Observed 10–20-Day Deep-Current Variability at 5°N, 90.5°E in the Eastern Indian Ocean

Jinghong Wang aState Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China
bUniversity of Chinese Academy of Sciences, Beijing, China

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Yeqiang Shu aState Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China

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https://orcid.org/0000-0003-0033-6738
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Dongxiao Wang cSchool of Marine Sciences, Sun Yat-sen University, Guangzhou, China

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Ju Chen aState Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China

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Yang Yang dSchool of Marine Sciences, Nanjing University of Information Science and Technology, Nanjing, China

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Weiqiang Wang aState Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China

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Binbin Guo eNational Engineering Research Center of Gas Hydrate Exploration and Development, Guangzhou Marine Geological Survey, Guangzhou, China

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Ke Huang aState Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China

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Yunkai He aState Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China
bUniversity of Chinese Academy of Sciences, Beijing, China

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Abstract

In the eastern off-equatorial Indian Ocean, deep current intraseasonal variability within a typical period of 10–20 days was revealed by a mooring at 5°N, 90.5°E, accounting for over 50% of the total bottom subtidal velocity variability. The 10–20-day oscillations were more energetic in the cross-isobathic direction (STD = 3.02 cm s−1) than those in the along-isobathic direction (STD = 1.50 cm s−1). The oscillations were interpreted as topographic Rossby waves (TRWs) because they satisfied the TRWs dispersion relation that considered the smaller Coriolis parameter and stronger β effect at low latitude. Further analysis indicated significant vertical coupling between the deep cross-slope oscillations and cross-isobathic 10–20-day perturbations at the depth of 300–950 m. The 10–20-day TRWs were generated by cross-isobathic motions under the potential vorticity conservation adjustment. The Mercator Ocean output reproduced the generation of kinetic energy (KE) of deep current variability. The associated diagnostic analysis of multiscale energetics showed that the KE of TRWs was mainly supplied by vertical pressure work. In the seamount region (2°–10°N, 89°–92°E), vertical and horizontal pressure works were identified to be the dominant energy source (contributing to 94% of the total KE source) and sink (contributing to 98% of the total KE sink) of the deep current variability, transporting energy downward and redistributing energy horizontally, respectively.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yeqiang Shu, shuyeq@scsio.ac.cn

Abstract

In the eastern off-equatorial Indian Ocean, deep current intraseasonal variability within a typical period of 10–20 days was revealed by a mooring at 5°N, 90.5°E, accounting for over 50% of the total bottom subtidal velocity variability. The 10–20-day oscillations were more energetic in the cross-isobathic direction (STD = 3.02 cm s−1) than those in the along-isobathic direction (STD = 1.50 cm s−1). The oscillations were interpreted as topographic Rossby waves (TRWs) because they satisfied the TRWs dispersion relation that considered the smaller Coriolis parameter and stronger β effect at low latitude. Further analysis indicated significant vertical coupling between the deep cross-slope oscillations and cross-isobathic 10–20-day perturbations at the depth of 300–950 m. The 10–20-day TRWs were generated by cross-isobathic motions under the potential vorticity conservation adjustment. The Mercator Ocean output reproduced the generation of kinetic energy (KE) of deep current variability. The associated diagnostic analysis of multiscale energetics showed that the KE of TRWs was mainly supplied by vertical pressure work. In the seamount region (2°–10°N, 89°–92°E), vertical and horizontal pressure works were identified to be the dominant energy source (contributing to 94% of the total KE source) and sink (contributing to 98% of the total KE sink) of the deep current variability, transporting energy downward and redistributing energy horizontally, respectively.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yeqiang Shu, shuyeq@scsio.ac.cn

1. Introduction

Topographic Rossby waves (TRWs) are subinertial waves characterized by periods that span from several days to several hundreds of days and wavelengths ranging from tens to several hundreds of kilometers (Rhines 1970; Oey and Lee 2002). In recent decades, TRWs have been observed in deep ocean regions worldwide. These regions include the northwest Atlantic (Thompson 1971; Thompson and Luyten 1976), the northwest Pacific (Miyamoto et al. 2020), the Arctic Ocean (Zhao and Timmermans 2018), the Gulf of Mexico (GoM; Hamilton 2007, 2009), South China Sea (SCS; Shu et al. 2016; Q. Wang et al. 2019; Zheng et al. 2021b; Shu et al. 2022), East China Sea (ECS; Chen et al. 2022), Japan Sea (Shin et al. 2020), and Philippine Sea (Ma et al. 2019). TRWs are commonly regarded as the prevailing oscillating pattern of subinertial variability in deep oceans (e.g., Thompson and Luyten 1976; Johns and Watts 1986; Hamilton 1990, 2007, 2009; Oey and Lee 2002; Zheng et al. 2021a). For instance, TRWs could explain over 40% of the total deep current variance over rough topographic region in the SCS according to mooring observations and numerical studies conducted in that region (Q. Wang et al. 2019; Wang et al. 2021; Quan et al. 2021a) and accounted for more than 80% of the total deep-current variance in the GoM based on observations (Hamilton 2009). The excitation of TRWs occurs due to cross-isobathic motion, where fluid columns are stretched or compressed over sloping topography under the adjustment of potential vorticity (PV) conservation (Rhines 1970; Oey and Lee 2002). Previous studies have elucidated that upper-layer intraseasonal variability can act as the energy reservoir of TRWs, such as the Loop Current (LC) and LC eddies in the GoM (Hamilton 1990, 2007; Zhu and Liang 2020), Kuroshio intrusion (Quan et al. 2021b) and the upper-ocean eddies in the northern SCS (Q. Wang et al. 2019; Zheng et al. 2021a), and the Kuroshio meanders (Chen et al. 2022) in the ECS.

