Generation and evolution of internal solitary waves in the southern Taiwan Strait

ABSTRACT

The generation processes and potential energy sources of internal solitary waves (ISWs) in the southern Taiwan Strait are investigated by driving a high resolution non-hydrostatic numerical model with realistic background conditions. Two main types of ISWs are clarified according to their different energy sources. One is generated by the nonlinear disintegration of remote internal tides emanating from Luzon Strait, and the other type is generated by local tide-topography interaction at the continental slope. The basic properties and evolution processes differ between these two kinds of ISWs. The waves originated from the remote internal tides at Luzon Strait have amplitudes comparable to previous field observations. In contrast, the ISWs generated locally are much weaker than observed waves, even in the presence of a steady offshore background current, which intensifies the generation of onshore ISWs. The ISWs induced by remotely generated M₂ internal tides are stronger than those induced by K₁ internal tides, and the fraction of internal wave energy transmitted onto the shelf is not significantly influenced by the intensity of remotely generated internal tides.     

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.     

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.     

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.     

Planetons: An example of large amplitude solitary waves

Abstract

The term ‘‘solitary wave'’ is usually used to denote a steadily propagating permanent form solution of a nonlinear wave equation, with the permanency arising from a balance between steepening and dispersive tendencies. It is known that large-scale thermal anomalies in the ocean are subject to a steepening mechanism driven by the beta effect, while at the smaller deformation scale, such phenomena are highly dispersive. It is shown here that the evolution of a physical system subject to both effects is governed by the ‘‘frontal semi-geostrophic equation'’ (FSGE), which is valid for large amplitude thermocline disturbances. Solitary wave solutions of the FSGE (here named planetons) are calculated and their properties are described with a view towards examining the behavior of finite amplitude solitary waves. In contrast, most known solitary wave solutions belong to weakly nonlinear wave equations (e.g., the Korteweg—deVries (KdV) equation).

The FSGE is shown to reduce to the KdV equation at small amplitudes. Classical sech² solitons thus represent a limiting class of solutions to the FSGE. The primary new effect on planetons at finite amplitudes is nonlinear dispersion. It is argued that due to this effect the propagation rates of finite amplitude planetons differ significantly from the ‘‘weak planeton'', or KdV, dispersion relation. Planeton structure is found to be simple and reminiscent of KdV solitons. Numerical evidence is presented which suggests that collisions between finite amplitude solitary waves are weakly inelastic, indicating the loss of true soliton behavior of the FSGE at moderate amplitudes. Lastly, the sensitivity of solitary waves to the existence of a nontrivial far field is demonstrated and the role of this analysis in the interpretation of lab experiments and the evolution of the thermocline is discussed.     

High-frequency vertical current observations in stratified seas

Although large-scale tidal and inertial motions dominate the kinetic energy and vertical current shear in shelf seas and ocean, short-scale internal waves at higher frequencies close to the local buoyancy frequency are of some interest for studying internal wave breaking and associated diapycnal mixing. Such waves near the upper limit of the inertio-gravity wave band are thought to have relatively short O (10²–10³ m) horizontal scales and to show mainly up- and downward motions, which contrasts with generally low aspect ratio large-scale ocean currents. Here, short-term vertical current (w) observations using moored acoustic Doppler current profiler (ADCP) are presented from a shelf sea, above a continental slope and from the open ocean. The observed w, with amplitudes between 0.015 and 0.05 m s⁻¹, all span a considerable part of the water column, which is not a small vertical scale O(water depth) or O (100–500 m, the maximum range of observations), with either 0 or π phase change. This implies that they actually represent internal waves of low vertical modes 1 or 2. Maximum amplitudes are found in layers of largest stratification, some in the main pycnocline bordering the frictional bottom boundary layer, suggesting a tidal source. These ‘pycnocline-w’ compose a regular train of (solitary) internal waves and linearly decrease to small values near surface and bottom.     

A mechanism for angular momentum mixing

Abstract

If a contained homogeneous, rotating fluid is forced near to a resonance for elastoid-inertia waves, strong vortices are observed to form. Numerical experiments reported here lend support to the explanation that these are due to a redistribution of the angular momentum by the waves. If the waves grow until the Angular momentum gradient is overturned somewhere, turbulent mixing there make the redistribution irreversible, resulting in a vortex. The process is analogous to the formation of steps in a stratified fluid by breaking internal waves.     

On the influence of stratification and tidal forcing upon mixing in sill regions

A cross-sectional non-hydrostatic model with idealized topography was used to examine the processes influencing tidal mixing in the region of sills. Initial calculations with appropriate parameters for the sill at the entrance to Loch Etive showed that the model could reproduce the main features of the observed mixing in the region. In particular, the hydraulic jump in the sill region was reproduced, as was an intense mid-water jet that was observed to separate from the lee side of the sill. Shear instabilities associated with the jet appeared to be a source of mixing within the thermocline. In addition, internal lee waves were generated on the lee side of the sill, with the observed amplification because of trapping during the flood stage. Their magnitude and hence the mixing increased with increasing Froude number (F _r). In the case of vertically varying buoyancy frequency, its value near the sill top determined the F _r number, with its value below influencing internal waves magnitude at depth. At high F _r values particularly with strong currents, short waves and overturning occurred.     

