Near-inertial Motions Research Articles

Observations of Diurnal Coastal-Trapped Waves with a Thermocline-Intensified Velocity Field

AbstractUsing 18 days of field observations, we investigate the diurnal (D1) frequency wave dynamics on the Tasmanian eastern continental shelf. At this latitude, the D1 frequency is subinertial and separable from the highly energetic near-inertial motion. We use a linear coastal-trapped wave (CTW) solution with the observed background current, stratification, and shelf bathymetry to determine the modal structure of the first three resonant CTWs. We associate the observed D1 velocity with a superimposed mode-zero and mode-one CTW, with mode one dominating mode zero. Both the observed and mode-one D1 velocity was intensified near the thermocline, with stronger velocities occurring when the thermocline stratification was stronger and/or the thermocline was deeper (up to the shelfbreak depth). The CTW modal structure and amplitude varied with the background stratification and alongshore current, with no spring–neap relationship evident for the observed 18 days. Within the surface and bottom Ekman layers on the shelf, the observed velocity phase changed in the cross-shelf and/or vertical directions, inconsistent with an alongshore propagating CTW. In the near-surface and near-bottom regions, the linear CTW solution also did not match the observed velocity, particularly within the bottom Ekman layer. Boundary layer processes were likely causing this observed inconsistency with linear CTW theory. As linear CTW solutions have an idealized representation of boundary dynamics, they should be cautiously applied on the shelf.

Features of internal tides observed near the shelf break in the northern South China Sea

Features of internal tides in the northern South China Sea are investigated using measurements of two moorings at 506 m (MR1) and 260 m (MR2) working between April and November of 2014. The diurnal internal tides at MR1 are significantly enhanced in June–July and display a regular fortnight modulation, whereas at shallower MR2, the June–July intensification is absent and the fortnight cycle becomes irregular. Fortnight cycle peaks of diurnal internal tides have a regular time-lag of ~ 2.8 days after those of diurnal barotropic tides (at MR1). We derive a mathematical relationship indicating that this time-lag of fortnight cycle peaks is around twice the time for the diurnal internal tides propagating from the generation place to the mooring site. Semidiurnal internal tides are dominated by the mode-1 (~ 70%), while diurnal internal tides exhibit multi-modal structures, with the contribution of ~ 20–30% for each of the first three modes. The diurnal mode-1 contribution varies fortnightly, and eddy passages are highly correlated with the increasing contribution of semidiurnal high modes (at MR1). Furthermore, we find that the nonlinear interaction between internal tides and near-inertial motions is weak in summer, even during periods of strong near-inertial motions (at MR2), because in summer, the shear of near-inertial currents is maximum at a depth shallower than the depth of maximum internal tide shear.

Decay Rates of Internal Tides Estimated by an Improved Wave–Wave Interaction Analysis

AbstractRecent numerical and observational studies have reported that resonant wave–wave interaction may be a crucial process for the energy loss of internal tides and the associated vertical water mixing in the midlatitude deep ocean. Special attention has been directed to the remarkable latitudinal dependence of the resonant interaction intensity; semidiurnal internal tides promptly lose their energy to near-inertial motions through parametric subharmonic instability equatorward of the critical latitudes 29°N/S, where half the tidal frequency coincides with the local inertial frequency. This feature contradicts the classical theoretical prediction that resonant wave–wave interaction does not play a major role in the tidal energy loss in the open ocean. By reformulating the kinetic equation for long internal waves and developing its calculation method, we estimate the energy decay rates of the low-vertical-mode semidiurnal internal tides interacting with the “ubiquitous” oceanic internal wave field. The result shows rapid energy decay of the internal tides, typically within O(10) days for the lowest-mode component, near their critical latitudes. This decay time is severalfold shorter than those in the classical studies and, additionally, varies by a factor of 2 depending on the local depth and density structure. We suggest from this study that the numerical integration of the kinetic equation is a more effective approach than recognized to determine the decay parameter of wave energy, which is indispensable for the global ocean models.