In the Northern Hemisphere tropical Indian Ocean, the upper-ocean circulation exhibits strong intraseasonal variations, which are mainly influenced by atmospheric intraseasonal oscillations (e.g., the Madden–Julian oscillation; Madden and Julian 1971; Hendon and Glick 1997; Webster et al. 2002; Shinoda et al. 2013). Off the equatorial regions, such as the Bay of Bengal, certain intraseasonal signals like variations in thermocline and sea surface height can be attributed to remote equatorial intraseasonal winds. This is achieved through the propagation of equatorial Kelvin waves (KWs) and the reflection of coastal KWs, which subsequently transform into westward-propagating Rossby waves (RWs) (Cheng et al. 2013; Girishkumar et al. 2013). Chen et al. (2017) observed strong 30–50-day meridional currents above ∼150 m at 5°N, 90.5°E, where the topography is steep; mooring Q3 used in the present study was located in this region (Fig. 1a). The 30–50-day variability of near-surface currents is linked to westward-propagating RWs, which are mainly induced by equatorial wind forcing and equatorial KWs reflection at the eastern boundary. These abundant oceanic wave processes and complex topography of off-equatorial regions (e.g., around mooring Q3) provide conducive conditions to TRW generation in the deep ocean. The response of deep currents to complex topography, and whether TRWs exist in this area is still an unknown scientific question. Owing to the absence of direct observational data, our understanding of the variability of deep currents in this region is currently limited.

Fig. 1.
Fig. 1.

The study region. (a) Mooring location. (b) Topography of the seamount region. The yellow star represents the location of mooring Q3. The red box indicates the seamount region (2°–10°N, 89°–92°E). The red dotted line in (b) represents the scatterplot of zonal and meridional bottom flows from 28 Aug to 10 Nov 2017. The blue line in (b) depicts the standard deviation ellipse derived from the 10–20-day bandpass-filtered velocities.

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0082.1

Recently, there has been a growing interest in the study of deep-ocean energy pathways and oceanic processes (e.g., D. Wang et al. 2019). As vertical downward energy transport has been frequently reported (Huang et al. 2018, 2020; Chen et al. 2022; Ma et al. 2022), vertical pressure work (PW) is acknowledged as the primary energy source in the deep ocean based on numerical studies (e.g., Maslo et al. 2020; Yang et al. 2021; Quan et al. 2022). TRWs are widely believed to play a pivotal role in the energy transfer pathway from the upper to the deep ocean. For instance, part of the energy originating from upper mesoscale perturbations is transferred to TRWs and redistributed in the deep ocean via TRW propagation (Hamilton 2009; Oey and Lee 2002; Q. Wang et al. 2019; Wang et al. 2021). That is to say, TRWs are the result of the vertical connection of energy between the upper and deep ocean, gain the energy transferred in the vertical direction, and further redistribute the energy horizontally. In some cases, the vertical coupling between the upper and bottom currents can be attributed to the formation of TRWs (Q. Wang et al. 2019; Zhu and Liang 2020). Therefore, detailed information on dynamics associated with TRWs is essential to understanding deep current variability and energy pathways in this region.

With the feasibility of more extensive measurements in recent years, data on both upper and deep currents are now available from a long-term deep mooring station located at around 5°N, 90.5°E (yellow star in Fig. 1a). Strong intraseasonal variability of deep currents with a typical period of 10–20 days is observed in both along- and cross-slope directions (Fig. 2). Therefore, the principal aim of this research is to comprehend the 10–20-day deep-current variability and elucidate the underlying dynamics from the perspective of energetics. The remaining sections of the article are structured as follows. Section 2 offers an extensive account of the data and methodologies employed in the study. Subsequently, section 3 presents the results derived from the analysis of data. Section 4 discusses the findings. Finally, section 5 provides a summary.

Fig. 2.
Fig. 2.

Power spectrum analysis of the bottom velocities. The results of (a) along-isobathic and (b) cross-isobathic velocities were obtained from observations (red solid line) and Mercator Ocean output (blue solid line) at mooring Q3, respectively. The 95% confidence level based on the red noise test is indicated by the dotted lines.

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0082.1

2. Data and methods

a. Data

A mooring (Q3), referred to as Q3, was installed in the southern Bay of Bengal at around 5°N, 90.5°E (as shown in Fig. 1a). The deployment site is characterized by numerous seamounts and steep and complex topography (Fig. 1b). The mooring is equipped with two 75-kHz upward-looking acoustic Doppler current profilers (ADCPs) in the upper ocean and a NORTEK Aquadopp current meter at the bottom. The NORTEK Aquadopp current meter recorded the bottom velocity data for over 3 years (from 28 March 2016 to 10 May 2019) at the water depth of ∼3306 m (∼30 m above the seafloor), and the ADCPs measured the velocity profiles for approximately 1 year (from 16 March 2017 to 15 February 2018) over the depth from 39 to 948 m with a vertical interval of 8 m. The velocities from the current meter and ADCPs were sampled at intervals of 600 and 3600 s, respectively. To ensure data quality, the observed velocities underwent essential quality assurance procedures. Any short gaps in the data, typically lasting a few hours and caused by suspect data or mooring redeployment, were filled using linear interpolation. Next, a fourth-order Butterworth bandpass filter with a cutoff frequency of 0.33 cpd (i.e., period of 3 days), was applied to velocities data to eliminate tidal effect. Then, the current data were averaged on a daily basis to obtain the daily zonal (U) and meridional (V) velocities. Subsequently, the velocity components were rotated for further analysis. The zonal component (U) was transformed into the parallel component (u) to the isobaths, while the meridional component (V) was transformed into the perpendicular component (υ) to the isobaths. In this context, the raw data were represented by u and υ, respectively, with a negative υ value implying downslope direction. The downslope direction was determined by the smoothed bathymetry data with a 50 × 50 km2 area average.

