The Generation and Propagation of Wind- and Tide-Induced Near-Inertial Waves in the Ocean

Abstract

Near-inertial waves (NIWs), a special form of internal waves with a frequency close to the local Coriolis frequency, are ubiquitous in the ocean. NIWs play a crucial role in ocean mixing, influencing energy transport, climate change, and biogeochemistry. This manuscript briefly reviews the generation and propagation of NIWS in the oceans. NIWs are primarily generated at the surface by wind forcing or through the water column by nonlinear wave-wave interaction. Especially at critical latitudes where the tidal frequency is equal to twice the local inertial frequency, NIWs can be generated by a specific subclass of triadic resonance, parametric subharmonic instability (PSI). There are also other mechanisms, including lee wave and spontaneous generation. NIWs can propagate horizontally for hundreds of kilometers from their generating region and radiate energy far away from their origin. NIWs also penetrate deep into the ocean, affecting nutrient and oxygen redistribution through altering mixing. NIW propagation is influenced by factors such as mesoscale eddies, background flow, and topography. This review also discussed some recent observational evidence of interactions between NIWs from different origins, suggesting a complicated nonlinear interaction and energy cascading. Despite the long research history, there are still many areas of NIWs that are not well defined.

1. Introduction

Near-inertial internal waves (NIWs) are a special form of internal waves whose frequencies are close to the local Coriolis frequency f ($f=2\Omega sin\phi$, where $\Omega$ is the rotation frequency of the earth and $\phi$ indicates the local latitude). NIWs are ubiquitous in the ocean and can be observed in the ocean at an extensive range of latitudes and depths [1,2,3,4]. In the Garrett–Munk (GM) internal wave spectrum, the continuous curve shows a prominent peak near the near-inertial frequency, i.e., close to the local Coriolis frequency f. NIWs are one of the highest-energy internal waves, accounting for almost half of the total energy in the internal band [1,5], and globally the energy input of NIWs is comparable to that of the internal tides (ITs) [2,6].

Compared to other internal waves, the appearance of NIWs is more intermittent, and the energy changes are more drastic. For example, after hurricanes and typhoons, the flow velocity of the near-inertial internal wave can be up to 1 m s⁻¹ when it is most active [7]. The downward propagation of energy is more pronounced, and the vertical modes are higher than other internal waves. The vertical scale of NIWs can be as small as a few meters. NIWs have smaller vertical fluctuation when they are of the same energy [8,9,10,11,12,13] and therefore are more difficult to be captured by observations. Low-mode NIWs have large vertical wavelengths and high propagation velocities, which allow them to propagate far away from their origins. Once generated, they can propagate hundreds of kilometers away from their source before breaking up [2,14,15] and radiating most of their energy to regions far away from their origin. These features allow NIWs with vertical scales as small as a few meters to have an important role in ocean mixing [16,17,18] and consequently influence a wide range of processes such as energy transport, climate change, and biogeochemistry in the ocean [19,20].

2. Governing Equation and Basic Characteristics

NIWs are solutions to linearized hydrostatic Boussinesq equations of motion on the f plane. The governing equations could be written as

$${\displaystyle \frac{\partial u}{\partial t}}=-{\displaystyle \frac{1}{{\rho }_0}}{\displaystyle \frac{\partial p}{\partial x}}+fv+{\displaystyle \frac{1}{{\rho }_0}}{\displaystyle \frac{\partial }{\partial z}}{\tau }_x$$

(1)

$${\displaystyle \frac{\partial v}{\partial t}}=-{\displaystyle \frac{1}{{\rho }_0}}{\displaystyle \frac{\partial p}{\partial y}}-fu+{\displaystyle \frac{1}{{\rho }_0}}{\displaystyle \frac{\partial }{\partial z}}{\tau }_y$$

(2)

$${\displaystyle \frac{\partial p}{\partial z}}=-g{\rho }^{\prime }$$

(3)

$$𝛻·\mathit{u}=0$$

(4)

$${\displaystyle \frac{\partial p^{\prime }}{\partial t}}={\displaystyle \frac{{\rho }_0}{g}}{N}^{2}w$$

