THE DYNAMIC OF INTERNAL WAVES IN LAKE SHIRA

In a large deep lake, the generation of internal Kelvin waves and internal Poincaré waves due to wind stress on the lake surface is a significant phenomenon. These internal waves play a crucial role in material transport within the lake and have profound effects on its ecosystem and environment. Our study, which investigated the modes of internal waves in Lake Biwa using the vertical temperature distribution from field observations, has yielded important findings. We have demonstrated the applicability of the frequency equation solutions, considering the Coriolis force. The period of the internal Poincaré waves, as observed in the field, was found to match the solutions of the frequency equation. For example, observational data collected in late October revealed excellent agreement with the theoretical solutions derived from the frequency equation, showing periods of 14.7 h, 11.8 h, 8.2 h, and 6.3 h compared to the theoretical values of 14.4 h, 11.7 h, 8.5 h, and 6.1 h, respectively. However, the periods of the internal Kelvin waves in the field observation results were longer than those of the theoretical solutions. The Modified Mathew function uses a series expansion around qi=0, making it difficult to estimate the periods of internal Kelvin waves under conditions where qi>1.0. Furthermore, in lakes with an elliptical shape, such as Lake Biwa, the elliptical cylinder showed better reproducibility than the circular cylinder. These findings have significant implications for the rapid estimation of internal wave periods using the frequency equation.

The results of a theoretical and experimental investigation of the phase structure of three-dimensional internal waves in a horizontal channel occupied by an exponentially stratified fluid are presented. The stationary internal waves excited by a source moving uniformly along the bottom of a channel with rigid covers are considered. A dispersion relation, on the basis of which the phase structure of the internal waves in the far zone is investigated, is obtained within the context of the linear theory. The dependence of the boundary of the region of wave disturbances on the internal Froude number F is found. The equation of the lines of constant phase is obtained in the first approximation for large F. By means of an IAB-451 shadowgraph instrument, using the dark field method with vertical illumination, the phase patterns of the internal waves are obtained. The angles of the wave disturbance zone are measured in the region of relatively large F. Similarity of the phase patterns for the first three-dimensional mode is obtained experimentally for large F.

In boundary areas of the World Ocean, a semidiurnal tide propagates in the form of a Kelvin wave mode trapped by the coastline. Over wide continental shelves, the semidiurnal tide is no longer a pure Kelvin wave but attains features of a zero-mode edge wave. As a result, the wave structure and the alongshore energy flux concentrate over the continental shelf and slope topography and become very sensitive to the variations of shelf geometry. When a semidiurnal Kelvin wave encounters alongshore changes of the shelf width, its energy scatters into other wave modes, including internal waves. A particularly strong scattering occurs on wide shelves, where Kelvin wave structure undergoes significant modifications over short alongshore distances. These dynamics are studied using the Regional Ocean Modeling System (ROMS). This study found that when the alongshore energy flux in the Kelvin wave mode converges on the shelf, the offshore wave radiation occurs through barotropic waves, while for the divergent alongshore energy flux, internal waves are generated. Under favorable conditions, more than 10% of the incident barotropic Kelvin wave energy flux can be scattered into internal waves. For the surface-intensified stratification mostly the first internal mode is generated, while for the uniform with depth stratification, multiple internal modes are present in the form of an internal wave beam. A nondimensional internal wave scattering parameter is derived based on the theoretical properties of a Kelvin wave mode, bottom topography, and stratification.

In this paper, data from the Barents Sea stationary acoustic range experiment carried out in October 1983 are analyzed. The experiment used a tonal acoustic source at 100 Hz and a horizontal array that consisted of 48 hydrophones extending over 450 m, mounted on the bottom. From the measured phase difference between a reference signal and the signal received by the individual hydrophones, phase front fluctuations have been obtained. Continuous measurements of the sound-speed profile showed fluctuations of the thermocline boundary caused by long period (3.5 h) internal waves with 10-m amplitude. Simultaneously, acoustic measurements were made of the deviations from linearity of the phase front along the array. Using spatial Fourier analysis, it was seen that the variability of the phase front showed several scales. To explain the spatial phase fluctuations we used results from a horizontal refraction theory for shallow water and a theory of phase dislocation in a waveguide [Kravtsov et al., Sov. Phys. Acoust. 30, 45–47 (1984); Sov. Phys. Acoust. 35, 156–159 (1989)]. Calculations showed that long period phase fluctuations were produced by long period internal waves and short period fluctuations were produced by the interference of direct waves and waves reflected from the shore. It was also possible to account for some of the parameters of the internal waves and the reflected waves.