To investigate the correlation between upper-ocean mesoscale variability and deep current variability during the observation period, we employed the 0.25° × 0.25° sea surface geostrophic current anomaly data with a 1-day temporal resolution from the French Archiving, Validation, and Interpretation of Satellite Oceanographic dataset (AVISO; Ducet et al. 2000). The 1/60° × 1/60° topography data obtained from ETOPO1 (Amante and Eakins 2009) were utilized to calculate the slope and the downslope direction. The 0.25° × 0.25° climatological hydrographic field from the World Ocean Atlas 2018 (WOA18) was used to calculate the abyssal Brunt–Väisälä frequency (N), which was depth averaged from 3000 to 3300 m in this study.

Because of the limited data of a single mooring, the daily output of velocity during 2014–19 from the Global Mercator Ocean Reanalysis (GLORYS12) product (Lellouche et al. 2018) with 1/12° horizontal resolution and 50 vertical levels, was used to investigate the energy transfer of deep-ocean variability and dynamical processes. The Mercator Ocean (MO) output has been proven to reproduce the activity of TRWs and utilized to diagnose deep-sea dynamics in the Pacific Ocean (Ma et al. 2019).

b. Multiscale energetics

To explore the energetics of deep current variability in the seamount region around Q3, we adopted multiscale energy and vorticity analysis (MS-EVA; Liang 2016), which has been widely utilized to assess oceanic and atmospheric processes in previous studies (Liang and Robinson 2009; Ma and Liang 2017; Yang et al. 2021; Yang and Liang 2019; Yang et al. 2020; Quan et al. 2021b). The process of scale separation can be achieved by using multiscale window transform (MWT; Liang and Anderson 2007), a method that orthogonally breaks down the function space into multiple subspaces referred to as scale windows. Using MWT, a given time series u(t) defined on the interval [0, 1], can be reconstructed into three temporal-scale windows, as follows:
u(t)=ϖ=02uϖ(t),
where ϖ = 0, 1, 2, corresponding to the fields filtered through low-pass, bandpass, and high-pass methods, and uϖ(t) represents the reconstruction of u within window ϖ. The term uϖ(t) can be expressed as follows:
uϖ(t)=n=02j21u^nϖφnj2(t),
u^nϖ=01uϖ(t)φnj2(t)dt,
where u^nϖ denotes the MWT coefficient, φ(t) represents a localized scaling basis, j (j0 < j1 < j2) stands for the scale level, and n signifies the discrete time increment within the sampled domain (Liang and Anderson 2007). Equations (3) and (2) constitute the transformation–reconstruction pair of MWT.

By applying this method to the MO reanalysis data, we separated three temporal-scale windows in the present study, namely, the low-frequency background flow window (ϖ = 0), TRW window (ϖ = 1; discussed later), and synoptic window (ϖ = 2). Details regarding the cutoff period for each window are presented in section 4.

Through the application of MWT to the hydrostatic and Boussinesq fluid flow equations, the tendency equation for multiscale kinetic energy (KE) on window ϖ [Kϖ=(1/2)vĥϖvĥϖ] and available potential energy (APE) on window ϖ [APEϖ;APEϖ=(1/2)c(ρ^ϖ)2, where c=g2/(ρ02N2)] can be obtained as follows (Liang 2016):
Kϖt=12[(vvĥ)ϖ:vĥϖ(vvĥ)ϖvĥϖ]ΓKϖ+{[12(vvĥ)ϖvĥϖ]}QKϖ+[h(1ρ0vĥϖP̂ϖ)]hQpϖ+[z(1ρ0ŵϖP̂ϖ)]zQpϖ+(gρ0ρâϖŵϖ)bϖ+FKϖ,
APEϖt=c2[(vρâ)ϖρâϖρâϖ(vρâ)ϖ]ΓAϖ+{[12(cρâ)ϖ(vρa)̂ϖ]}QAϖ+(gρ0ρâϖŵϖ)bϖ+12ρâϖ(wρa)̂ϖczSAϖ+FAϖ,
where Kϖ/t and APEϖ/t represent the tendencies of Kϖ and APEϖ, the right-hand-side term ΓKϖ (ΓAϖ) is the cross-scale KE (APE) transfer, QKϖ (QAϖ) is the convergence of KE (APE) flux, hQpϖ (zQpϖ) is horizontal (vertical) pressure flux convergence, bϖ represents buoyancy conversion, SAϖ denotes the apparent source/sink arising from the nonlinearity of reference stratification, and FKϖ (FAϖ) is a residual term that includes all the effects of external forcing and unresolved subgrid processes. The colon operator (:) is defined as follows, for a pair of dyads (e.g., AB and CD), (AB) : (CD) = (AC)(BD), and other symbols are conventional. For convenience, the terms QKϖ, QAϖ, hQpϖ, and zQpϖ are written as ΔQKϖ, ΔQAϖ, ΔhQPϖ, and ΔzQPϖ, respectively. Note that the sum of all cross-scale transfer processes Γϖ is zero, without energy generation or loss as a whole, described as follows:
ϖnΓnϖ=0,
where summations ϖ and n involve all scale windows ϖ and sampling time steps, respectively. This property, which is not satisfied in classic energetics formalism, is in accurate alignment with the principles of the conventional instability theory (Liang and Robinson 2007); thus, Γ is termed “canonical transfer” for distinction (Liang 2016). The canonical transfers (Γϖ terms) in Eqs. (4) and (5) must be further decomposed via “interaction analysis” (Liang and Robinson 2005). The superscripts 0 → 1 and 2 → 1 are used to represent these window-to-window transfers. For instance, ΓK01 (ΓA01) denotes the conveyance of KE (APE) originating in the background flow window (ϖ = 0) to the TRW window (ϖ = 1), and a positive value of ΓK01 (ΓA01) indicates a forward energy cascade via barotropic (baroclinic) instability (Liang and Robinson 2007). Likewise, ΓK21 (ΓA21) denotes the scale interaction between ϖ = 2 and ϖ = 1, with a positive value indicating an inverse cascade of KE (APE). In this study, our primary emphasis was on energetics within window ϖ = 1, which corresponds to the observed typical period of deep current variability.