(5)

where $p^{\prime }\left(x,y,z,t\right)$ is the perturbation density difference from a mean density $\overline{\rho }\left(z\right)$ and $N^2=-{\displaystyle \frac{g}{{\rho }_0}}{\displaystyle \frac{\partial \overline{\rho }}{\partial z}}$ is the squared buoyancy frequency, representing the background stratification. When at sea surface, $\left({\tau }_x,{\tau }_y\right)$ means the surface wind stress. After introducing the fluctuation solution $\widehat{u}=e^{i\left(kx+ly+mz-\omega t\right)}$, the dispersion relation of NIWs is obtained as:

$${\omega }^2=f^2+{\displaystyle \frac{N^2\left(k^2+l^2\right)}{m^2}}=f^2+{\displaystyle \frac{N^2{\mathit{k}}_H^2}{m^2}}$$

(6)

where ${\mathit{k}}_H^2=k^2+l^2$ is the horizontal wavenumber, and m represents the vertical wavenumber. The vertical group velocity of NIWs is:

$$C_{gz}={\displaystyle \frac{\partial \omega }{\partial m}}\approx -{\displaystyle \frac{N^2{\mathit{k}}_H^2}{m^{3}f}}$$

(7)

Both background vorticity and strain affect the wave frequency. After taking both into account, the dispersion relationship can be written as [21]:

$$\omega =\sqrt{{\displaystyle \frac{N^2{\mathit{k}}_{\mathit{H}}^2+f_{eff}^2{m}^2}{{\mathit{k}}^2}}}+\mathit{k}·\overrightarrow{\mathit{U}}$$

(8)

where $\mathit{k}$ is the wavenumber and $\overrightarrow{\mathit{U}}\left(U,V\right)$ is the background flow. $f_{eff}=f+{\displaystyle \frac{\zeta }{2}}$ is the effective Coriolis frequency and $\zeta ={\displaystyle \frac{\partial v}{\partial x}}-{\displaystyle \frac{\partial u}{\partial y}}$ is the vertical component of relative vorticity. If strain dominates, the frequency $\omega$ is modulated by the Doppler shift effect by the mean flow $\overrightarrow{\mathit{U}}$. If vorticity dominates, NIWs with $\omega$ between $f$ and $f_{eff}$ is trapped in the region of $\zeta <0$, such as in a warm core mesoscale eddy.

This study of NIWs began in the 1930s with Ekman, who considered such motions to be near-inertial oscillations [22]. After the 1960s, more observations of near-inertial oscillations were made possible by the Woods Hole Oceanographic Institution’s Moored Current Instrument. Webster concluded that most of the observed NIWs occurred in the upper ocean [23]. Leaman and Sanford analyzed vertical profiles of velocities separated by about half an inertial period in time and further inferred that NIWs have a vertical scale of 100–300 m and rotate clockwise with depth, i.e., the energy propagates downward [9]. The development of observational tools, such as the acoustic Doppler current profiler (ADCP), the use of vertical profile microstructure instruments, and mooring profilers [24], has significantly improved the temporal resolution of observed vertical profiles. For example, the moored profiler measured a NIW propagating downward over 1000 m in the South China Sea [25] and over 3000 m near the Mendocino bluff [26]. Its vertical shear was clockwise polarized, and the phase line sloped upward with time, indicating downward energy propagation. In the ocean interior, NIWs may play a more important role in mixing compared to ITs due to smaller vertical scales and greater vertical shear. Near-inertial motion in the mixed layer leads to shear in the thermocline, separating the mixed layer from the ocean interior, which is the primary mechanism for mixing and deepening of the mixed layer after a storm [27,28,29,30]. Local dissipative enhancements associated with near-inertial internal waves have been observed by Hebert and Moum, Alford and Gregg, and Fer [31,32,33]. Diffusion coefficients for the upper 500 m parameterization computed with ARGO buoy data provide further evidence of the importance of near-inertial internal waves for upper ocean mixing [34,35].