Abstract. The design and implementation of boundary conditions for the robust generation and simulation of periodic finite-amplitude internal waves is examined in a quasi two-layer continuous stratification using a spectral-element-method-based incompressible flow solver. The commonly used Eulerian approach develops spurious, and potentially catastrophic small-scale numerical features near the wave-generating boundary in a non-linear stratification when the parameter A/(δc) is sufficiently larger than unity; A and δ are measures of the maximum wave-induced vertical velocity and pycnocline thickness, respectively, and c is the linear wave propagation speed. To this end, an Euler–Lagrange approach is developed and implemented to generate robust high-amplitude periodic deep-water internal waves. Central to this approach is to take into account the wave-induced (isopycnal) displacement of the pycnocline in both the vertical and (effectively) upstream directions. With amplitudes not restricted by the limits of linear theory, the Euler–Lagrange-generated waves maintain their structural integrity as they propagate away from the source. The advantages of the high-accuracy numerical method, whose minimal numerical dissipation cannot damp the above near-source spurious numerical features of the purely Eulerian case, can still be preserved and leveraged further along the wave propagation path through the robust reproduction of the non-linear adjustments of the waveform. The near- and far-source robustness of the optimized Euler–Lagrange approach is demonstrated for finite-amplitude waves in a sharp quasi two-layer continuous stratification representative of seasonally stratified lakes. The findings of this study provide an enabling framework for two-dimensional simulations of internal swash zones driven by well-developed non-linear internal waves and, ultimately, the accompanying turbulence-resolving three-dimensional simulations.

A numerical investigation into the bottom boundary layer flow and vertical structure of internal waves on a continental slope

Data from a thermistor chain and wind sensor collected over an annual stratification cycle in Lake Kinneret (Israel) during 2000 were used to investigate the seasonal evolution of wind/internal wave resonance. Internal wave periods determined from an analytical model were compared with observations, and we show that resonance during 2000 occurred during three distinct times of the year—at the onset of stratification (March), during the heating phase (June), and during the cooling phase (November). In all cases, resonance was between the wind and the dominant radial, azimuthal, and vertical mode‐one cyclonic (Kelvin) wave previously observed in Lake Kinneret.

Observations of internal waves and associated mixing phenomena in the Portimao Canyon area

The impact of subsurface currents induced by internal waves on nonlinear Stokes surface waves is theoretically analyzed. An analytical and numerical solution of the modulation equations are found under the conditions close to the group velocity resonance. It is shown that smoothing of the down current surface waves is accompanied by a relatively high-frequency modulation while the profile of the opposing current is reproduced by the surface wave’s envelope. The possibility of generation of an internal wave forerunner, that is a modulated surface wavepacket, is established. Long surface waves can form the wave modulation forerunner ahead of the internal wave, while the relatively short surface waves create the trace of the internal wave. Modulation of surface waves by the periodic internal wave train may have the characteristic period less than the internal wave period and be no uniform while crossing the current zone. Surface wave excitation by internal waves, observable at their group resonance is efficient only on the opposing current.

The resonant interaction between surface and internal gravity waves propagating along a uniform channel in a two-fluid system has been investigated both experimentally and theoretically. The wave coupling is induced by a shelf which runs along one side of the channel and large resonant internal waves are generated around certain frequencies. The shallow water approximation is used in the theoretical treatment of the problem and resonant frequencies and wave modes are calculated. Good experimental agreement is obtained near the resonant modes of low frequency, and the agreement deviated in the expected direction for higher frequency mode interactions. Measurements are also presented for the structure of the waves near the resonant frequencies. This is a laboratory model of a mechanism for the generation of long period internal waves in oceanic straits and channels.