3. Results

a. 10–20-day deep-current variability

The most significant characteristics of the observed deep currents were the dominant period in the 10–20-day intraseasonal frequency band and the occurrence of spectral peaks on 11 days in both directions (Fig. 2). Based on spectral analysis, the raw data were 10–20-day bandpass filtered to extract deep oscillations. To assess the influence of these oscillations on the overall variability of bottom subtidal currents, we presented the 10–20-day bandpass-filtered and the 3-day low-pass-filtered velocities in Fig. 3 and calculated the ratios of their standard deviations (STD). Both the ratios of the velocity components were above 50%, indicating that the 10–20-day fluctuations accounted for more than 50% of the overall variability of subtidal deep currents. Of note, the STD of 10–20-day υ (3.02 cm s−1) was 2 times that of u (1.50 cm s−1), implying that the fluctuations were stronger in the cross-slope direction. The maximum amplitude of the 10–20-day oscillations was 10.71 cm s−1 (5.63 cm s−1) in the cross-slope (along-slope) direction.

Fig. 3.
Fig. 3.

Observed 3-day low-pass filtered and 10–20-day filtered bottom (a) u and (b) υ at mooring Q3. Gray and black lines indicate the 3-day low-pass and 10–20-day filtered velocities, respectively. The title of each panel displays the ratio between the STD of 10–20-day bandpassed velocities and the STD of 3-day low-pass filtered velocities.

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0082.1

b. Dynamics for TRWs in low-latitude region

Energetic deep–current variability in a complex topography is associated with TRWs in many cases (e.g., Hamilton 2009; Wang et al. 2021; Shu et al. 2022). Beginning with the linear, hydrostatic, and Boussinesq equations, the governing equation for TRWs can be expressed in Cartesian coordinates as follows:
t[pxx+pyy+1N2(2t2+f02)pzz]+βpx=0.
Assuming time dependence of e−iωt, Eq. (7) can be revised as follows:
t[pxx+pyy+f02ω2N2pzz]+βpx=0.
The boundary conditions consist of a rigid lid and no normal flow through the bottom; that is,
tpz=0,atz=0,
tpz=N2f0(pxhypyhx),atz=h,
where h represents the water depth, f0 indicates the local Coriolis parameter, and (hx, hy) is the horizontal gradient of the topography. Substituting the solution of the form
p=A(z)ei(kx+lyωt)
into (8) and the boundary conditions (9) and (10), we obtain
A(z)=A0cosh(λz),
λ2=(k2+l2+βkω)(N2f02ω2),
ω=N2f0λtanh(λh)(khylhx),
where A0 is a constant and 1/λ represents the TRW vertical trapping scale. Substituting Eq. (13) into Eq. (14), we obtain TRW dispersion relation that considers the smaller Coriolis parameter f0 and stronger β effect in the subtropical region, as follows:
ω=N(kKlhylKlhx)f02ω2f0tanh(λh)1+βkωKl2=N(Kl×hz)f02ω2f0Kltanh(λh)1+βkωKl2=N|h|sinθtanh(λh)1ω2f021+βkωKl2,
where Kl = (k, l) is the horizontal wavenumber vector, Kl=k2+l2 is the magnitude of Kl, z is the unit vector along the z axis, Kl × ∇hz represents the z component of Kl × ∇h, and θ indicates the clockwise angle that Kl forms with cross-isobathic downslope direction Dir(∇h), satisfying θ = Dir(∇h) − Dir(Kl). In Eq. (15), all terms must be greater than zero except (Kl × ∇hz) and f0. To keep ω positive, the sign of Kl × ∇hz should be the same as that of f0. Therefore, the direction of the wavenumber vector points to the right (left) of the downslope direction, indicating that TRWs propagate with deep water on its left (right) in the Northern (Southern) Hemisphere.
If the motion is low frequency [i.e., (f02/ω2)>10] and the topographic β effect (βTopo) is dominant [i.e., βTopo=(f0|h|/h)>10β], both 1+[βk/(ωKl2)] (term Ι) and 1(ω2/f02) (term Π) are approximately 1; then [with tanh(λh) = 1], Eq. (15) is simplified as ω = N|∇h|sinθ, which was commonly used in previous studies in the SCS and GoM (e.g., Oey and Lee 2002; Shu et al. 2016). However, in our case, these conditions could not be satisfied. Considering the dominant period of motion to be within 10–20-day period band (ω is within 3.64–7.27 × 10−6 s−1), f0 = 12.7 × 10−6 s−1, |∇h| ∼ 0.01, and h ∼ 3000 m, then the value of f02/ω2 is within 3.1–12.2 and βTopo ≈ 2β; in other words, the ω2/f02 and β terms in Eq. (15) cannot be ignored. This is not surprising because the mooring is located at 5°N, resulting in a much smaller f0 and a stronger β effect. Previous studies suggested that the 10–20-day TRWs satisfy the short-wavelength assumption based on their observations (e.g., Shu et al. 2016, 2022; Q. Wang et al. 2019; Wang et al. 2021), which assumes a wavelength L < 200 km (Hamilton 2009). For the short waves with a period of 10–20 days, we could infer that Kl=2π/L>2π/200000m1=3.14×105m1 and zonal wavenumber k = Kl cos 154.30° < −2.8 × 10−5 m−1, then values of 1+[βk/(ωKl2)] (term Ι) exceeded 0.9 and that of 1(ω2/f02) (term Π) ranged from 0.82 to 0.96 (Figs. 4a,b). Therefore, the ratio of term Ι and term Π (i.e., term I/term II) was within 0.94–1.22, thus
λ=NKlf01+βkωKl21ω2f02=NKlf0termΙtermΠ>0.0019,
and tanh(λh ≥ 5.78) = 1, indicating tanh(λh) = 1 is valid under the short-wavelength assumption. It should be noted that the group velocity Cg=(ω/k,ω/l) is not perpendicular to the wave vector if the βk/(ωKl2) of term Ι is kept in the TRW dispersion relation [i.e., ω=N|h|sinθ1(ω2/f02)/1+[βk/(ωKl2)]], but remains normal to Kl if only ω2/f02 term is kept [i.e., ω=N|h|sinθ1(ω2/f02)], mainly because ω is dependent (independent) on the magnitude of Kl and KlCg=KlKlω0(=0) when the βk/(ωKl2) of term Ι is kept (dropped) (Oey and Lee 2002).
Fig. 4.
Fig. 4.