Following the internal wave polarization relationship, the vertical distribution of the horizontal velocity vector (u + iv) can be decomposed into two components, positive and negative wave numbers, which denote the counter-clockwise (CCW) and clockwise (CW) components of rotation with depth, respectively (Figure 1). For linear internal waves propagating freely under stable stratification, the component of rotated CW with depth increasing indicates downward energy propagation and upward phase propagation [16].

3. Generation

With respect to the generation of NIWs, Fu concluded two ways from observations [8]: “local”—waves with frequencies close to the local Coriolis frequency f generated in the vicinity of the observing site; or “remote”—internal waves generated distantly with a frequency ω higher than the local inertial frequency propagate to the vicinity of the observation point, whose frequency is close to the inertial frequency f of the observation point. The main mechanisms for the generation of NIWs include localized sea surface wind stress [36,37,38], nonlinear wave–wave interactions [39,40], lee waves generated when geophysical currents flow through the topography [41,42] and spontaneous generation. In this review, we will focus on the first two mechanisms, which are more important.

3.1. Wind

Wind pulses or fluctuations at near-inertial frequencies can resonantly force near-inertial motions [13]. Pollard first studied NIWs caused by wind stress and proved through numerical simulation and observation that the transient wind stress is the main driver of the near-inertial motion of the ocean [43] (Figure 2). Hurricanes, typhoons, and mid-latitude storms contain strong inertial rotation components that generate NIWs in the ocean through wind stress [7,36,44]. Near-inertial oscillations are excited within the mixed layer after the passage of storms whose spatial scale is usually on the order of hundreds of kilometers. Because of the $\beta$ effect, the frequency of near-inertial oscillations excited within the mixed layer at different latitudes varies [45]. Thus, within a few days after the storm passed, the near-inertial oscillations at different latitudes weakened each other, resulting in a shrinkage of their meridional scales to less than 100 km, which made it easier to propagate into the ocean interior [13]. In addition, diurnal sea breezes match midlatitudes near 30° resonantly [46]. Synoptic timescales of low-latitude regions near the equator are on the order of a few days, the same as that of the local inertial period, thus seawater is resonant with local wind [47]. The global winds work on NIWs has been estimated to be between 0.16 and 1.4 terawatts (TW) based on numerical models [2,48,49,50,51,52,53], which is comparable to the power converted from barotropic tides to ITs [54,55,56].

Transient wind stresses during the passage of tropical cyclones, storms, and cold fronts are the primary driver of NIWs in the ocean, especially tropical cyclones [13,57]. This is due to their strong wind stress, smaller lateral scales, and more rapid vertical propagation compared to mid-latitude storms [13]. On a global scale, NIWs generated by tropical cyclones may contribute up to 10% of wind-induced NIWs [48].

As an effective exciter of an NIW, typhoons and hurricanes can excite NIWs with considerable magnitude in the ocean. Sanford et al. found that the magnitude of NIWs induced by Hurricane Frances is up to 1.5 m s⁻¹ [30], which may be the strongest NIWs reported in previous studies. This record was broken by Typhoon Mangkhut in 2018, which produced NIWs throughout the water column on the continental slope of the South China Sea, with a maximum greater than 1.5 m s⁻¹ in the upper ocean [58]. Due to the asymmetry of typhoons, the ocean response always exhibits a rightward bias [59,60]. The near-inertial velocity is larger on the right side of the path than the left. The wind-stress vector turns CW at the right side of the track in the northern hemisphere, same as the rotation of NIWs generated. There is a resonance effect between the two, which increases the amplitude of the near-inertial velocity. On the left side, the rotation of the wind-stress vector is opposite to that of NIWs, which inhibits the increase of near-inertial velocity amplitude. Typhoon-induced near-inertial energy (NIE) is mainly distributed from the bottom of the mixed layer to the upper thermocline and decays rapidly within a few inertial periods [37,61].