Dependence of Energy Flux from the Wind to Surface Inertial Currents on the Scale of Atmospheric Motions

AbstractAtmospheric features such as translating cold fronts and small lows with horizontal scales of about 100 km are traditionally thought to be most important in exciting near-inertial motions in the ocean. However, recent studies suggest that a significant fraction of energy flux from the wind to surface inertial currents may be supplied by atmospheric systems of larger scales. Here, the dependence of this energy flux on the scale of atmospheric motions is investigated using a high-resolution atmosphere reanalysis product and a slab model. It is found that mesoscale atmospheric systems with scales less than 1000 km are responsible for almost all the energy flux from the wind to near-inertial motions in the midlatitude North Atlantic and North Pacific. Transient atmospheric features with scales of ~100 km contribute significantly to this wind energy flux, but they are not as dominant as traditionally thought. Owing to the nonlinear nature of the stress law, energy flux from mesoscale atmospheric systems depends critically on the existence of the background, larger-scale wind field. Finally, accounting for relative motions in the stress calculation reduces the net wind energy flux to near-inertial motions by about one-fifth. Mesoscale atmospheric systems are found to be responsible for the majority of this relative wind damping effect.

A study on some basic features of inertial oscillations and near-inertial internal waves

Abstract. Some basic features of inertial oscillations and near-inertial internal waves are investigated by simulating a two-dimensional (x − z) rectangular basin (300 km × 60 m) driven by a wind pulse. For the homogeneous case, near-inertial motions are pure inertial oscillations. The inertial oscillation shows typical opposite currents between the surface and lower layers, which is formed by the feedback between barotropic waves and inertial currents. For the stratified case, near-inertial internal waves are generated at land boundaries and propagate offshore with higher frequencies, which induce tilting of velocity contours in the thermocline. The inertial oscillation is uniform across the whole basin, except near the coastal boundaries ( ∼ 20 km), where it quickly declines to zero. This boundary effect is related to great enhancement of non-linear terms, especially the vertical non-linear term (w ∂ u∕ ∂ z). With the inclusion of near-inertial internal waves, the total near-inertial energy has a slight change, with the occurrence of a small peak at ∼ 50 km, which is similar to previous research. We conclude that, for this distribution of near-inertial energy, the boundary effect for inertial oscillations is primary, and the near-inertial internal wave plays a secondary role. Homogeneous cases with various water depths (50, 40, 30, and 20 m) are also simulated. It is found that near-inertial energy monotonously declines with decreasing water depth, because more energy of the initial wind-driven currents is transferred to seiches by barotropic waves. For the case of 20 m, the seiche energy even slightly exceeds the near-inertial energy. We suppose this is an important reason why near-inertial motions are weak and hardly observed in coastal regions.

Space–Time Scales of Shear in the North Pacific

AbstractThe spatial, temporal, and directional characteristics of shear are examined in the upper 1400 m of the North Pacific during late spring with an array of five profiling moorings deployed from 25° to 37°N (1330 km) and simultaneous shipboard transects past them. The array extended from a regime of moderate wind generation at the north to south of the critical latitude 28.8°N, where parametric subharmonic instability (PSI) can transfer energy from semidiurnal tides to near-inertial motions. Analyses are done in an isopycnal-following frame to minimize contamination by Doppler shifting. Approximately 60% of RMS shear at vertical scales >20m (and 80% for vertical scales >80 m) is contained in near-inertial motions. An inertial back-rotation technique is used to index shipboard observations to a common time and to compute integral time scales of the shear layers. Persistence times are O(7) days at most moorings but O(25) days at the critical latitude. Simultaneous shipboard transects show that these shear layers can have lateral scales ≥100 km. Layers tend to slope downward toward the equator north of the critical latitude and are more flat to its south. Phase between shear and strain is used to infer lateral propagation direction. Upgoing waves are everywhere laterally isotropic. Downgoing waves propagate predominantly equatorward north and south of the critical latitude but are isotropic near it. Broadly, results are consistent with wind generation north of the critical latitude and PSI near it—and suggest a more persistent and laterally coherent near-inertial wave field than previously thought.

