On the generation and propagation of internal solitary waves in the southern Andaman Sea: A numerical study

Numerous internal solitary waves(ISWs) have been observed in the southern Andaman Sea. In this study, the two-dimensional Massachusetts Institute of Technology general circulation model is applied to investigate the dynamics of ISWs and explore the effects of the bottom topography and tidal forcing on the generation and propagation of ISWs in the southern Andaman Sea. The results show that the large-amplitude depression ISWs are mainly generated via the oscillating tidal flow over the sill of the Great Channel, and the generation of ISWs is subject to the lee wave regime. The Dreadnought Bank cannot generate ISWs itself; however, it can enhance the amplitudes of eastward-propagating ISWs generated from sill A, owing to constructive interference of internal tide generation between the sill of the Great Channel and the Dreadnought Bank. The eastward-propagating ISWs generated by the eastern shallow sill near the continental shelf can propagate to the shelf, where they evolve into elevation waves because of the shallow water. Sensitivity runs show that both the semidiurnal and diurnal tides over the sill of the Great Channel can generate ISWs in this area. However, the ISWs generated by diurnal tides are much weaker than those generated by semidiurnal tides. Mixed tidal forcing has no significant effect on the generation of ISWs.     

Internal waves over the shelf in the western Bay of Bengal: a case study

Generation and propagation of internal waves (IWs) in the coastal waters of the extended shelf of the western Bay of Bengal are investigated for late winter by using the Massachusetts Institute of Technology General Circulation Model (MITgcm). The model is forced with astronomical tides and daily winds. Monthly climatological temperature and salinity fields are used as initial conditions. The simulations are compared with time series observations of temperature and currents from acoustic Doppler current profiler (ADCP) and conductivity-temperature-depth (CTD) moored at three locations south of Gopalpur: two at a local depth of 100 m and another at 400-m depth during 19–21 February 2012. The comparison of the spectral estimates for the time series of temperature from the model and observations are in reasonable agreement for the near-tidal frequency waves. The peak of temperature spectra is always found near the shelf break region which steadily lost its intensity over the continental shelf. The calculation of Richardson number reflected the presence of local mixing due to density overturning in the shelf region. To understand further the generation and propagation of internal tides in the region, energy flux and conversion of barotropic-to-baroclinic M₂ tidal energy are examined. The model simulations suggest that the internal tide is generated all along the shelf slope. The energy flux analysis shows that the internal tides propagate to either side of the generation sites.     

Internal tides and waves near the continental shelf edge

Abstract

The subject is reviewed from the viewpoints of theory, internal tide and wave structure and their implications.

A wider theoretical context suggests scope for further investigation of natural or nearly-trapped forms above the inertial frequency.

Although internal tides in many locations are observed to have first-mode vertical structure, higher modes are seen offshore from shallow shelf-break forcing and for particular Froude numbers, and may be expected locally near generation. Bottom intensification is often observed where the sea floor matches the characteristic slope. Solitons form from internal tides of large amplitude or at large changes of depth.

Internal tides and solitons are observed also at many sills and in straits, and to intensify in canyons.

Non-linear effects of the waves, especially solitons, include the conveyance of water, nutrients, ‘‘mixing potential'’ etc. away from their source to other locations, and the generation of mean currents. The waves transfer energy and possibly heat between the ocean and shelf, may be a source of medium frequency waves on the shelf (periods of minutes) and can contribute to interior mixing and overturning, bottom stirring and sediment movement.     

An Overview of Internal Solitary Waves in the South China Sea

Internal solitary waves (ISWs) are the nonlinear large amplitude waves existing in the oceanic pycnocline. They are very active in the northern South China Sea (SCS). With more and more remote sensing data, in situ observational data and the development of the numerical simulation technology, a number of studies on the characteristics, the source site, the generation, and evolution of the ISWs in the SCS are reported. In this paper, earlier studies on the ISWs in the SCS are summarized and some problems worthy of study are put forward.     