Typhoon-induced NIWs are often characterized by upward-propagating phases and downward-propagating energy [16,37,62], which means the CW components dominate in the typhoon-induced NIWs. The characteristics of these NIWs (e.g., wave amplitude, duration, phase propagation, and frequency shift) are largely modulated by the wind fields and background flows [13,63]. Previous observations showed that the vertical scale of typhoon-induced NIWs ranges from about 100 to 600 m [16,64,65]. Typhoon-induced NIWs can persist for several days or even more than 10 days after a typhoon [37,64,66,67]. The typhoon-induced NIWs are determined by typhoon characteristics, such as track, maximum wind speed, translational speed, maximum wind radius, and distance from the observation site et al. [64,68,69]. In the northern South China Sea, characterization of NIWs induced by Typhoon Meranti and Megi suggested that the weaker Typhoon Meranti produced stronger NIWs than the stronger Typhoon Megi, which may be related to the faster moving speed of Meranti [64]. The stratification can also affect the characteristics of NIWs [70]. Recent studies have shown that typhoon-induced NIWs exhibit significant differences between shallow- and deep-water regions. An important difference is the dominant pattern of NIWs. NIWs in shallow-water regions are usually dominated by mode-1 [18,71,72,73,74], whereas higher modes account for more of the total NIE of NIWs in deep-water regions than mode-1 [53,75]. Overall, the first 4 vertical modes account for over 70% of the NIE [76]. After a typhoon passes, the resulting NIWs can persist for several days before decaying. In shallow water, typhoon-induced NIWs can persist for more than 10 days [71,77]. In deep water, NIWs typically dissipate rapidly with an e-folding time of less than 1 week [37]. Typhoon-generated NIWs are not only able to accumulate in the surface mixed layer but also propagate downward, thus affecting the deep mixing. NIE penetration is critical for deep-sea turbulent mixing, which affects the redistribution of nutrients, oxygen, and suspended matter [78]. Not all NIE could propagate to the deep. Ma et al. estimated that about 29% of the NIE flux driven by Typhoon Mindulle in the South China Sea could penetrate to 1400 m [25].

3.2. Parametric Subharmonic Instability and Other Nolinear Wave-Wave Interactions

When energy from winds and tides is fed into the ocean, they act on spatial scales of tens to hundreds of kilometers, while turbulent mixing occurs on ~centimeter scales. It is widely believed that there is a downward energy cascade here, in which energy is transferred from large-scale waves to smaller internal waves and ultimately to small-scale waves associated with dissipation. Nonlinear wave–wave interactions redistribute energy over the wave spectrum due to the resonant wave component and are thought to play a key role in this internal wave energy cascade [79,80,81,82,83,84], which can transfer energy between waves of different wavenumbers and frequencies. These triadic resonant interactions occur between triple waves that satisfy the condition that the combination of the sum or difference of their frequencies is zero, resulting in the growth or decay of the energy of the different waves. McComas and Bretherton classified nonlinear wave–wave interactions into three main categories, namely induced diffusion, elastic scattering, and parametric subharmonic instability (PSI) [80]. Particularly, PSI can transfer energy from a high-frequency, low-mode, large-scale parent wave (e.g., diurnal or semidiurnal ITs) to a pair of low-frequency, high-mode, small-scale daughter waves (e.g., NIWs). The vertical wavenumbers of daughter waves have opposite signs, and the frequency is equal to half the frequency of the parent wave [82,85,86]. PSI does not seem to be a very efficient mechanism in terms of the time scale of energy transfer (O(100) days) in early estimations [87], order-of-magnitude longer than the observations. This discrepancy may be due to a random phase assumption in the calculation [88].

The occurrence of PSI involves the energy exchange between a high-frequency, low-mode wave (with a larger vertical wavelength) and two low-frequency, high-mode waves with opposite signs of the vertical wavenumbers (one propagating upward and one propagating downward), where the frequency of the high-mode wave is equal to half the frequency of the low-mode wave. This interaction is possible at any latitude as long as the frequencies of these triple waves remain in the inner wave band ($f<\omega <N$), but PSI is particularly efficient at latitudes where the frequencies of the two daughter waves are equal to the local inertial frequency. These critical latitudes are approximately 28.80°, 29.91°, 14.52°, and 13.44° for the M₂, S₂, K₁, and O₁ ITs, respectively (schematic diagram of the PSI of M₂ ITs shown in Figure 3) [89,90,91,92]. MacKinnon and Winters, through numerical simulations, found a sudden decrease in semidiurnal IT energy and a sharp increase in NIE when traveling northwards and crossing the critical latitude [39]. In addition, tidal energy losses estimated from satellite altimetry also appear to peak at the critical latitude [93].