Near-inertial motions in the Brazil Current at 24°S-36°S: Observations by satellite tracked drifters

Increased spatial and temporal resolution of recent observations and modeling have pointed out the importance of small scale structures (in the range of 1–50km) for the mixing processes in the ocean. Based on high-frequency drifter measurements, we show here that the near-inertial currents (NICs) can contribute significantly to the surface kinetic energy in the Brazil Current (BC) region and, therefore, should be properly taken into account in the studies of transport and mixing processes. To characterize these submesoscale features, we examine the current response to the wind forcing in the Brazilian ocean margin between 24°S and 36°S using 3-hourly sampled trajectories of satellite-tracked drifters. Our results indicate a preference for anti-cyclonic circular motions, with a rotating period close to the local inertial period, consistent with near-inertial motions in the Southern Hemisphere (SH). Wind stress time series, from three months of wind measurements, along with synoptic weather charts, are used to relate the observed NICs to the atmospheric forcing. During SH spring, NICs occur in 4.7−15 day bursts and account for 15–45% of the total surface current variance. This intermittency is related to atmospheric cold frontal passages, low pressure systems, and sea breeze/land breeze circulations. The predominance of NICs south of 28°S appears to be related to the increased Effective Inertial Frequency (EIF), which is the inertial frequency changed by the sub-inertial background flow.

Surface Wave Effects on the Wind-Power Input to Mixed Layer Near-Inertial Motions

AbstractOcean surface waves play an essential role in a number of processes that modulate the momentum fluxes through the air–sea interface. In this study, the effects of evolving surface waves on the wind-power input (WPI) to near-inertial motions (NIMs) are examined by using momentum fluxes from a spectral wave model and a simple slab ocean mixed layer model. Single-point numerical experiments show that, without waves, the WPI and the near-inertial kinetic energy (NI-KE) are overestimated by about 20% and 40%, respectively. Globally, the overestimate in WPI is about 10% during 2005–08. The largest surface wave effects occur in the winter storm-track regions in the midlatitude northwestern Atlantic, Pacific, and in the Southern Ocean, corresponding to large inverse wave age and rapidly varying strong winds. A relatively low frequency of occurrence of wind sea is found in the midlatitudes, which implies that the influence of evolving surface waves on WPI is intermittent, occurring less than 10% of the total time but making up the dominant contributions to reductions in WPI. Given the vital role of NIMs in diapycnal mixing at the base of the mixed layer and the deep ocean, the present study suggests that it is necessary to include the effects of surface waves on the momentum flux, for example, in studies of coupled ocean–atmosphere dynamics or climate models.

The variation of turbulent diapycnal mixing at 18°N in the South China Sea stirred by wind stress

The spatial and temporal variations of turbulent diapycnal mixing along 18°N in the South China Sea (SCS) are estimated by a fine-scale parameterization method based on strain, which is obtained from CTD measurements in yearly September from 2004 to 2010. The section mean diffusivity can reach ~10–4 m2/s, which is an order of magnitude larger than the value in the open ocean. Both internal tides and wind-generated near-inertial internal waves play an important role in furnishing the diapycnal mixing here. The former dominates the diapycnal mixing in the deep ocean and makes nonnegligible contribution in the upper ocean, leading to enhanced diapycnal mixing throughout the water column over rough topography. In contrast, the influence of the wind-induced near-inertial internal wave is mainly confined to the upper ocean. Over both flat and rough bathymetries, the diapycnal diffusivity has a growth trend from 2005 to 2010 in the upper 700 m, which results from the increase of wind work on the near-inertial motions.

Efficient boundary mixing due to near-inertial waves in a non-tidal basin: Observations from the Baltic Sea

Diapycnal mixing in large nontidal basins is often assumed to be related to the effect of near-inertial waves. While the role of near-inertial shear for the generation of shear instabilities in the stratified interior is relatively well understood, much less is known about the impact of near-inertial motions on boundary mixing processes in nontidal systems, mainly owing to the lack of appropriate observations. Here, an extensive data set is discussed, describing the variability of boundary mixing induced by near-inertial motions near the sloping topography of one of the main basins of the Baltic Sea. These data reveal the existence of a vigorously turbulent bottom boundary layer of a few meters thickness covering the entire slope region above and below the permanent halocline that constitutes the main obstacle for vertical transport in the Baltic Sea. Near-bottom turbulence was driven by the near-inertial shear in the frictional boundary layer rather than by breaking of near-inertial waves near critical slopes. Large regions of the bottom boundary layer remained strongly stratified, and therefore, different from the traditional view of inefficient boundary mixing, mixing efficiencies reached values typical for the ocean's interior.