Variability of baroclinic tidal currents on the Mackenzie Shelf,the Southeastern Beaufort Sea

Semidiurnal tidal currents on the outer shelf of the Mackenzie Shelf in the Beaufort Sea were found to be strongly influenced by the locally generated baroclinic tide. Two primary factors are involved in this process: (1) the sharp shelf break along the northeastern Mackenzie Shelf, promoting the generation of vigorous internal tidal waves; and (2) the proximity to critical latitudes for M₂ and N₂ motions locking these waves and preventing them from leaving the source region. As a result, internal tides are resonantly trapped between the shelf and critical latitudes. The physical properties and temporal variations of tidal motions were examined using current meter measurements obtained from 1987–1988 at four sites (SS1, SS2, SS3, and SS4) offshore of the shelf break at depths of ∼200 m. Each mooring had Aanderaa RCM4s positioned at ∼35 m below the surface and ∼50 m above the bottom. Complex demodulation was used to compute the envelopes (amplitude modulation) of these components. A striking difference in the variability of clockwise (CW) and counterclockwise (CCW) tidal currents was found. The CW tides are highly variable, have greater amplitude, exhibit a burst-like character associated with wind events and contain about 80% of the total energy of the semidiurnal tidal currents. In contrast, the CCW components have a more regular temporal regime with distinct monthly, fortnightly and 10-day modulation at astronomical periodicities associated with frequency differences M₂–N₂ (0.03629 cpd), S₂–M₂ (0.06773 cpd), and S₂–N₂ (0.10402 cpd). Significant horizontal correlation of the CW current envelopes was found only between stations near the northeast Mackenzie Shelf, indicating this to be the main area of baroclinic internal wave generation.     

Dynamical Control of Pacific Oceanic Low-frequency Variability on Western Boundary and Marginal Seas

The adjustment of sea surface height (SSH) around the coasts of the Japan/East Sea (JES) and the South China Sea (SCS) basins subjected to extratropical Pacific Oceanic low frequency variability is studied using a Kelvin-planetary wave model and a high resolution numerical model. It is found that the modulation of SSH around the coast of Japan is mainly determined by slow adjustment of planetary waves, which radiate from the west coast of Honshu and Hokkaido due to the coastal Kelvin wave. In contrast, the SSH modulation around the cost of the South China Sea basin is mainly determined by the coastal Kelvin wave, which transfers the anomalous SSH into the SCS via the Luzon Strait and out via the Mindoro Strait. The planetary waves radiating from the west coast of Palawan establish a nearly uniform SSH anomaly in the southern part of the SCS, bounded by an eastward jet at the latitude of the Mindoro Strait. Along the western boundary, SSH anomaly decreases almost linearly toward the south, in accordance with the changing local deformation radius. In these two marginal seas, the mean subtropical Pacific gyre circulation enhances SSH modulation induced by extratropical Pacific low frequency variability. Overall, the SSH adjustment in the JES and the SCS predicted by the analytical model agrees well with the numerical model simulation. Application of this model to interaction between these marginal seas and the open ocean is discussed.     

Interactions between tides and other frequencies in the Indonesian seas

Interactions of tidal constituents and the transfer of energy from the tidal frequencies to other frequencies are investigated using 3-D tidal simulations for the Indonesian seas, focusing on an area of active internal tides. Semidiurnal tides strongly affect diurnal tides; however, semidiurnal tides are essentially unaffected by diurnal tides. The semidiurnal and diurnal constituents interact with each other through non-linear interference, both destructive and constructive. Semidiurnal tides generate harmonics at nearly the diurnal frequency and higher vertical wavenumbers. In Ombai Strait, these harmonics are out of phase with the diurnal tides and interact destructively with the diurnal tides, effectively negating the diurnal response in some locations. However, this is not a general response, and interactions differ between locations. Energy is also transferred from both semidiurnal and diurnal tides to other frequencies across the spectrum, with more energy originating from semidiurnal tides. These energy transfers are not homogeneous, and the spectral responses differ between the Makassar and Ombai Straits, with the region east of Ombai showing a more active surface response compared to a more intense benthic response in Makassar. In deep water away from topography, velocity spectra generally follow the Garrett–Munk (GM) relation. However, in areas of internal tide generation, spectral density levels exceed GM levels, particularly between 4 and 8 cycles per day (cpd), indicating increased non-linear interactions and energy transfer through resonant interactions. The model indicates strong surface trapping of internal tides, with surface velocity spectra having significantly higher energy between 4 and 8 cpd even 100 km away from the prominent sill generating the internal tides.     