PSI has been shown to play an important role in the cascading of internal tidal energies and generating NIWs [3,94,95,96,97,98,99,100], at the Hawaiian Ridge [3,61,90,97,101], the South China Sea [89,102,103], and other regions [104], even in the ocean interior [40,105].

Nonlinear wave interaction can also occur outside the critical latitudes. Observations from the Hawaiian Ocean Mixing Experiment (HOME) suggest that PSI is still active near the origin of the inner tides [90,101]. In addition, numerical simulation studies support the idea that PSI can generate subharmonics with frequencies different from half the frequency of the parent wave when the weak nonlinear instability is transformed into a strong nonlinear instability [106]. Korobov and Lamb found that PSI occurred in the region of strong nonlinear instabilities, involving a triad of waves with frequencies ω, 0.57ω, and 0.43ω. Recently, both observations and numerical simulations [40,105,107] on the continental slope of the northern South China Sea have confirmed that the PSI of the semidiurnal ITs generates NIWs and subharmonics with a frequency of D2-f (D2 is the frequency of the semidiurnal ITs), where two daughter waves do not have frequencies equal to half of the parent wave frequency. In addition, other wave–wave interactions also contribute to NIW generation, such as triad resonant interaction (TRI). Previous studies have shown that the GM wave spectrum can only be generated and maintained when both wind and tides provide energy. Chen et al. [108] through numerical simulation experiment demonstrated that in the range of latitude 17°–29°, where there is no wind but only tidal forcing, PSI and TRI work in conjunction with internal wave break-up and tidal-topographic interactions to form and maintain an internal wave field similar to that described by the GM internal wave spectrum. More specifically, NIWs can be initiated by internal wave breaking and further enhanced by PSI. There is also evidence that the wind-induced and tide-induced NIWs can enhance each other through nonlinear interaction in Luzon Strait [109]. In general, resonant and non-resonant nonlinear wave–wave interactions work continuously and transfer energy to motions with local inertial frequency. Therefore, it is difficult to rule out the effect of possible mechanisms.

4. Propagation

The NIWs propagate both horizontally and vertically. When NIWs propagate vertically, the buoyancy frequency N(z) affects the pathway and leads to a refraction. However, the redness of the spectrum suggests that part of the energy immediately deposited over a thousand meters deep, possibly explaining the observed season cycle of energy there [110,111]. These part waves may be reflected or scattered at the bottom, and due to the lack of direction observation, the final fate of this part of NIWs is unknown. On the other hand, long-distance propagation of NIWs has been studied for a long time (Figure 4). Munk and Phillips described some phenomena induced by the propagation of NIWs in the β-plane [112]. Specifically, waves with frequencies larger than the local inertial frequency ($\omega >f$) propagating toward the poles will arrive at a turning latitude where the meridional group velocity ($C_{gy}$) of the waves is zero. The Wentzel–Kramers–Brillouin (WKB) theory can be used to show that their propagating rays turn smoothly toward the equator, but is invalid very close to the turning latitude [113,114]. β-refraction theory predicts that NIWs propagate equatorward due to latitudinal variations in inertial frequency [1], which is supported by observations in the open ocean and on the continental shelf [2,74]. Observations by Alford suggest that low-mode NIWs propagate long distances from the source toward the equator (rather than toward the poles) for hundreds of kilometers [2], so that the NIWs appear in the spectrum slightly above the local inertial frequency, while NIWs with high wavenumber remain in the source region due to their slower propagation speed. Numerical simulations and observations have also shown that NIWs can propagate poleward. Fu, based on turning point theory and a numerical model, suggested that local inertial peaks observed over smooth topography can be explained by poleward propagating waves generated at low latitudes [8]. NIWs propagating poleward may preferentially propagate into weakly layered transition regions in the deep ocean, potentially enhancing local dissipation [114].