Some observations of internal wave current fluctuations at the shelf-edge and their implications for sediment transport

Observations of internal wave current fluctuations at a site on the European continental shelf are described. These have revealed current ‘pulses’ of regular tidal (M₂) phase which may be associated with internal tides generated at the shelf-edge. Current ‘pulses’ have been observed with amplitudes of 30 to 40 cm s^?1 superimposed on peak spring tidal currents of the order 60 to 70 cm s^?1. The measurements have shown that these fluctuations extended throughout the bottom mixed layer to within at least 2 m of the sea bed where they may play an important role in modifying sediment transport rates.     

Celtic Sea and Armorican current structure and the vertical distributions of temperature and chlorophyll

Vertical sections of temperature and chlorophyll a across the slopes and shelf of the Celtic Sea in the summer show the characteristic regimes; oceanic, slope, shelf, frontal, and mixed. Increases of surface chlorophyll a are commonly observed along the shelf tidal fronts where the thermocline outcrops at the surface, and also at the shelf-break. The variations in phytoplankton biomass are most readily interpreted in terms of the effects of physical mixing processes due to wind and tide on the availability of inorganic nutrients and light energy. On the shelf, mixing processes, both due to internal waves, inertial currents, and to boundary induced turbulence caused by tidal shear associated with the sea floor, play an important role in determining the observed vertical structures. A numerical model is used to define regions where tidal mixing processes are likely to be relatively important and provides the physical framework for interpreting the temperature and chlorophyll a profiles.     

On the generation of baroclinic rossby waves in the presence of a semi-circular boundary

Abstract

An analytical model is constructed for the generation of baroclinic Rossby waves by a vorticity source in the presence of a semi-circular boundary. The vorticity source is used to represent the effect of the Agulhas retroflection to the south of Southern Africa. The displacement of the interface between the two layers of the model ocean consists of quantized waves near the coast and a train of Rossby waves drifting westward further offshore.     

Observations indicating parametric instabilities in internal gravity waves at thermospheric heights

Abstract

Theoretical studies predict a parametric instability of finite-amplitude internal gravity waves which hitherto has been observed only in laboratory experiments. The occurrence of this process in the atmosphere is of basic interest because finite-amplitude gravity waves, which are almost ubiquitous especially at upper atmospheric heights, would produce unstable flows even at large Richardson numbers. Maximum entropy power spectra of a strong internal gravity wave in the thermosphere, which was generated by a volcanic eruption and detected on records of the Doppler shift of high-frequency radio waves, in fact show good agreement with the spectra of synthetic Doppler records obtained from a calculated unstable gravity wave. The frequencies and wavenumbers observed in the gravity wave domain satisfy in particular the theoretically predicted resonance conditions. The observed Doppler records also show two significant lines in the acoustic domain which probably result from a nonlinear interaction with the basic gravity wave. It is suggested that acoustic double peaks, which are commonly observed in high-frequency Doppler spectra in the presence of nearby thunderstorms, represent parametric instabilities of internal gravity waves generated by penetrative cumulus convection.     

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.     

Internal waves,baroclinic energy fluxes and mixing at the European shelf edge

The energy flux in internal waves generated at the Celtic Sea shelf break was estimated by (i) applying perturbation theory to a week-long dataset from a mooring at 200 m depth, and (ii) using a 2D non-hydrostatic circulation model over the shelf break. The dataset consisted of high resolution time-series of currents and vertical stratification together with two 25-h sets of vertical profiles of the dissipation of turbulent kinetic energy. The observations indicated an average energy flux of 139 W m⁻¹, travelling along the shelf break towards the northwest. The average energy flux across the shelf break at the mooring was only 8 W m⁻¹. However, the waves propagating onshelf transported up to 200 W m⁻¹, but they were only present 51% of the time. A comparison between the divergence of the baroclinic energy flux and observed dissipation within the seasonal thermocline at the mooring showed that the dissipation was at least one order of magnitude larger. Results from a 2D model along a transect perpendicular to the shelf break showed a time-averaged onshelf energy flux of 153–425 W m⁻¹, depending on the magnitude of the barotropic forcing. A divergence zone of the energy flux was found a few kilometre offshore of the location of the observations in the model results, and fluxes on the order of several kW m⁻¹ were present in the deep waters further offshelf from the divergence zone. The modelled fluxes exhibited qualitative agreements with the phase and hourly onshelf magnitudes of the observed energy fluxes. Both the observations and the model results show an intermittent onshelf energy flux of 100–200 W m⁻¹, but these waves could only propagate ∼20–30 km onshore before dissipating. This conclusion was supported by a 25-h dataset sampled some 180 km onto the shelf, where a weak wave energy flux was found going towards the shelf break. We therefore conclude that shelf break generated internal waves are unlikely to be the main source of energy for mixing on the inner part of the shelf.     

