Internal Solitons Research Articles

Generation of second mode solitary waves by the interaction of a first mode soliton with a sill

Abstract. Results of an experimental and theoretical study of the interaction of a first mode internal solitary wave with a localised bottom topography (sill) are presented. Laboratory experiments have been performed in a 10m long and 0.33m wide channel filled with a stratified fluid. The interface between the two layers (fresh and salt water) is diffuse and has a finite thickness. Soliton-type disturbances of the interface having characteristics of the first baroclinic mode are generated at one channel end. They move along the channel and encounter an underwater obstacle (sill) in the middle of the channel, where they break into reflected and transmitted waves. Two types of internal waves are produced by the interaction: a fast first mode internal soliton and a slower (by a factor of approximately 3) second mode soliton-like wave. A numerical model, based on the two-dimensional Navier-Stokes equations in the Boussinesq approximation, is used tore produce the laboratory experiment. The detailed analysis of the horizontal and vertical structures of transmitted and reflected waves showed that the fast reflected and transmitted waves observed in the experiment can be interpreted as a first mode internal solitary wave whose characteristics are very close to those of the K-dV solitons. It is also demonstrated that the slow speed waves, generated during the interaction behind the first fast wave have vertical and horizontal structures very close to the second mode internal K-dV solitons.

The variability of strongly non-linear solitary internal waves observed during an upwelling season on the Portuguese shelf

Observations of non-linear internal waves propagating onto the Portuguese shelf were made for 1 month during the summer upwelling season, using a thermistor chain mooring. The strongly non-linear waves had a typical amplitude of about 35 m and length of order 150 m, significantly longer than weakly non-linear KdV internal solitons. They appeared each semi-diurnal tidal cycle within the troughs of the internal tide and their phase speed (0.57 m s −1) was close to both that of the linear internal tide and that suggested by non-linear internal wave theory. The arrival time of the waves relative to local high water varied by over 5 h during the month and was closely correlated with wind events, with stronger upwelling favourable winds apparently causing the waves to arrive later. Analysis of the observations indicated that this modulation was primarily linked to wind driven currents, rather than fluctuations in the internal wave phase speed due to changes in the stratification. The intensification of the Ekman drift in an offshore upwelling filament may have played an important role in this variability. There appeared to be little correlation between the size of the waves and variations in tidal range. In fact the wave amplitude was close to the theoretical strongly non-linear maximum, even on neap tides. Considerable doubt remains about the origin of the waves; although the observations suggest that they were generated at the local shelf break by the semi-diurnal tide, their amplitude is too large to be explained in terms of the cross shelf tidal currents. It is possible that three-dimensional aspects of the topography and tidal regime are involved.

Observations of highly nonlinear internal solitons generated by near‐inertial internal waves off the east coast of Korea

Solitary internal wave packets were observed in May 1999, propagating toward the east coast of Korea with thermocline displacements up to twentysix meters downward from the initial depth of twenty meters. High nonlinearity of these waves is represented by the second‐order KdV model better than KdV equations. Regular occurrence of solitary internal wave packets with the period of about nineteen hours suggests the generation by near‐inertial internal waves, which has not been reported in the literature yet.

Nonlinear evolution of ocean internal solitons propagating along an inhomogeneous thermocline

Measurements of the upper ocean thermal structure show that on the continental shelves the thermocline depth may shoal or deepen generally depending on the bottom topography. Thermocline shoaling and deepening cause changes in the phase speeds of internal waves as described by linear wave theories. On the other hand, the ocean area where internal waves have variable phase speeds may be treated as a dynamically inhomogeneous medium. In this case, theories of nonlinear dispersive wave propagation in inhomogeneous media developed by Tappert and Zabusky [1971] may stand. We used these theories to analyze the evolution of ocean internal solitary waves passing over a seamount in the Gulf of Aden. The results indicate that a surprisingly sharp recess of an internal solitary wave packet, imaged by the space shuttle Discovery, is a signature of spatial phase delay caused by thermocline shoaling over the seamount. Soliton fission due to thermocline shoaling was also observed in the imagery. The observed number of transmitted solitons over the seamount agrees with theoretical predictions. Relative soliton amplitudes measured from the imagery also agree qualitatively with predictions.