Only 15–25% of the energy input of wind work is radiated from its generating region in the form of low-mode NIWs [2,115,116]. Two important implications of the long-range meridional propagation of NIWs are that (1) peaks throughout the near-inertial band of the internal wave spectrum may not be locally generated but rather result from waves with frequencies ω much larger than the inertial frequency of the originating region propagating poleward and eventually stopping in regions with frequencies ω equal to the local inertial frequency [8]; and (2) NIWs generated in regions with inertial frequencies f can propagate toward the equator until they reach a region where their frequency is twice the local inertial frequency, and these NIWs become unstable due to PSI [117,118,119].

The propagation of NIWs is influenced by many factors, and NIWs may interact with the background flow and the topography. NIWs may interact strongly with mesoscale eddies along their propagation paths, thus complicating the propagation and producing localized effects along the propagation path. Once trapped in the negative relative vorticity of a mesoscale eddy or in the tilted isopycnals of strongly baroclinic current, NIWs reflect on both sides and propagate rapidly downward into the ocean interior [110,120,121,122,123,124], which is known as the inertial chimney effect [121]. This effect has been explored by Zhai et al. [125,126] through analyzing numerical simulations. They showed that anticyclonic eddies act to drain NIE from the surface to the deep ocean. More recently, Asselin and Young also demonstrated the inertial chimney effect of turbulent baroclinic quasi-geostrophic eddies in an idealized storm experiment, which they referred to as an inertial drainpipe [127]. Vic et al. investigated the relationship between observed NIE and altimetrically derived relative vorticity at a horizontal resolution of O(100) km over the Mid-Atlantic Ridge and showed that the NIE preferentially funnels down into anticyclonic flows [128]. Chen et al. found that the NWs generated by Typhoon Sanvu were confined within 100 m of the upper ocean, propagated rapidly downward after encountering the mesoscale anticyclonic eddy, and eventually stagnated in the critical layer [129]. As NIWs propagate to the bottom of the negative vorticity region, the amplitude of NIWs increases and the vertical wavelength decreases. Vertical shear and nonlinear effects are then able to extract and dissipate wave energy, ultimately promoting mixing in the deep ocean [130].

The background flow plays an important role in the NIE redistribution. Huang et al. observed NIWs induced by Typhoon Haima show significant energy redistribution in the South China Sea [131]. High-mode (n > 3) NIWs are more readily carried away by the background flow and simultaneously propagate downward into the subsurface layer, resulting in a significant increase in vertical shear. The presence of the western boundary current also affects the propagation of NIWs. Observations and numerical simulations demonstrate that the negative vorticity region to the right of the Kuroshio acts as a waveguide for the propagation of NIWs and that the strong flow of the Kuroshio propagates NIWs poleward [132]. Li et al. indicated that the Kuroshio prevents the NIE generated by Typhoon Fitow and Danas on either side from propagating across it [133]. They modeled the entire East China Sea and the western Pacific Ocean and found that along the path of Typhoon Danas, there is a gap in the NIE near the Kuroshio. The results of ray tracing also showed that NIWs turned around near the Kuroshio (Figure 5). NIWs can also be amplified and trapped by the strong baroclinicity of sea surface fronts [134] and coastal upwelling [135]. Whitt and Thomas found that the strong baroclinicity of western boundary currents, such as the Gulf Stream, trapped and amplified NIWs with frequencies below the local effective Coriolis frequency [124]. Kawaguchi et al. found that the vertical shear of geostrophic flows has a significant effect on the vertical propagation of the NIE in their observations near the Tsushima Oceanic Front [136]. Li et al. found the baroclinicity of the Kuroshio extended the range of surface NIWs propagating downward [133].

The propagation of NIWs is also affected by topography. Chinn et al. observed NIWs that were influenced by canyon walls, changing the usual circular rotation [137]. In addition, the propagation of NIWs on the continental shelf is further complicated by the presence of lateral and bottom boundaries, and MacKinnon and Gregg indicated that the NIE is mainly concentrated in low-mode NIWs in the New England Shelf region [138]. Subsequent observations in the same region have shown that bottom drag also plays an important role in the evolution of NIWs, contributing to the transfer of NIE from low-mode NIWs to the higher mode and then dissipating [139]. Merrifield and Pinkel also showed that NIW propagation is affected by subsurface flow under a weak stratification [140]. Thus, the propagation of NIWs may be more complex on the continental shelf than in the ocean.