Near-inertial motions in the DeSoto Canyon during Hurricane Georges

Hurricane Georges passed directly over an array of 13 moorings deployed in the DeSoto Canyon in the northern Gulf of Mexico on 27–28 September 1998. Current velocity data from the mooring array were analyzed together with a primitive-equation model simulation with realistic hurricane forcing, to characterize the generation and propagation of the hurricane-generated near-inertial waves. The model successfully reproduces the observed mean (sub-inertial) and near-inertial motions. The upper ocean response is strongly impacted by the canyon ‘wall’: a strong jet is formed along the slope, and the near-inertial motions on the shelf are rapidly suppressed. The model results moreover suggest that strong near-inertial waves in the mixed layer are mostly trapped in an energy flux recirculating gyre around the canyon. This gyre retains the near-inertial energy in the canyon region and enhances the transfer of near-inertial energy below the mixed layer. Additional simulations with idealized topographies show that the presence of a steep slope rather than the canyon is fundamental for the generation of this recirculating gyre. The near-inertial wave energy budget shows that during the study period the wind generated an input of 6.79×10–2Wm–2 of which about 1/3, or 2.43×10–2Wm–2, was transferred below the mixed layer. The horizontal energy flux into and out of the canyon region, in contrast, was relatively weak.

The Total Energy Flux Leaving the Ocean’s Mixed Layer

AbstractThe total energy flux leaving the ocean’s spatially and seasonally varying mixed layer is estimated using a global ⅝1/10° ocean general circulation model. From the total wind-power input of 3.33 TW into near-inertial waves (0.35 TW), subinertial fluctuations (0.87 TW), and the time-mean circulation (2.11 TW), 0.92 TW leave the mixed layer, with 0.04 TW (11.4%) due to near-inertial motions, 0.07 TW (8.04%) due to subinertial fluctuations, and 0.81 TW (38.4%) due to time-mean motions. Of the 0.81 TW from the time-mean motions, 0.5 TW result from the projection of the horizontal flux onto the sloped bottom of the mixed layer. This projection is negligible for the transient fluxes. The spatial structure of the vertical flux is determined principally by the wind stress curl. The mean and subinertial fluxes leaving the mixed layer are approximately 40%–50% smaller than the respective fluxes across the Ekman layer according to the method proposed by Stern. The fraction related to transient fluctuations tends to decrease with increasing depth of the mixed layer and with increasing strength of wind stress variability.

Forced Near-Inertial Motion and Dissipation of Low-Frequency Kinetic Energy in a Wind-Driven Channel Flow

AbstractUsing primitive equation simulations, a zonally periodic channel is considered. The channel flow is forced by a combination of steady and high-frequency winds. The high-frequency forcing excites near-inertial motion, and the focus is on how this influences the low-frequency, nearly geostrophic part of the flow. In particular, this study seeks to clarify how Reynolds stresses exerted by the near-inertial modes affect the low-frequency kinetic energy. In the system considered, the near-inertial Reynolds stresses (i) serve as a sink term in the low-frequency kinetic energy budget and (ii) transfer low-frequency kinetic energy downward from the mixed layer. Transfer spectra show the bulk of this sink to occur at relatively small horizontal wavenumber (i.e., in the mesoscale, not the submesoscale). The presence of near-inertial motion can also affect the kinetic-to-potential energy exchanges, especially within the low-frequency band.

