,f). However, the 3.3–4.7-day signal was not detected in the surface geostrophic current, possibly due to the relatively low temporal resolution of the satellite observations used to derive the AVISO dataset. In addition to the upper-layer mesoscale perturbations, deep eddies are abundant around Caiwei, which has been revealed by the model study of Jiang et al. (2021). The upper-layer mesoscale perturbations and deep eddies with a fairly broad band of frequencies and spatial scales (Greene et al. 2009; Gula et al. 2016; Zhang et al. 2016) might provide energy to excite intermittent 13–24- and 3.3–4.7-day TRW or seamount-trapped wave cases (Hamilton 2009; Quan et al. 2021).
Sea surface mesoscale perturbations. The sea level anomaly (SLA) map in (a) 1–15 Aug 2012, (b) 25 Sep–5 Oct 2012, (c) 15 Nov–10 Dec 2012, and (d) 16–20 Jan 2013; power spectra of the (e) meridional and (f) zonal geostrophic surface velocities during the period between June 2012 and July 2015 near the center of Caiwei Guyot. In (a)–(d), geostrophic surface velocities are overlaid, and green squares represent mooring stations at the slope. In (e) and (f), red lines represent a significance level of 95%.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0121.1
Codiga (1997) proposed a scenario in which TRW rays are confined in a re-entrant waveguide around the seamount and resonant to reinforce themselves, ultimately forming seamount-trapped waves. The standing cross-slope (radial and vertical) structure of an inviscid seamount-trapped wave can be considered due to a superposition of equal amplitude TRW rays propagating upslope and downslope. It indicates that the generation of seamount-trapped waves may be closely related to the TRWs. This scenario is based on the assumption of circular symmetry of the seamount topography and the seamount perimeter being an integral multiple of the along-slope wavelength of TRW rays. The waveguide of TRW rays is a sloping region bounded by weaker slopes on both sides (shallower and deeper) than a critical value
5. Summary
In this study, we examined the subinertial topographically trapped waves at Caiwei Guyot based on analyzing mooring records around the slope. Caiwei Guyot is a low-latitude deep guyot in the western equatorial Pacific and the Pacific Prime Crust Zone. The current and temperature measurements at the slope showed bottom-intensified energy in the 13–24- and 3.3–4.7-day bands, with elongated current ellipses nearly aligned with the isobaths (Fig. 5). From August 2012 to March 2013, they were mainly attributed to four intermittent time periods when seamount-trapped waves were observed and four intermittent time periods when TRWs were observed.
The observed 13–24- and 3.3–4.7-day seamount-trapped waves in cases 2, 3, and 4 were consistent with two counterrotating cells of horizontal currents on opposite flanks of the seamount, which were comparably energetic but somewhat asymmetric. The azimuthal velocity (and temperature) on opposite flanks of the seamount exhibited nearly opposite phase, also indicative of an odd azimuthal wavenumber. By comparing these observations with idealized seamount-trapped wave solutions that assume a circularly symmetric topography (Brink 2018), we explained the 13–24-day seamount-trapped waves in cases 2 and 3 as the radial–vertical mode 5 of an azimuthal wavenumber-1 seamount-trapped wave with a period of 17.8 days, while the 3.3–4.7-day seamount-trapped waves in case 4 were explained as the radial–vertical mode 3 of an azimuthal wavenumber-3 seamount-trapped wave with a period of 4.0 days. The 13–24-day (3.3–4.7-day) seamount-trapped waves were estimated to have a wavelength of ∼227 (76) km and a phase velocity of ∼0.15 (0.22) m s−1, where the estimates are localized and apply only along the 2500-m isobath. Due to the bottom friction and nonpersistent energetic ambient perturbations, during certain portions of the record, the seamount-trapped waves encircling the whole seamount broke apart into a more localized type of topographically trapped wave and their energy decayed over 1–6 weeks.
In case 1 (cases 5, 6, and 7), the 13–24-day (3.3–4.7-day) energy was energetic only at one flank of the seamount and weakened upward (i.e., from 261 to 590 mab at station E2) more significantly than the seamount-trapped wave cases. With a Burger number of ∼0.67, this more localized type of topographically trapped wave cannot be a form of internal Kelvin waves. These 13–24-day (3.3–4.7-day) waves were inferred to have an orientation angle of the group velocity vector from the isobath of 176.6° (13.4°–17.1°), which were approximately consistent with the dispersion relation for TRWs. Hence, they were explained as TRWs with ∼192–379-m vertical trapping scale and ∼14.3–28.2-km wavelength.
Excitation of seamount-trapped waves or TRWs might be determined by whether the ambient perturbations influence the entire seamount or only one flank. No clear correlation was found between the burst of topographically trapped waves and the spring–neap cycle, and we inferred that mesoscale perturbations from upper layer might provide energy for exciting these waves in deep layer. Due to the limited observations, we are presently unable to confirm whether the idealized scenario proposed by Codiga (1997), in which propagating TRWs reinforce to form seamount-trapped waves, occurs in the real ocean.
Acknowledgments.
We deeply cherish the memory of professor Qiang Xie (Institute of Deep-Sea Science and Engineering, Chinese Academy of Sciences), and thank him for his valuable contribution to this work. Grateful acknowledgements are given to Dr. Daniel L. Codiga, Dr. Kenneth H. Brink, Dr. Qiang Ma, Dr. Wenhu Liu, and Dr. Isabella B. Arzeno-Soltero for their helpful discussions. This work was supported by the National Natural Science Foundation of China (91958202, 42206033, 42076019), the Basic Frontiers and Innovative Development 2023 “Integration” Project of South China Sea Institute of Oceanology (SCSIO2023QY02), the Marine Geological Survey Program of China Geological Survey (DD20221706, DD20230065), Guangdong Basic and Applied Basic Research Foundation (2020A1515111083), the Key Research and Development Project of Guangdong Province (2020B1111510001), and Research Foundation of National Engineering Research Center for Gas Hydrate Exploration and Development (Innovation Team Project 2022GMGSCXYF41003). We thank the China Ocean Mineral Resources R&D Association, which supported field measurements in the Chinese Da‐Yang Survey 27, 29, 32, and 36.
Data availability statement.
AVISO gridded sea level anomaly (SLA) and surface geostrophic current data can be obtained from https://www.aviso.altimetry.fr. Due to privacy and ethical concerns, other data cannot be made available. The idealized seamount-trapped wave model can be found at https://darchive.mblwhoilibrary.org/handle/1912/10528.
APPENDIX
General Setup of the Brink Code
Before running the model code, the Coriolis parameter, stratification, topography, mean flow, bottom friction, and numerical grid points in the radial and vertical directions need to be set (see section 2 of this paper). You can apply a forcing with a guessed frequency through the surface boundary condition, and ω is searched near the guessed frequency for a maximum response so as to establish a complex frequency corresponding to azimuthal wavenumber 1. The inverse resonance parameter (rrr = inverse of the integral of r|p|2 over r and z) will be calculated for each ω estimate. When the inverse resonance parameter becomes very small (i.e., at a resonance), the solution converges onto a seamount-trapped wave modal frequency and gives the modal structure. If the inverse resonance parameter is several orders of magnitude lower than neighboring values and the modal structure is meaningful for seamount-trapped waves, it is a good solution. In this paper, we ran the code with the guessed frequency ranging from 30- to 2.5-day period at a step size of 0.2-day period. At every good solution (i.e., a radial–vertical mode), the program was rerun with the ω solution to calculate modes with azimuthal wavenumber 1–7. Finally, the dispersion relations of idealized seamount-trapped waves are determined.
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