The ray-tracing method is a strong support for determining the propagation paths of NIWs. Kunze used mathematical equations to establish the basic ray tracing method but did not take into account the situation that the background flow has insignificant vorticity and significant baroclinicity [141]. On this basis, Whitt and Thomas further developed a two-dimensional ray-tracing method that specifically takes the baroclinicity of background flow into account. Given that the observations were located in a region of strong baroclinicity near the Kuroshio, Li also adopted this ray-tracing method [133]. Figure 6 shows the results of the comparison between the case with and without considering the background baroclinicity. However, there are some limitations to this method. Its applicability in real flow fields is somewhat restricted, making it more suitable for application in an idealized experimental setting.

5. Discussion

NIWs have been extensively studied for decades, but there are still insufficiently well-defined parts. Wind is undoubtedly the dominant NIW generation mechanism in general. Almost all wind stresses at the inertial frequency could force inertial motions. Undoubtedly, resonant winds excite near-inertial motions within the mixed layer, and these motions then propagate into the ocean interior in the form of NIWs. The association of winds with NIWs can be seen in the local downward propagation of high-mode waves, the seasonal cycles of NIE in the upper and deep ocean, and the loose geographic correlation between storm tracks, inertial mixed-layer motions, and low-mode equatorward-propagating energy [13]. However, some unclear parts remain. For downward propagating NIE, previous studies in the open ocean at low latitudes have shown that a large fraction of the NIE dissipates in the upper ocean before the remaining energy can propagate to the deep ocean. D’Asaro found that the energy in the mixed layer decreased by 36% ± 10% after 3 weeks of a storm in the Northeast Pacific, indicating that a portion of this NIE propagated away from the site [142]. Numerical simulations by Furuichi et al. showed that 15% of the NIE input to the mixed layer could propagate to depths of ~150 m [143]. Observations at the Ocean Station Papa showed that a large amount of energy was input to the mixed layer, and about 12% to 33% of this reached the deep ocean [16]. Raja et al. [53] showed that only 19% of the global wind-generated NIE could be transported to more than 500 m deep, based on a 30-day simulation of the global (1/25)° hybrid coordinate ocean model (HYCOM). It is now generally believed that 30% to 50% of the NIE can penetrate to the ocean interior [16,143], but more high-resolution in situ observations are necessary to reduce the large uncertainties in these specific proportions. In addition, for the hysteresis of the NIW response to strong winds below the mixed layer [116,144], the longer response time and decay time of NIWs below the mixed layer compared to in the mixed layer, and the mechanisms and parameterized schemes of the significantly faster-than-theoretical vertical NIW propagation are all issues that need to be addressed in the future.

In addition, PSI was demonstrated by numerous observations [3,61,89,90,97,101,102,103,104] and numerical simulations [39,95,96]. Some parts of the actual contribution and the latitude of occurrence remain unclear. Generally, PSI is most effective at a certain latitude, which is called the critical latitude. For the semidiurnal IT M₂, this critical latitude is approximately 28.88° [145]. PSI involves the transfer of energy from a parent wave to two daughter waves with frequencies almost half that of the parent wave [80]. However, due to the differences in latitude and topography, PSI manifests itself differently. The strength of PSI is affected by a variety of factors, including background geostrophic flow and nonuniform stratification. Richet et al. showed that the Doppler effect of the mean flow can change the frequency of the main ITs and, therefore, further change the position of the PSI critical latitude [146]. However, Yang et al. and Dong et al. found that in the simulation the relative vorticity induced by spatially varying background geostrophic flow can change the PSI efficiency by changing the local effective Coriolis frequency, which is more convincing [86,147]. This is further supported in the observations near the Kuroshio [148]. In addition, the efficiency of PSI shows strong temporal variability, and the change of semidiurnal tidal energy flux may not be fully responsible for it. The relative vorticity field caused by the background flow may be a factor, but it still needs more investigations. It is considered an effective way to transfer energy from the internal tide band to the inertial band to generate NIWs with a smaller vertical wavelength. Conventionally, PSI is believed to generate identical subharmonic daughter waves and happens near the critical latitudes. However, theory and idealized numerical simulation have proven that daughter waves can have unequal frequencies. Shen et al. tracked the M₂-ray path and found that incident semidiurnal IT beams emanating from the shelf break and reflecting from the surface and bottom boundaries inevitably leave regions on the continental shelf of strong nonlinear instability, which leads to the generation of daughter waves of unequal frequency by the PSI [107]. This is likely to occur in regions of strong nonlinear instability, which can be caused by drastic topographic varieties. In this case, PSI may occur in a much wider range and has more signatures on the frequency domain. Thus, its importance in the ocean may be underestimated. To further prove this speculation, more in situ observations with higher resolution are essential. A numerical model with higher horizontal and vertical resolution, which is able to approximate the actual terrain closely, is helpful to understand the problem too.