Double-Diffusive Convection in a Stochastic Shear

AbstractAn attempt is made to quantify the impact of stochastic wave–induced shears on salt fingers associated with internal waves in the ocean. The wave environment is represented by the superposition of Fourier components conforming to the Garrett–Munk (GM) spectrum with random initial phase distribution. The resulting time series of vertical shear are incorporated into a finger-resolving numerical model, and the latter is used to evaluate the equilibrium diapycnal fluxes of heat and salt. The proposed procedure makes it possible to simulate salt fingers in shears that are representative of typical oceanic conditions. This study finds that the shear-induced modification of salt fingers is largely caused by near-inertial motions. These relatively slow waves act to align salt fingers in the direction of shear, thereby rendering the double-diffusive dynamics effectively two-dimensional. Internal waves reduce the equilibrium vertical fluxes of heat and salt by a factor of 2 relative to those in the unsheared three-dimensional environment, bringing them close to the values suggested by corresponding two-dimensional simulations.

Role of Near-Inertial Internal Waves in Subthermocline Diapycnal Mixing in the Northern Gulf of Mexico

AbstractMoored ADCP data collected in the northern Gulf of Mexico are analyzed to examine near-inertial internal waves and their contribution to subthermocline diapycnal mixing based on a finescale parameterization of deep ocean mixing. The focus of the study is on the impact of near-inertial internal waves generated by an extreme weather event—that is, Hurricane Katrina—and by month-to-month variation in weather patterns on the diapycnal mixing. The inferred subthermocline diapycnal mixing exhibits pronounced elevation in the wake of Katrina. Both the increased near-inertial (0.8–1.8f, where f is the Coriolis frequency) and superinertial (>1.8f) shear variances contribute to the elevated diapycnal mixing, but the former plays a more dominant role. The intense wind work on near-inertial motions by the hurricane is largely responsible for the energetic near-inertial shear variance. Energy transfer from near-inertial to superinertial internal waves, however, appears to play an important role in elevating the superinertial shear variance. The inferred subthermocline diapycnal mixing in the region also exhibits significant month-to-month variation with the estimated diffusivity in January 2006 about 3 times the values in November and December 2005. The subseasonal change in the diapycnal mixing mainly results from the subseasonal variation of the near-inertial wind work that causes intensification of the near-inertial shear in January 2006.

Latitudinal Dependence of Wind-Induced Near-Inertial Energy

AbstractMidlatitude storms, accounting for the majority of wind energy input to near-inertial motions in the ocean, are known to shift their track significantly from one year to another. The consequence of such storm track shifts on wind-induced near-inertial energy (NIE) is yet unknown. Here, the latitudinal dependence of wind-induced NIE is first analyzed in the framework of the slab model and then tested using two numerical ocean models. It is found that the NIE input by pure inertial wind stress forcing, which dominates the wind energy input to near-inertial motions, is independent of latitude. As a consequence, the NIE generated by white-noise wind stress forcing is also latitudinally independent. In contrast, the NIE generated by red-noise wind stress forcing shows strong dependence on latitude owing to longer inertial periods at lower latitudes capable of sampling greater inertial wind stress forcing. Given that the observed surface wind stress spectra are red, results from this study suggest that an equatorward shift of the storm track is likely to result in an increase in wind-induced NIE in the ocean, while the opposite is true for a poleward shift.

Interannual variability of wind power input to near-inertial motions in the North Atlantic

Near-inertial oscillations are ubiquitous in the ocean and are believed to play an important role in the global climate system. Studies on wind power input to near-inertial motions (WPI) have so far focused primarily on estimating the time-mean WPI, with little attention being paid to its temporal variability. In this study, a combination of atmospheric reanalysis products, a high-resolution ocean model and linear regression models are used to investigate for the first time the relationship between interannual variability of WPI in the North Atlantic and the North Atlantic Oscillation (NAO), motivated by the idea that the NAO serves as a good indicator for storminess over the North Atlantic and that storms account for the majority of WPI. It is found that WPI at low and high latitudes of the North Atlantic is significantly correlated to the NAO, owing to its influence on the configuration of the storm track. Positive (negative) NAO conditions are associated with increased WPI in the subpolar (subtropical) ocean. Basin-wide WPI is found to be significantly enhanced under negative NAO conditions, but is not significantly different from the climatological average under positive NAO conditions. This indicates a weak inverse relationship between basin-wide WPI and the NAO, contradicting intuitive expectations. The asymmetric impact of the NAO on basin-wide WPI results from greater sensitivity of WPI to near-inertial wind forcing at lower latitudes due to the variation of the Coriolis parameter with latitude.