Topographic Rossby wave dispersion elements. (a) Term Ι {1+[βk/(ωKl2)]} for varying zonal wavenumber and (b) term Π [1(ω2/f02)] for varying frequency. (c) STD ellipse of 10–20-day filtered bottom currents. The red and blue ellipses were derived from the 10–20-day filtered velocities obtained from observation and model output. The Dir(Kl) of the observation and MO model output was derived from the minor axis of their STD ellipse and represented by purple and blue arrows, respectively. The theoretical range of Dir(Kl) derived from the TRW theory was indicated by the green dashed line domain.

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0082.1

To validate the observed 10–20-day fluctuations as TRWs, we compared the observed Dir(Kl) with the theoretical range of the wavenumber direction Dir(Kl) derived from the TRW dispersion relation. First, we calculated the STD ellipse of 10–20-day filtered currents to obtain the observed Dir(Kl), which is represented by the minor axis direction of the STD ellipse (Hamilton 2009). To the north of the equator, TRWs propagate with deep water on their left, indicating the θ is within (0, π/2) or (π/2, π) when Dir(Kl) points downslope or upslope (Oey and Lee 2002). In our case, Dir(∇h) = 213.10°, observed Dir(Kl) was 154.30° and pointed downslope (purple arrow in Fig. 4c). With tanh(λh) = 1, two roots of θ could be calculated from TRW dispersion relation [Eq. (16)], and its value should be within (0, π/2)
θ=sin1(ωN|h|1+βkωKl21ω2f02).
Then, the theoretical Dir(Kl) can be expressed as follows:
Dir(Kl)=Dir(h)θ.
Given|∇h|, N, k, Kl, and ω, the theoretical range of Dir(Kl) could be derived from Eqs. (16) and (17). Considering that the ω was within 3.64–7.27 × 10−6 s−1 (i.e., a period of 10–20 days), Dir(Kl) pointed downslope, the environmental parameters |∇h| = 0.011 and N = 7.8 × 10−4 s−1 at mooring Q3, we obtained the theoretical θ ranging from 24.83° to 90.00°; thus, theoretical Dir(Kl) was within (123.10°, 188.27°), which was indicated by the green dashed line domain in Fig. 4c. In other words, the energetic 10–20-day fluctuations at Q3 could be considered as TRWs due to the observed Dir(Kl) closely conforming to the dispersion relation of 10–20-day TRWs.

c. Association between the 10–20-day oscillations of deep currents and upper-ocean processes

To identify the burst period of energetic TRWs, we employed wavelet analysis to the raw velocity data (i.e., u and υ), and the 10–20-day eddy kinetic energy (EKE) was calculated using bandpass-filtered data. The significantly enhanced period of the deep 10–20-day oscillations was similar in both directions (Figs. 5a,b) and coincident with the intensification of the 10–20-day EKE (Fig. 5c). Previous studies have suggested that TRWs may be generated by upper-layer mesoscale oscillations, such as upper-layer eddies (Ma et al. 2019; Shu et al. 2022; Wang et al. 2021). The 10–20-day surface EKE was obtained from the 10–20-day filtered geostrophic velocities from the AVISO dataset to illustrate the intensity of surface eddies. Here, we assumed that the EKEs of the energetic bottom TRW and upper-layer eddy are larger than their STDs (marked in black and blue bars in Figs. 5c,d, respectively). Evidently, upper-layer eddies do not appear to be related to the occurrence of strong bottom TRWs.

Fig. 5.
Fig. 5.

(a) Wavelet power spectrum of observed bottom along-isobathic and (b) cross-isobathic velocities at mooring Q3. The 95% confidence level is indicated by the black contours. (c) The 10–20-day filtered bottom and (d) surface EKEs, calculated from the 10–20-day filtered velocities and AVISO dataset, respectively. EKEs exceeding their STDs are highlighted in black and blue, respectively. Red dashed lines indicate the start and end times of upper-layer observations. Green shading represents the energetic period of bottom TRWs selected for further analysis.

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0082.1

To understand the association between the 10–20-day oscillations of deep currents and other upper-layer processes, velocity data over 39–948 m derived from the ADCPs were used. The 10–20-day oscillations of cross-slope currents were more energetic below 500 m than those near the surface, while the 10–20-day oscillations of along-slope currents were mostly present above 300 m and decreased in strength with increasing depth (Figs. 6a,b). Subsequently, we used this frequency band to extract signals in the upper ocean and applied correlation analysis to the 10–20-day upper and deep oscillations in both directions. In the along-slope direction, the correlation between the upper and bottom oscillations was weak, with most correlation coefficients being <0.2 and below the 95% confidence level (gray line in Fig. 6c). In contrast, almost all correlation coefficients below 300 m in the cross-slope direction were larger than 0.2 and exceeded the 95% confidence level, indicating a strong association between deep 10–20-day variability and cross-slope subthermocline (300–950 m) oscillations (Fig. 6d).