Remote imaging of internal solitons in the coastal ocean

During a combined in situ and airborne remote sensing exercise off Oceanside, CA, a Compact Airborne Spectrographic Imager (CASI) observed alongshore lineations, which were associated with an internal soliton packet accompanying a tidally generated internal solitary wave (solibore). The soliton packets were most evident in the images at green wavelengths, which penetrate the deepest into the water column, and only weakly evident at optical wavelengths with shallower penetration. We believe that this is the first observation of internal soliton packets determined from remotely sensed upwelled radiance. We hypothesize that the lineations were produced by changes in the upwelling radiance from the interior of the water column, not by changes in surface reflectance. Using a simulation, it is demonstrated that such lineations can be produced by vertical modulation of the inherent optical properties (IOPs) during the passage of the internal soliton packet. Since surface manifestations are not always present, this opens the potential for broadly based inventories of internal solitons in coastal waters.

Internal and interfacial tides: Beam scattering and local generation of solitary waves

Analytical solutions of a linear internal-tide generation problem are presented for a stratification that involves both an interface (thermocline) and a lower layer of constant stratification. It is shown that an internal tidal beam scatters strongly at a moderately developed thermocline but much less at a thermocline that is either very weak or very strong. This scattering goes along with a local wave activity at the thermocline as well as with a downward leaking from the thermocline. It is argued that these processes offer a clue to explaining observations in the Bay of Biscay of ‘local generation’ of internal soliton packets. This is substantiated by numerical results from a nonlinear nonhydrostatic model, which is derived in this paper. Also, the effects of Coriolis dispersion are discussed. It appears that the observations from solitary waves in the Bay of Biscay can be contrasted with those in the Sulu Sea, to which a different stratification regime applies. An interpretation is given in terms of the modal structure.

Determining Static Stresses of Deformed Solitons

An equation for the quasi-static soliton ansatz depending on an arbitrary set of collective variables is covariantly derived on the basis of the variational approach to the method of collective variables. The field configuration and the static stresses of the deformed $\Phi ^4$-kink that are produced by the excitation of the internal soliton mode are exactly determined. The kink interaction potential at large distances is considered for the example of the nonlinear Klein-Gordon system. A general approach to the problem of exactly determining the intersoliton potential for the entire set of physically admissible two-soliton configurations is discussed.

Damping of internal soliton modes in media with quadratic nonlinearity

Optical solitons in media with quadratic nonlinearity and frequency dispersion are theoretically analyzed. Internal soliton modes and the rate of their radiative damping as a function of detuning from the phase-matching condition and the nonlinear shift of phase velocity for different soliton dimensions (d=1, 2, 3) are found. The length of a nonlinear medium required to form a stationary soliton is determined.

Space-time sound fluctuations due to internal solitons in shallow water

In this paper results of numerical modeling of sound propagation in shallow-water waveguide with internal waves are presented on the basis of experimental data about internal solitons (IS) registered in the Japan sea [A. N. Serebryany, Sov. Phys. Oceanol. 27, 225–226 (1987)]. These IS constitute some sequences of oscillations with amplitude up to 10 m moving toward coastal line with the velocity about 0.25 m/s. The wavelength of separate oscillations in this group is about 325 m; total length of the packet is about 4 km. Three-dimensional sound-speed distribution is constructed using the mentioned data. On the basis of this model, space-time fluctuations of intensity of the sound propagating in such medium are calculated. The modeling is carried out within the framework of the parabolic equation method in the horizontal plane and the modal approach in the vertical one. These fluctuations can be interpreted as the forming of a sound waveguide in the horizontal plane; space-time scales of fluctuations correlate with space-time scales of IS. Different numerical examples are presented; possible experimental setup is discussed. [Work supported by RFBR, Grant 00-05-64752.]

Low-frequency horizontal acoustic refraction caused by internal wave solitons in a shallow sea

The effect of internal wave solitons on the sound field generated by a point source in a shallow sea is considered. In the framework of the theory of “horizontal rays and vertical modes,” the sound field pattern governed by the aforementioned hydrodynamic effect is investigated. It is shown that solitons can induce time-periodic focusing and defocusing of horizontal rays propagating at shallow angles to the internal wave front. This may result in the formation of “dynamical” horizontal sound channels, which, in its turn, results in considerable temporal fluctuations of the field along the acoustic track oriented along the internal wave front. For the sound field calculations, an approach is developed on the basis of the parabolic approximation in the horizontal plane and the mode representation in the vertical direction. The results obtained can be used for remote monitoring of internal wave packets in a shallow sea.

Rotation of orbital currents in the trains of internal solitons in the ocean

We analyze the results of measurements of currents in the trains of internal solitons on the New-York shelf of the Atlantic Ocean performed in the course of the Joint US/Russia Internal Wave Remote Sensing Experiment (JUSREX). It was discovered that the thermocline is characterized by an almost monotonic anticyclonic variation of the direction of orbital currents in the trains of solitons but the direction of waves in each train is practically constant. As a rule, the current significantly deviates to the left from the direction of waves in the leading soliton and approaches the indicated direction in the rear solitons of the train. The angular rotation current velocity corresponded to periods varying within the range 12–24h and, on the average, was close to the local inertial period. It is shown that this rotation cannot be caused by the distorting influence of advection of background shear currents but, most likely, is connected with the unknown properties of internal solitons in the rotating ocean.