SMLTM simulations of the diurnal tide: comparison with UARS observations

Wind and temperature observations in the mesosphere and lower thermosphere (MLT) from the Upper Atmosphere Research Satellite (UARS) reveal strong seasonal variations of tides, a dominant component of the MLT dynamics. Simulations with the Spectral mesosphere/lower thermosphere model (SMLTM) for equinox and solstice conditions are presented and compared with the observations. The diurnal tide is generated by forcing specified at the model lower boundary and by in situ absorption of solar radiation. The model incorporates realistic parameter-izations of physical processes including various dissipation processes important for propagation of tidal waves in the MLT. A discrete multi-component gravity-wave parameterization has been modified to account for seasonal variations of the background temperature. Eddy diffusion is calculated depending on the gravitywave energy deposition rate and stability of the background flow. It is shown that seasonal variations of the diurnal-tide amplitudes are consistent with observed variations of gravity-wave sources in the lower atmosphere.     

A numerical study of the barotropic tides and tidal energy distribution in the Indonesian seas with the assimilated finite volume coastal ocean model

The tides and tidal energetics in the Indonesian seas are simulated using a three-dimensional finite volume coastal ocean model. The high-resolution coastline-fitted model is configured to better resolve the hydrodynamic processes around the numerous barrier islands. A large model domain is adopted to minimize the uncertainty adjacent to open boundaries. The model results with elevation assimilation based on a simple nudge scheme faithfully reproduced the general features of the barotropic tides in the Indonesian Seas. The mean root-mean-square errors between the observed and simulated tidal constants are 2.3, 1.1, 2.4, and 1.5 cm for M₂, S₂, K₁, and O₁, respectively. Analysis of the model solutions indicates that the semidiurnal tides in the Indonesian Seas are primarily dominated by the Indian Ocean, whereas the diurnal tides in this region are mainly influenced by the Pacific Ocean, which is consistent with previous studies. Examinations of tidal energy transport reveal that the tidal energy for both of the simulated tidal constituents are transported from the Indian Ocean into the IS mainly through the Lombok Strait and the Timor Sea, whereas only M₂ energy enters the Banda Sea and continues northward. The tidal energy dissipates the most in the passages on both sides of Timor Island, with the maximum M₂ and K₁ tidal energy transport reaching about 750 and 650 kW m^–1, respectively. The total energy losses of the four dominant constituents in the IS are nearly 338 GW, with the M₂ constituent dissipating 240.8 GW. It is also shown that the bottom dissipation rate for the M₂ tide is about 1–2 order of magnitudes larger than that of the other three tidal components in the Indonesian seas.     

地中海直布罗陀海峡附近内孤立波的地球物理特征

本文主要利用地震海洋学方法研究地中海直布罗陀海峡附近内孤立波的结构特征,此处内孤立波为第一模态下沉型,为中幅度和大幅度内孤立波,垂向振幅最大可达74.5m,振幅随深度增加呈增大趋势,传播速度随振幅增大而增大,可以确定“真”最大振幅位置位于密跃层附近.由于类多普勒效应和孤立波与测量船之间存在夹角的原因,从地震剖面上得到的为视半高宽参数,需要进行校正后才能得到比较真实的半高宽参数,校正后半高宽最高可达到1721.8m,但是校正后的半高宽与理论结果有些差距,这可能与内孤立波的发育稳定程度有关.随着内孤立波包不断向东运动,整体波宽变大,垂向速度变小.本文将地震海洋学方法拓展应用于地中海区域内孤立波分析,进一步证明了利用地震海洋学方法研究海水运动的可行性.     