Fig. 6.
Fig. 6.

Power spectrum of the observed upper (a) u and (b) υ by mooring Q3. (c) Correlation coefficients between upper velocities at different depths and deep velocities in along-isobathic and (d) cross-isobathic directions, respectively. In (c) and (d), coefficients exceeding the 95% confidence level based on the Student’s t test are plotted in red.

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0082.1

To further understand the dynamics between upper-layer and deep-sea flows, we employed the empirical orthogonal function (i.e., EOF) analysis to the subthermocline raw velocities over 300–950 m during the energetic TRW period (from 25 May to 10 November 2017, 170 days; green shading in Fig. 5c). The first, second, and third modes (i.e., EOF1, EOF2, and EOF3) contributed to over 80% of the total variance (Figs. 7a,b). Next, we calculated the power spectra of the principal components (PCs) of the first and second modes to reveal the general pattern of subthermocline flows. Spectral peaks in the 10–20-day period were detected in the first PC (PC1) alone in both directions, while the spectral power of cross-isobathic flows was relatively strong in the period band of 10–20 days (Figs. 7c–f). Therefore, we calculated the lag correlation coefficients between the 10–20-day bandpass-filtered PCs and deep flows (Fig. 8). The most significant correlation was at zero lag (3 days) in the cross- (along-) slope direction (Figs. 8a,b), indicating coupling between cross-slope subthermocline and deep motions. Since TRWs are generated by cross-isobathic motions as water columns are compressed and stretched over a sloping topography (Oey and Lee 2002), we hypothesized that subthermocline cross-slope motions induced deep cross-isobathic motions through the barotropic mode (i.e., EOF1), providing the necessary conditions for TRWs generation.

Fig. 7.
Fig. 7.

First three modes of EOF decomposition of the observed upper (a) u and (b) υ between 300 and 950 m. Power spectrum analysis of the (c) PC1 and (d) PC2 of upper-ocean u between 300 and 950 m. Power spectrum analysis of the (e) PC1 and (f) PC2 of upper-ocean υ between 300 and 950 m. The 95% confidence level test against red noise was indicated by the dotted red lines in (c)–(f).

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0082.1

Fig. 8.
Fig. 8.

Time-lag correlations. (a) Lag correlation between the bottom u and PC1 of upper u. (b) Lag correlation between the bottom υ and PC1 of upper υ. Coefficients over the 95% significance level based on Student’s t test are indicated in red.

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0082.1

Figure 9 showed the 10–20-day filtered velocity profiles and depth-averaged (300–950 m) subthermocline velocities. The energetic periods of the subthermocline (black bars; Figs. 9c,d) and deep (red bars; Figs. 9c,d) motions were defined as absolute values larger than their STDs. A clear vertical coupling structure was noted in the υ components, whose energetic period was from late May to early November 2017 in both subthermocline and deep ocean (Fig. 9d). As subthermocline υ increased in June 2017, deep υ was strengthened subsequently and tended to be in the same phase as in the upper flows, consistent with the feature of the barotropic mode (Fig. 9d). When the water column was compressed or stretched, the TRWs burst due to potential vorticity conservation.

Fig. 9.
Fig. 9.

Observed upper and bottom velocities at mooring Q3. (a) Profiles of 10–20-day bandpass-filtered u and (b) υ in the upper layer. The 10–20-day filtered upper velocities averaged from 300 to 950 m (gray bars) and bottom velocities (red lines) in (c) along-isobathic and (d) cross-isobathic directions. In (c) and (d), the upper averaged and bottom velocities exceeding their STDs are plotted in black and red bars, respectively.

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0082.1

4. Discussion

Although the above analysis showed that the 10–20-day deep-sea TRWs were dynamically linked to subthermocline oscillations, detailed energetics and energy transfer dynamics of this deep-sea variability remained unknown. Mooring observation is limited to a single location and may not capture the full extent of the underlying energetics. Therefore, we used the MO model output to analyze the energetics of TRWs. The prerequisite of using model output is that the model can reproduce the observed TRWs. First, we compared the power spectrum and the STD ellipse between model output and observation. The result showed that there were significant 10–20-day oscillations in the bottom velocities derived from model output (blue solid line; Fig. 2). The magnitude of the STD ellipse calculated from model output was similar to that calculated from observation, despite the wavenumber direction (128.65°; blue arrow in Fig. 4c) being different from the observed value (154.30°), which might result from the uncertainty of environmental parameters [e.g., |∇h| and Dir(∇h)] and smoothing scale of topography in the model. Second, we examined if the 10–20-day oscillations in the MO model satisfy the TRW dispersion relation. It was obvious that the Dir(Kl) obtained from the MO model (blue arrow in Fig. 4c) was within the theoretical range, suggesting that the 10–20-day oscillations in the MO model also satisfy the TRW dynamic. In other words, the discrepancy of Dir(Kl) between observation and MO was acceptable in TRW theory. Third, as the study specifically focused on the energetics of oscillations in the 10–20-day period band, we compared the burst of the 10–20-day EKEs between the observation and MO model output in Fig. 10 (values smaller than their STDs are not shown in Figs. 10b,d). Both the 10–20-day upper-layer and bottom EKEs from the model output had similar enhancement time periods to that of the observations (Fig. 10). Moreover, the amplitude of upper-ocean and bottom EKE from model output was comparable to that of observation, that is to say, the model accurately simulated the timing, generation, and intensity of 10–20-day oscillations throughout the observation period. In other words, the MO model output could reproduce 10–20-day oscillations and associated generation processes, indicating its usefulness in exploring deep-sea energetics and energy transfer from the upper to deep ocean.