Another issue worth discussing is the interaction of wind-induced with tide-induced NIWs. Previous numerical and theoretical studies tend to isolate the effect of wind and tide to simplify the physical framework, which has been proven to be very helpful to understand the mechanism. The derivative of PSI usually assumes the amplitudes are sufficiently small and the energy transfer is in an equilibrium state. In the real ocean, this may not be the case. There is growing evidence indicating that there is an insignificant interaction of the two on NIWs. Omidvar et al. found that the interaction of winds and tides can significantly affect the generation of internal waves, especially in the presence of K₁ tides [149]. This interaction may lead to changes in the energy transfer rate and the frequency of internal wave observations. Chen et al. showed that the combined effect of wind and tide can mutually enhance NIWs [109]. Specifically, wind-induced and tide-induced NIWs can mutually enhance each other near the Luzon Strait, producing more NIE than wind or tidal forcing alone, with an enhancement ratio of about 25%. The tide-induced NIWs could enhance the wind power input slightly. The presence of wind-induced NIWs can enhance the sub-inertial velocity, thus increasing the energy transferred from the ITs into the subharmonic waves, i.e., NIWs. In addition, steeper terrain (e.g., ridges) contributed to stronger enhancements. A similar numerical study also suggested that more tidal energy is transferred to NIWs in the presence of wind-induced NIWs, while extreme winds (e.g., cyclones) inject less NIE in the presence of tide-induced NIWs [150]. Xu et al. found that Typhoon Danas effectively enhanced the subsurface NIE near the critical latitude of semidiurnal tide and proposed a different mechanism [151]. During the typhoon passed by, there was an increasing PSI energy transfer rate, which eventually may be related to the typhoon-induced baroclinic internal tide energy flux anomaly. Therefore, more internal tide energy is transferred into the near-inertial frequency band through, leading to the enhancement of subsurface NIE [151]. Although the interaction of wind- and tide-induced NIWs has started drawing more attention, a comprehensive understanding of the specific mechanisms behind the phenomena has not been reached yet.

Overall, understanding the generation and propagation of NIWs together with nonlinear interactions on the pathway is crucial to investigating the NIWs. It is widely accepted, even a cliché, that NIWs play an important role in ocean mixing and energy cascade. Limited by in situ observational data and numerical models, there are still many unknown issues about the generation and propagation of NIWs. Currently, there is a lack of full-depth observation of NIWs. There are still some pressing problems to be solved for NIW numerical simulations. The inadequate understanding of the mechanisms generating NIWs, together with their intermittency and potentially more complex mesoscale eddy refraction and interactions, make the parameterization of NIWs still a work in progress, which needs more observations to determine and test. Since NIW mixing is likely to occur mainly in the upper ocean, where the heat stored in will be exchanged with the atmosphere on seasonal and even decadal timescales, a deeper understanding of the processes of generation, propagation, and dissipation of NIWs is important for predicting and modeling energy exchanges between the ocean and the atmosphere. In light of these challenges, future research needs to focus on improving the ability to observe NIWs at full depth, developing more accurate numerical modeling methods, and deepening the understanding of the processes of breaking and mixing of NIWs. This will not only advance our understanding of the dynamics of the ocean interior but will also provide critical data and theoretical support for global climate change research.