Internal waves and temperature inversion in the East China Sea

Several shallow-water acoustics experiments were performed in the Zhoushan offshore area of the East China Sea from 1996 to 1998. The water depth is about 55 m at the mooring locations. Temperature chains sampling once per 6.4 s or 1 min provide the oceanographic data. One clearly sees the long-wavelength internal tides. The dominant component of the internal wave field is the semidiurnal tide of 10-m height. High-frequency internal waves with 10–15 min duration and 2-m amplitude ride on top of the internal tide. These rank-ordered waves are likely internal solitons, which is validated by recent SAR images. The asymmetry of the initial and final states indicates that the solibore description is somewhat applicable to this case, but more evidence is needed. The inversion phenomenon of temperature and salinity frequently occurs in the long and narrow East China Sea area off the coast of Jiangsu and Zhejiang. Temperature inversion is noted via the measurements and shows yearly variations. Its structure and generation mechanism are discussed. [Work supported by NSFC.]

Acoustic normal mode fluctuation statistics in the 1995 SWARM internal wave scattering experiment

In order to understand the fluctuations imposed upon low frequency (50 to 500 Hz) acoustic signals due to coastal internal waves, a large multilaboratory, multidisciplinary experiment was performed in the Mid-Atlantic Bight in the summer of 1995. This experiment featured the most complete set of environmental measurements (especially physical oceanography and geology) made to date in support of a coastal acoustics study. This support enabled the correlation of acoustic fluctuations to clearly observed ocean processes, especially those associated with the internal wave field. More specifically, a 16 element WHOI vertical line array (WVLA) was moored in 70 m of water off the New Jersey coast. Tomography sources of 224 Hz and 400 Hz were moored 32 km directly shoreward of this array, such that an acoustic path was constructed that was anti-parallel to the primary, onshore propagation direction for shelf generated internal wave solitons. These nonlinear internal waves, produced in packets as the tide shifts from ebb to flood, produce strong semidiurnal effects on the acoustic signals at our measurement location. Specifically, the internal waves in the acoustic waveguide cause significant coupling of energy between the propagating acoustic modes, resulting in broadband fluctuations in modal intensity, travel-time, and temporal coherence. The strong correlations between the environmental parameters and the internal wave field include an interesting sensitivity of the spread of an acoustic pulse to solitons near the receiver.

Modeling mode arrivals in the 1995 SWARM experiment acoustic transmissions

As part of the Shallow Water Acoustics in a Random Medium (SWARM) experiment, a 16 element WHOI vertical line array (WVLA) was moored in 70 m of water off the New Jersey coast. A 400-Hz acoustic tomography source was moored some 32-km shoreward of this array, such that an acoustic path was created that was anti-parallel to the primary propagation direction for shelf-generated internal wave solitons. The presence of these soliton internal waves in the acoustic waveguide causes significant coupling of energy between propagating acoustic modes, creating fluctuations in modal intensities and modal peak arrival times, as well as time spreading of the pulses. Two methods by which acoustic propagation and scattering in soliton-filled waveguides can be modeled are presented here in order to understand and explain the scattering observed in the SWARM field data. The first method utilizes the Preisig and Duda [IEEE J. Ocean. Eng. 22, 256-269 (1997)] Sudden Interface Approximation (SIA) to represent the solitons. The second method, which is computationally slower, uses a finely meshed, "propagated" thermistor record to simulate the solitons in the SWARM experiment waveguide. Both numerical methods are found to generate scattering characteristics that are similar to the SWARM field data.

Thermal lenses and internal solitons in Chapala Lake, Mexico

Instrumental measurements of the circulation and thermic regimen of tropical Chapala Lake revealed the surface temperature variations in its eastern part. In all of the cross-sections, spatial variations of 3°C were ordinarily registered over a distance of just 100–300 m. The movements of the internal thermal front in the water body with 2°C fluctuation were registered at a buoy station. The front’s forepart was accompanied by intensive internal waves in the form of internal KdeV solitons. The front near the buoy station was formed by the movement of the warm water body coming from the eastern shallow part of the lake and stimulated by the morning breeze.