Quantifying High-Frequency Wind Energy Flux into Near-Inertial Motions in the Southeast Pacific

AbstractWind-forced internal waves close to the inertial frequency are ubiquitous throughout the world’s oceans, but observational constraints on their global energetics and impact on subsurface mixing remain scarce. This study reports on velocity measurements from three Electromagnetic Autonomous Profiling Explorers (EM-APEX) deployed in February 2009. These floats observed downward-propagating near-inertial internal waves near the Subantarctic and Polar Fronts of the Antarctic Circumpolar Current. These waves were episodic and enhanced at middepth between 500 and 1000 m. Depth-integrated kinetic energy varied between 1 and 7 kJ m−2 and averaged 1.6 kJ m−2 with typical group velocities of 40 m day−1, implying an average energy flux of 3 mW m−2 at the mixed layer base decreasing to approximately 25% of that value at 1500 m. Modeled currents forced by reanalysis winds along each float track agree with observed surface currents from EM-APEX, provided that mixed layer depth is restricted to the layer of weakest observable stratification (interpreted as the maximum depth that can remain mixed over an inertial period given the continual balance between mixing and restratification). This model estimates an average wind power of 3 mW m−2. Shipboard wind and current observations during a strong storm show an integrated wind work of 3.5 kJ m−2, comparable to the vertically integrated kinetic energy over the following month. Model wind work estimates are considerably less, likely because of the mixed layer depth used. A model with varying stratification in response to the wind provides a better match to the observations, emphasizing the importance of stratification within the mixed layer in amplifying wind energy input.

Features of near-inertial motions observed on the northern South China Sea shelf during the passage of two typhoons

Features of near-inertial motions on the shelf (60 m deep) of the northern South China Sea were observed under the passage of two typhoons during the summer of 2009. There are two peaks in spectra at both sub-inertial and super-inertial frequencies. The super-inertial energy maximizes near the surface, while the sub-inertial energy maximizes at a deeper layer of 15 m. The sub-inertial shift of frequency is induced by the negative background vorticity. The super-inertial shift is probably attributed to the near-inertial wave propagating from higher latitudes. The near-inertial currents exhibit a two-layer pattern being separated at mid-depth (25–30 m), with the phase in the upper layer being nearly opposite to that in the lower layer. The vertical propagation of phase implies that the near-inertial energy is not dominantly downward. The upward flux of the near-inertial energy is more evident at the surface layer (<17 m). There exist two boundaries at 17 and 40 m, where the near-inertial energy is reflected upward and downward. The near-inertial motion is intermittent and can reach a peak of as much as 30 cm/s. The passage of Typhoon Nangka generates an intensive near-inertial event, but Typhoon Linfa does not. This difference is attributed to the relative mooring locations, which is on the right hand side of Nangka’s path (leading to a wind pattern rotating clockwise with time) and is on the left hand side of Linfa’s path (leading to a wind pattern rotating anti-clockwise with time).

Resonant Generation and Energetics of Wind-Forced Near-Inertial Motions in a Geostrophic Flow

AbstractA slab mixed layer model and two-dimensional numerical simulations are used to study the generation and energetics of near-inertial oscillations in a unidirectional, laterally sheared geostrophic current forced by oscillatory winds. The vertical vorticity of the current ζg modifies the effective Coriolis frequency , which is equivalent to the local resonant forcing frequency. In addition, the resonant oscillatory velocity response is elliptical, not circular, because the oscillation periodically exchanges energy with the geostrophic flow via shear production. With damping, this energy exchange becomes permanent, but its magnitude and sign depend strongly on the angle of the oscillatory wind vector relative to the geostrophic flow. However, for a current forced by an isotropic distribution of wind directions, the response averaged over all wind angles results in a net extraction of energy from the geostrophic flow that scales as the wind work on the inertial motions times (ζg/f)2 for ζg ≪ f. For ζg ~ f, this sink of geostrophic kinetic energy preferentially damps flows with anticyclonic vorticity and thus could contribute toward shaping the positively skewed vorticity distribution observed in the upper ocean.