The TKE dissipation rate in the northern South China Sea

The microstructure measurements taken during the summer seasons of 2009 and 2010 in the northern South China Sea (between 18°N and 22.5°N, and from the Luzon Strait to the eastern shelf of China) were used to estimate the averaged dissipation rate in the upper pycnocline 〈ε _p〉 of the deep basin and on the shelf. Linear correlation between 〈ε _p〉 and the estimates of available potential energy of internal waves, which was found for this data set, indicates an impact of energetic internal waves on spatial structure and temporal variability of 〈ε _p〉. On the shelf stations, the bottom boundary layer depth-integrated dissipation \( {\widehat{\varepsilon}}_{\mathrm{BBL}} \) reaches 17–19 mW/m², dominating the dissipation in the water column below the surface layer. In the pycnocline, the integrated dissipation \( {\widehat{\varepsilon}}_{\mathrm{p}} \) was mostly ∼10–30 % of \( {\widehat{\varepsilon}}_{\mathrm{BBL}} \). A weak dependence of bin-averaged dissipation \( \overline{\varepsilon} \) on the Richardson number was noted, according to \( \overline{\varepsilon}={\varepsilon}_0+\frac{\varepsilon_{\mathrm{m}}}{{\left(1+ Ri/R{i}_{\mathrm{cr}}\right)}^{1/2}} \), where ε ₀ + ε _m is the background value of \( \overline{\varepsilon} \) for weak stratification and Ri _cr = 0.25, pointing to the combined effects of shear instability of small-scale motions and the influence of larger-scale low frequency internal waves. The latter broadly agrees with the MacKinnon–Gregg scaling for internal-wave-induced turbulence dissipation.

     

Variations of vertical velocity in the deep oceans simulated by a 1/10° OGCM

This paper analyzes variations of vertical velocity w simulated by the 1/10° Ocean General Circulation Model for the Earth Simulator (OFES). Strong w-variability is found in the deep oceans. When w is WKBJ-normalized, the standard deviation averaged over the Southern Ocean increases with depth and is larger than 8 × 10^− 3 cm/s throughout the water column below 1,500 m. Evidences are presented that link this w-variability to internal waves generated by quasi-steady currents over topography. The aliasing errors in lag-3-day correlations suggest a bottom generation of near-inertial waves. A scale analysis indicates that vertically propagating waves that can be resolved by the OFES model are waves with frequencies of the order of inertial frequency and wavelengths comparable to the order of the grid size. The vertical energy flux associated with these waves is substantial. When integrated globally, the vertical energy flux is upward in the upper 4 km and reaches maximum values of about 0.8 TW at about 1 to 2 km depth. Thus, the w-variability in the 1/10° OFES integration points not only to a strong bottom generation of near-inertial internal waves in the deep Southern Ocean but also to the possibility that the power provided by internal waves generated by non-tidal currents over topography can be comparable to the power provided by internal waves generated by tidal flows over topography.     

Propagation of internal gravity waves to the altitudes of the ionospheric <Emphasis Type="Italic">D</Emphasis> and dynamo regions in the seismic region (Kamchatka): Preliminary results

A spectral analysis of simultaneous diurnal variations in the E _z component of the quasi-static electric field in the near-Earth atmosphere, VLF radio noise, and the horizontal component of the geomagnetic field, observed at Kamchatka in September 1999, has been performed. These geophysical parameters are indirectly used to study wave processes in the near-Earth atmosphere and in the ionospheric D and dynamo regions within the band of periods of internal gravity waves (T = 0.5?3.5 h). The correlation method in the frequency region is used to analyze the interrelation between the wave processes in these atmospheric regions. The power cross-spectra of various pairs of geophysical parameters have been studied depending on meteorological, seismic, and geomagnetic activities. It is shown that the oscillations in the power spectra in the T ～ 1–1.5 h band of periods are caused by the sources of internal gravity waves in the near-Earth atmosphere and by the remote sources above the dynamo region of the ionosphere within the T ～ 1.5–3 h band of periods.     