Internal waves and sound-speed distributions in the Yellow Sea

The theory of resonant scattering of sound by internal solitons in the Yellow Sea is well known [Zhou et al., J. Acoust. Soc. Am. 90, 2042–2054 (1991)]. However, the oceanographic measurements made were rather sparse. In this paper, the time dependencies and the vertical structures of the internal waves and the resulting sound speeds over a period of 49 h 49 min in a strong seasonal thermocline of the Yellow Sea are presented. A temperature chain, sampling once per 6.42 s and consisting of 32 sensors spaced 0.4 m apart, provides the data. It is found that the volume sound speeds are significantly perturbed in the presence of the internal waves. At a fixed depth, the sound-speed perturbations may exceed 45 ms−1. The mean sound-speed gradient is −8.3 s−1, but the gradient becomes −25 s−1 when the thermocline is the strongest. The sound-speed distributions show the diurnal periodicity of the internal wave activity. The 6-h component, with high-frequency fluctuations riding on top of it, is also clearly seen. However, the data give no evidence of the presence of solitons although the internal waves are indeed nonlinear. [Work supported by NSFC.]

On the adiabaticity of acoustic propagation through nongradual ocean structures

The adiabaticity of acoustic propagation is attractive for acoustic field description, data interpretation, and inverse scheme consideration. It is well known that, in general, the adiabaticity can be held for gradual medium, and the criteria of adiabaticity have been given by Milder (1969), Brekhovskikh (1973), and Brekhovskikh and Lysanov (1982), respectively. In this paper, the adiabaticity of acoustic propagation through nongradual ocean structures is investigated both theoretically and numerically. Here, the term nongradual means that the scale of the ocean structure M is smaller than the modal interference distance Dmn between mode ‘‘m’’ and mode ‘‘n.’’ Two examples of the nongradual ocean structures are discussed: (1) polar frontal zone with a width of about 2 km, and (2) internal solitons in shallow water with a width about 0.8 km. Comments on the criteria given by Milder and Brekhovskikh will be addressed. [Work supported by ONR and NOAA.]

An Autonomously Recording Inverted Echo Sounder: ARIES II

Abstract A self-contained instrument, the Autonomously Recording Inverted Echo Sounder (ARIES II), carrying two 250-kHz beam side-scan sonars and with the capacity to record sonar data sampled at 3.2 kHz for 168 h with the sonars operating with a pulse repetition rate of 2 Hz, has been constructed and tested in a mooring deployment that lasted for 25 days near the edge of the continental shelf west of Scotland. The mean water depth was 146 m. ARIES II was positioned at a mean transducer depth of 34.6 m with sonars directed upward at 20° to the horizontal to obtain acoustic returns from targets at or near the sea surface. The instrument was preprogrammed to record continuously over periods of 2, 4, and 13 h, the last to cover the M2 tidal cycle dominant in the area. Sonographs are presented to illustrate observations of surface waves and wave groups, internal solitons, rain showers, and Langmuir circulation. An analysis is made of the effects of surface waves, currents, and internal waves on the instrument...

The Coupling between Harbor Seiches at Palawan Island and Sulu Sea Internal Solitons*

Between 1989 and 1991 the authors made observations that confirm and elucidate the coupling between harbor seiches at Puerto Princesa on Palawan Island in the Philippines and tide-generated internal solitons in the Sulu Sea. Published tidal current predictions for Basilan Strait in the Sulu Archipeligo were used to produce an index to the daily ebb tidal flows near Pearl Bank where the solitons originate. The coherence between predicted maximum ebb tidal current speed and observed seiche activity was 0.60 and the phase lag between the two quantities closely matched published estimates of the time required for solitons to cross the Sulu Sea. Arrival of the Sulu Sea waves immediately offshore of Puerto Princesa in the form of internal bores corresponded in time to the initiation of harbor seiche activity. A more precise estimate of soliton travel time was determined from the time difference between predicted maximum ebb current and the initiation of seiche activity, and it was found to have a remarkably regular seasonal pattern, which can be largely explained by seasonal variations in Sulu Sea temperature and salinity stratification. Therefore, the timing of seiche events at Puerto Princesa can be forecast based on Sulu Archipeligo tide predictions and soliton travel time. In general, the fortnightly pattern of seiche magnitude follows that of tidal current predictions, but day-to-day deviations are common. Seiche magnitude varies seasonally with generally low activity during the winter (northeast) monsoon and usually maximum activity late in the summer (southwest) monsoon.

Are Solitary Internal Waves Solitons?

Results of fully nonlinear numerical simulations of the interaction of two mode‐1 solitary internal waves, both propagating in the same direction, are presented. After the interaction, two solitary internal waves emerge. The large wave is slightly larger than the initial large solitary wave, while the small one is slightly smaller than the initial small solitary wave. Some small‐amplitude trailing mode‐1 and mode‐3 waves are generated by the interaction.