Fig. 10.
Fig. 10.

(a) The 10–20-day filtered upper-layer (100–950 m) and (b) bottom EKE obtained from observational data at mooring Q3. (c),(d) The corresponding results from Mercator Ocean model output. EKEs were derived from the 10–20-day bandpass-filtered velocities. In (b) and (d), only values exceeding their STDs are shown.

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0082.1

To better understand the energetics at mooring Q3, we employed MS-EVA (Liang 2016) on the MO model output. Since the window bounds and length of the time series were exponential functions of base 2 for MS-EVA, we selected a window of 8–16 days to extract the energy of TRWs, and the data ranged from 1 January 2014 to 10 August 2019 (2048 days). It should be noted that APE1 was one order smaller than K1 near the bottom (Figs. 11a,b). Moreover, except b1, which appeared in both Eqs. (4) and (5), the other terms in Eq. (5) were much less than ΔzQp1 and ΔhQp1 in Eq. (4) (not shown here). Therefore, we will not analyze the result of Eq. (5).

Fig. 11.
Fig. 11.

Profiles of the energy reservoir and energetics terms (a) K1, (b) APE1, (c) ΔzQp1, (d) b1, (e) ΔhQp1, (f) ΓK01, (g) ΔQK1, and (h) Fk1. The other terms are negligible and not shown.

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0082.1

The deep-layer K1 burst with a bottom-intensified characteristic, which was consistent with the TRW feature (Fig. 11a). Among the terms of the K1 budget [Eq. (4)], the horizontal and vertical pressure work (ΔhQp1 and ΔzQp1) were relatively larger than the other terms (Fig. 11). The positive vertical pressure work ΔzQp1 indicated that K1 was transported downward from the upper ocean. The negative horizontal pressure work ΔhQp1 implied that K1 was horizontally redistributed by the horizontal pressure gradient and acted as a sink for the K1 reservoir. We noticed that almost each burst of K1 robustly corresponded to an enhanced positive ΔzQp1 value (negative ΔhQp1 value) from 2014 to 2019, indicating that ΔzQp1 (ΔhQp1) typically served as the dominant energy source (sink) for bottom TRWs (Figs. 11a,c,e). As described by Quan et al. (2021a), the mesoscale perturbations from the upper ocean can transport energy to deep oscillations via deforming the isopycnals to do work (i.e., vertical pressure work ΔzQp1). This vertical process can explain the vertical linkage between the upper-layer and deep-sea current variability from an energetics aspect, which is reported in the Kuroshio Extension region (Yang et al. 2021). The buoyancy conversion b1 signals were weaker in the interior ocean but stronger beneath the water depth of ∼3000 m and showed a bottom-intensified distribution (Fig. 11d). From this result, APE1 could be converted to K1, thus favoring TRW generation in the deep ocean. In addition, the canonical transfer ΓK01 and advection of KE ΔQK1 also showed overwhelmingly positive and bottom-intensified patterns in the deep layer, with their positive timing corresponding to some strong K1 events (Figs. 11f,g). Note that the positive ΔQK1 might imply the effect of TRW propagation from upstream, the result suggested that energetic bottom TRWs can gain energy locally through the release of background-flow KE via barotropic instability and nonlocally through advective transport of K1 (possibly via TRWs propagation), which is coincident with the mechanisms revealed by Ma et al. (2019) and Quan et al. (2021b). The residual term Fk1 showed alternating positive and negative signals (Fig. 11h), while its time- and depth-averaged value was negative (Fig. 13a), indicating part of K1 might be dissipated by bottom friction.

To explore the universal dynamics in the seamount region (2°–10°N, 89°–92°E), we time averaged the ∼6-yr variables in the K1 budget equation and integrated from 2000 m to the bottom (Fig. 12). Over the long-term perspective, pressure work significantly dominated the K1 budget in comparison to other terms, by at least 3 times the other terms. In the subequatorial region, the vertical pressure work ΔzQp1 was mainly positive, while the horizontal pressure work ΔhQp1 was mainly negative, and both peaked in the region southwest of Q3. This area also exhibited positive values for the advection term ΔQK1 and buoyancy conversion b1, as shown in Figs. 12a–d. These distribution patterns of the pressure work highlighted an energy pathway in the subequatorial deep layer (i.e., from 2000 m to bottom); as such, deep fluctuations were energized by energy transport from the upper ocean and radiated by horizontal pressure work process, and these processes were widespread and frequent in the seamount region.

Fig. 12.
Fig. 12.

Horizontal maps of the energetic terms (a) ΔQK1, (b) ΔzQp1, (c) ΔhQp1, (d) b1, (e) ΓK01, (f) ΓK21, and (g) Fk1 vertically integrated from 2000 m to the bottom. The black star indicates the location of mooring Q3. The grids without data are masked with gray shading. The black contours indicate the −2500, −3000, −3500, and −4000 m isobaths.

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0082.1

To quantify the contribution of each K1 budget term in the deep layer, depth-integrated variables in the entire seamount region were area averaged and then the ratios of these variables and the total K1 source were calculated, as shown in Fig. 13. At Q3, the vertical pressure work ΔzQp1 was the dominant energy source for K1, accounting for approximately 50% of the total K1 sources (Fig. 13a). The buoyancy conversion b1 played a secondary role in TRW generation (contributing to ∼25% of the total K1 sources), whereas the contribution of canonical transfer ΓK01 (∼19%) and advective transport of KE ΔQk1 (∼6%) to the total K1 sources were less. The horizontal pressure work ΔhQp1 was the primary mechanism that radiated K1 (contributing to ∼72% of the total K1 sinks), while the residual term Fk1 was the secondary mechanism that dissipated K1 and contributed to ∼28% of the sinks. Furthermore, the results for the entire seamount region confirmed that the vertical (horizontal) pressure work played a vital role in the generation (redistribution) of deep-layer K1 energy, accounting for 94% (98%) of the total K1 sources (sinks), consistent with the pattern in the southwest of Q3 (Figs. 12b,c and 13b). Although advective transport and buoyancy conversion were favorable for K1 generation in specific areas (e.g., southwest of Q3), their contributions were limited when averaged in the seamount region (Fig. 13).