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.     

A coupled oscillator model of shelf and ocean tides

The resonances of tides in the coupled open ocean and shelf are modeled by a mechanical analogue consisting of a damped driven larger mass and spring (the open-ocean) connected to a damped smaller mass and spring (the shelf). When both masses are near resonance, the addition of even a very small mass can significantly affect the oscillations of the larger mass. The influence of the shelf is largest if the shelf is resonant with weak friction. In particular, an increase of friction on a near-resonant shelf can, perhaps surprisingly, lead to an increase in ocean tides. On the other hand, a shelf with large friction has little effect on ocean tides. Comparison of the model predictions with results from numerical models of tides during the ice ages, when lower sea levels led to a much reduced areal extent of shelves, suggests that the predicted larger tidal dissipation then is related to the ocean basins being close to resonance. New numerical simulations with a forward global tide model are used to test expectations from the mechanical analogue. Setting friction to unrealistically large values in Hudson Strait yields larger North Atlantic _M2$M_2$ amplitudes, very similar to those seen in a simulation with the Hudson Strait blocked off. Thus, as anticipated, a shelf with very large friction is nearly equivalent in its effect on the open ocean to the removal of the shelf altogether. Setting friction in shallow waters throughout the globe to unrealistically large values yields even larger open ocean tidal amplitudes, similar to those found in simulations of ice-age tides. It thus appears that larger modeled tides during the ice ages can be a consequence of enhanced friction in shallower water on the shelf in glacial times as well as a reduced shelf area then. Single oscillator and coupled oscillator models for global tides show that the maximum extractable power for human use is a fraction of the present dissipation rate, which is itself a fraction of global human power consumption.     

Crustal microdeformations and tides in the coastal zone of the Sea of Japan

Based on experimental data and numerical modeling, the possible mechanisms of the effect of internal gravitational waves within the range of periods from tidal values to a few tens of minutes on crustal microdeformations in the coastal zone of the Sea of Japan are examined. The spectral analysis of oscillations in the sea level and microdeformations recorded in various seasons reveals common maximums of energy at diumal and semidiurnal periods, but the coincidence of the maximums at shorter periods is random and varies with time. The phase shifts between the surface tide and crustal deformations are also unstable in time. To explain the observed interrelations between the processes at sea and in the Earth’s crust, we modeled numerically the generation of internal tides, bores, and packets of short internal waves in terms of a nonlinear model of shallow water. It is shown that the observed effects can be caused (1) by the resonance between the wavelength of the internal tide and the shelf width and (2) by the reflection of bores and internal wave packets from a steep bottom and rocky shores or by their collapse.     

A note on edge waves on a flat shelf

Abstract

A variational approximation to the dispersion relation for trapped waves on a flat shelf of depth h ₁, bounded internally by a vertical coast and externally by a semi-infinite ocean of depth h ₂>h ₁, is obtained through an integral-equation formulation that accounts for all of the non-propagated modes that are excited at the discontinuity in depth (the conventional formulation of the edge-wave problem allows only for the propagated mode on the shelf and the dominant, non-propagated mode in the deep water). Coriolis effects are neglected. The exact result in the limit ω² h ₂/g↓0 (ω = angular frequency) is obtained by conformal mapping and compared with the variational approximation, which proves to be quite accurate over the entire range 1>h ₂/h ₁>x. The effects of the higher-order, non-propagated modes are found to be small for the long waves observed over the Southern California shelf by Snodgrass, Munk and Miller (1962).     

Physicochemical conditions in coastal waters off Syndney, central NSW, Australia

The continental shelf off Sydney is narrow and characterized by extensive areas of rocky reef and sandy sediment. The overlying coastal waters are dynamic with a complex current structure. Important oceanographic processes include East Australian Current (EAC) activity, northward propagating coastal trapped waves, local wind driven currents and relatively high frequency internal tides and waves. These produce influences on a wide range of temporal and spatial scales. The activity of the EAC and its eddies has been associated with episodic incursions of waters which can quickly replace large parts of the shelf waters off Sydney. Thermal stratification and the episodic presence of cold, nutrient rich waters intruded from the continental slope are important features of the water column. Thermal stratification of up to 6°C generally exists for all but a few months of the year. Nutrient concentrations are generally low in surface waters but are higher and more variable at depth because of irregular intrusions of slope waters from depths greater than 150–200 m. The trace element levels in surface seawater entering the Sydney area are expected to be extremely low.