Tidally generated internal waves in partially mixed estuaries

The generation of internal waves in the partially mixed estuaries is examined. The numerical experiments consider the barotropic tidal currents interacting with isolated obstacles in an open channel. The bottom boundary layer and longitudinal salinity gradient are included. Internal lee (arrested) waves are excited when the accelerating barotropic tidal current approaches the first-mode internal wave speed. The arrested waves are amplified, and are subsequently released when the decelerating tidal current falls below the first-mode internal wave speed. The power input from the barotropic tidal energy into internal wave energy is calculated. It is on the order of 10⁻² W/m², and is comparable to the estimated interior dissipation rate. This suggests that the tidally generated internal waves could be a significant energy source for mixing in the halocline.     

The TKE dissipation rate in the northern South China Sea

The microstructure measurements taken during the summer seasons of 2009 and 2010 in the northern South China Sea (between 18°N and 22.5°N, and from the Luzon Strait to the eastern shelf of China) were used to estimate the averaged dissipation rate in the upper pycnocline 〈ε _p〉 of the deep basin and on the shelf. Linear correlation between 〈ε _p〉 and the estimates of available potential energy of internal waves, which was found for this data set, indicates an impact of energetic internal waves on spatial structure and temporal variability of 〈ε _p〉. On the shelf stations, the bottom boundary layer depth-integrated dissipation $ {\widehat{\varepsilon}}_{\mathrm{BBL}} $ reaches 17–19 mW/m², dominating the dissipation in the water column below the surface layer. In the pycnocline, the integrated dissipation $ {\widehat{\varepsilon}}_{\mathrm{p}} $ was mostly ～10–30 % of $ {\widehat{\varepsilon}}_{\mathrm{BBL}} $ . A weak dependence of bin-averaged dissipation $ \overline{\varepsilon} $ on the Richardson number was noted, according to $ \overline{\varepsilon}={\varepsilon}_0+\frac{\varepsilon_{\mathrm{m}}}{{\left(1+ Ri/R{i}_{\mathrm{cr}}\right)}^{1/2}} $ , where ε ₀ + ε _m is the background value of $ \overline{\varepsilon} $ for weak stratification and Ri _cr?=?0.25, pointing to the combined effects of shear instability of small-scale motions and the influence of larger-scale low frequency internal waves. The latter broadly agrees with the MacKinnon–Gregg scaling for internal-wave-induced turbulence dissipation.     

Normal Mode Energetics for Far-field Tsunamis Generated by Dislocations and Landslides

— We apply the normal mode representation of tsunami waves, as introduced by Ward (1980) to the systematic study of the excitation of far-field tsunamis by both dislocation sources (represented by double-couples of moment M ₀), and landslides (represented by single forces). Using asymptotic representations of the continuation of the tsunami eigenfunction into the solid Earth, we derive analytical expressions of the spectral amplitude generated by both systems. We show that the quadrupolar corrections defined by Dahlen (1993) in the case of landslides can result in an increase of 1 to 2 orders of magnitude of the effective force. Even so, the spectrum of tsunami waves generated by landslides is found to be offset significantly to relatively high frequencies (10 mHz), where dispersion becomes important and eventually diminishes time-domain amplitudes. We proceed to calculate the total energy delivered into the tsunami modes by integrating the energy of multiplets for an average source geometry. In the case of dislocation sources, and taking into account the corner frequency of the source, we reproduce the scaling with M ₀ ^4/3 which was derived from purely static arguments by Kajiura (1981). We compare the directivity patterns of far-field tsunami waves by dislocations and landslides, and conclude that the latter cannot give rise to pronounced lobes of directivity for physically acceptable values of the velocity of the slide. Directivity thus constitutes a robust discriminant of the nature of the source which, when applied to the 1946 Aleutian tsunami in the far-field, requires generation by a dislocative source.     