Fig. 13.
Fig. 13.

Time-averaged (from 1 Jan 2014 to 10 Aug 2019, 2048 days) K1 budget terms vertically integrated from 2000 m to the bottom. Results (a) at mooring Q3 and (b) area averaged over the seamount region (2°–10°N, 89°–92°E).

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0082.1

Overall, these results suggested upper-layer perturbations were the energy source of deep current variability on window ϖ = 1, transporting energy into the deep ocean via vertical pressure work. The deep TRWs were triggered by the 10–20-day perturbations in subthermocline. The spectrum of observed velocities between 300 and 950 m showed that the signals with the 10–20-day periods were more energetic in the meridional direction than that in the zonal direction (not shown here). Such characteristics of the oscillations are similar to 10–20-day Yanai waves (also as mixed Rossby–gravity waves), which show a quasi-biweekly meridional variability generated by wind forcing or current instabilities in the equatorial Indian Ocean (Schott et al. 1994; Sengupta et al. 2004; Chatterjee et al. 2013; Arzeno et al. 2020). In the equatorial region south of Q3 (i.e., on the equator at 90°E), 10–20-day Yanai waves were observed by Masumoto et al. (2005), with signals mainly confined within the upper 100 m. In contrast, the observed 10–20-day meridional oscillations at Q3 were weak near the surface but energetic in the subthermocline, indicating that they were not generated locally but possibly originated from remote forcing. Therefore, we hypothesize that the subthermocline 10–20-day meridional oscillations are equatorial Yanai waves propagating downward and may still exhibit considerable strength near 5°N (e.g., Chatterjee et al. 2013), similar to the semiannual variability at the middepth (∼1200 m) of Q3 caused by the boundary-reflected downward-propagating Rossby waves (Huang et al. 2019). Note that we could not obtain the vertical trapping scale (htrap=1/λ) of TRWs from the bottom observation at a single depth. The vertical trapping scale 1/λ of TRWs can be estimated by the ratio of KE (RatioKE) between the two layers (e.g., z1 and z2) following RatioKE=[cosh(λz2)/cosh(λz1)]2 (Hogg 2000; Thompson and Luyten 1976). Based on the model output, z1 = 2866 m, z2 = 3220 m, λ = 0.0022, thus htrap=1/λ456m, the averaged Kl=(f/Nhtrap)(termΠ/termΙ)3.36×105m1 and L=2π/Kl=187km, which satisfied the short-wavelength assumption. Additional observations are required for detailed research on 10–20-day meridional oscillations in subthermocline and the vertical trapping scale of bottom TRWs in the future.

5. Summary

Based on the over 3 years of velocity records, we observed deep current variability with a typical period of 10–20 days in the eastern off-equatorial Indian Ocean, accounting for over 50% of the total bottom subtidal velocity variability. These deep oscillations are more energetic in the cross-isobathic direction (STD = 3.02 cm s−1) than in the along-isobathic direction (STD = 1.50 cm s−1), with maximum amplitude of 10.71 cm s−1 (5.63 cm s−1) in the cross-slope (along-slope) direction. Considering the smaller value of the Coriolis parameter and the stronger β effect at low latitude, we obtain the TRW dispersion relation (i.e., ω=[N|h|sinθ/tanh(λh)]{1(ω2/f02)/1+[βk/(ωKl2)]}) in the subtropical region, which is applicable in the situation that the motions are high frequency and planetary β is comparable to the topographic β (i.e., βTopo). The 10–20-day deep oscillations are interpreted as TRWs because they satisfy the dispersion relation. Our correlation analysis suggested that these deep oscillations were closely linked to the upper-layer 10–20-day perturbations in the cross-isobathic direction, which were energetic in the subthermocline at the depths of 300–950 m but weak near the surface. Further EOF decomposition and time-lag correlation analysis proved that the observed subthermocline cross-isobathic oscillations acted as the energy source of TRW variability, adjusting deep cross-isobathic currents through the barotropic mode (i.e., the first EOF). Therefore, the observed ∼11-day TRWs were generated by cross-isobathic motions under PV conservation adjustment.

The MO model output could reproduce the observed 10–20-day bottom current variability, and were therefore used to discuss deep-sea energetics. Applying MS-EVA to the MO output from 2014 to 2019, the vertical and horizontal pressure work were identified as the dominant source and sink of energy of the deep-ocean variability, respectively. In the entire off-equatorial seamount region (2°–10°N, 89°–92°E), the primary source of energy for deep-current variability was the vertical pressure work, which transported energy downward and accounted for approximately 94% of the total K1 sources. The deep-layer K1 was redistributed by the horizontal pressure work process, which contributed approximately 98% of the total K1 sinks.

Acknowledgments.

This work was supported by the National Natural Science Foundation of China (42076019, 42206033, 42176021), the Open Project Program of State Key Laboratory of Tropical Oceanography (Project LTOZZ2001), Basic Frontiers and Innovative Development 2023 “Integration” Project of South China Sea Institute of Oceanology (SCSIO2023QY02).

Data availability statement.

The AVISO data are available at https://www.aviso.altimetry.fr. The bathymetry and WOA18 data can be obtained at http://apdrc.soest.hawaii.edu/ and https://www.nodc.noaa.gov/OC5/woa18, respectively. Mercator Ocean reanalysis output can be obtained at https://resources.marine.copernicus.eu/product-detail/GLOBAL_MULTIYEAR_PHY_001_030.

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