南海东北部内孤立波包的地震海洋学和遥感研究

在南海东北部东沙环礁附近,内孤立波被大量地观测报道.在该地区内孤立波的传播和演化过程仍然存在许多待解决的问题.利用改进的地震海洋学处理方法对2009年夏的一段海洋勘探地震测线进行了重新处理,获得了50 m水深之下的水层反射图像,发现了包含8个内孤立波的下沉型内孤立波包.遥感仪器中分辨率成像光谱仪(MODIS)图像在该段...     

Parametrization of momentum and energy depositions from gravity waves generated by tropospheric hydrodynamic sources

The mechanism of generation of internal gravity waves (IGW) by mesoscale turbulence in the troposphere is considered. The equations that describe the generation of waves by hydrodynamic sources of momentum, heat and mass are derived. Calculations of amplitudes, wave energy fluxes, turbulent viscosities, and accelerations of the mean flow caused by IGWs generated in the troposphere are made. A comparison of different mechanisms of turbulence production in the atmosphere by IGWs shows that the nonlinear destruction of a primary IGW into a spectrum of secondary waves may provide additional dissipation of nonsatu-rated stable waves. The mean wind increases both the effectiveness of generation and dissipation of IGWs propagating in the direction of the wind. Competition of both effects may lead to the dominance of IGWs propagating upstream at long distances from tropospheric wave sources, and to the formation of eastward wave accelerations in summer and westward accelerations in winter near the mesopause.     

Array measurements of the bottom boundary layer and the internal wave field on the continental slope

Abstract

An array of current meters was placed on the continental slope and rise for two months in the autumn of 1970. The bottom boundary layer was penetrated on the slope. On the smallest array scale, of the order of 1 kilometer, the array functioned as a directional internal wave antenna. Moving shoreward, the current spectra show strong suppression of the inertial peak and strong enhancement of the semidiurnal tide. The measured wave number spectra show that the tidal energy is almost completely baroclinic, and probably being generated in the region where the slope becomes “critical” for the tidal period. If this area is typical of worldwide conditions, a substantial fraction of the dissipation of surface tides takes place on the continental slopes by conversion to baroclinic waves. The bottom boundary layer has been modeled by an extension of the work of Ellison (1956) to a sloping boundary in a fluid of positive stability. An equivalent constant eddy coefficient has the value 3 cm²/sec as determined from the measurements.     

A three-dimensional model study of near-inertial motion: generation and influence of an along-shelf flow

A three-dimensional baroclinic model of the Balearic Sea region is used to examine the processes influencing the distribution of near-inertial currents and waves in the region. Motion is induced by a spatially uniform wind impulse. By using a uniform wind, Ekman pumping due to spatial variability in the wind is removed with the associated generation of internal waves. However, internal waves can still be produced where stratification intersects topography. The generation and propagation of these waves, together with the spatial distribution of wind-forced inertial oscillations, are examined in detail. Diagnostic calculations show that in the near-coastal region inertial oscillations are inhibited by the coastal boundary. Away from this boundary the magnitude of the inertial oscillations increases, with currents showing a 180° phase shift in the vertical. The inclusion of an along-shelf flow modifies the inertial currents due to non-linear interaction between vorticity in the flow and the inertial oscillations. Prognostic calculations show that besides inertial oscillations internal waves are generated. In a linear model the addition of an along-shelf flow produces a slight reduction in the energy at the near-inertial frequency due to enhanced viscosity associated with the flow and changes in density field. The inclusion of non-linear effects modifies the currents due to inertial oscillations in a manner similar to that found in the diagnostic model. A change in the effective inertial frequency also influences the propagation of the internal waves. However, this does not appear to be the main reason for the enhanced damping of inertial energy, which is due to the along-shelf advection of water of a different density into a region and increased viscosity and mixing associated with the along-shelf flow.Responsible Editor: Phil Dyke