Internal seiches play a significant role in a broad range of physical, chemical, and biological processes in lakes. A detailed assessment of the impact of seiching requires an understanding of seiche structure, which is determined by bathymetry and stratification. In this study, internal seiche solutions are evaluated for arbitrary bathymetry and continuous stratification using a two‐dimensional numerical model. Formulated in terms of a stream function, the model produces a finite set of linear internal wave eigenmodes and allows the computation of the complete velocity field (over a grid) associated with each seiche mode. Several idealized configurations of continuous stratification and variable bathymetry are used to explore the effect of nonuniform systems on internal wave structure. In particular, we focus on bed velocity distribution and the resulting potential impact on scalar fluxes, sediment transport, and internal wave damping. Model results are also compared to thermistor chain data collected in the Upper Mystic Lake (UML, Winchester, Massachusetts). Using an idealized description of the UML bathymetry and density profiles which emulate the seasonal variation of stratification in the lake, the evolution of bed velocities during the autumnal breakdown in stratification is assessed, providing insight into the fate of the contaminants entering the lake.

Oceanographic observations were made with a subsurface oceanographic mooring over the summit and flanks of two neighbouring seamounts in the tropical Indian Ocean to identify processes that may be responsible for the aggregation of silvertip sharks (Carcharhinus albimarginatus) in the deep water drop-off surrounding the summits. The seamounts, which are in the Chagos Archipelago in the British Indian Ocean Territories, are narrow in horizontal extent (<10 km), have steeply sloping (>15°) sides that rise from depths of > 600 m, and flat summits at a depth of 70 m. They are subjected to forcing at subinertial, basin-scales and local scales that include a mixed tidal regime and storm-generated near inertial waves. At the drop-off, at a depth of between 70 and 100 m, isotherms oscillate at both diurnal and semidiurnal frequencies with amplitudes of ∼ 20–30 m. The waves of tidal origin are accompanied by short period (∼5 min) internal waves with amplitudes O(10 m) and frequencies close to the local buoyancy frequency, N, within the thermocline which is the maximum frequency possible for freely propagating internal waves. The tidal oscillations result from internal lee waves with 30 m vertical wavelength generated by the prevailing currents over the supercritical seamount flanks, whereby the bottom slope is greater than the internal tide wave slope. The ‘near-N’ waves are due to enhanced shear associated with the hydraulic jumps that form from the lee waves due to the abrupt transition from steeply sloping sides to a relatively flat summit. The jumps manifest themselves as bottom-trapped bores that propagate up the slope towards the summit. Further observations over the summit reveal that the bores subsequently flush the summits with cold water with tidal periodicity. The bores, which have long wave phase speeds more than double that of the bore particle velocities, are characterised by intense vertical velocities (>0.1 m s−1) and inferred local resuspension but relatively little turbulence based on temperature overturns. Our results strongly implicate lee waves as the dynamic mechanism of leading order importance to the previously observed accumulation of biomass adjacent to the supercritical slopes that are commonplace throughout the archipelago. We propose that further investigation should identify the spatiotemporal correlation between internal wave activity and fish schooling around the summit, and whether such schooling attracts predators.

在实施一十大型国际合作项目(BITEX'93)期间,作者在琵琶湖进行了一个大规模的内波野外观测9台垂直系留的潮流观测及其旋转谱分析的结果表明:除了众所周知的开尔文波以外,在表层有风的日变化造成的周期为24h的顺时针旋转的强迫振荡在温跃层.Pomcare波的第一调式(mode)占主导地位.Poincare波使温跃层附近的潮流以周期16-18h顺时针旋转在底层,周期为11h的不旋转的重力波非常明显以上结果表明,在垂直方向的不同水层占主导地位的内波是不同的.利用潮流的观测来研究内波的周期变化是一个根重要的方法.该方法可以把Poincare波从重力披中区分出来地转效应是导致流场及风场旋转的根本原因.因此,控制该湖成层期内波的主要动力过程可归结为:风应力、成层、地转效应及湖岸制约.;Field observations on internal waves in the North Basin of Lake Biwa were carried out during Biwako Transportation Experiment (BITEX'93). Rotary spectrum analyses of current show that beside the fundamental internal Kelvin waves, in the top epilimnion, there were waves rotating clockwise witb a period of 24h wbieh are thought to be wind-induced oscillations. In the tbermocline, pure Poincare waves of their first mode were found, which were the governing mode at the depth. The Poincare waves made the current at that depth rotate clockwise with a period of 16-18h. In (he hypolimnion bottom, seiehes with a period of 11 h were found which were not rotating and purely gravitational. All of these illustrate that there are different kinds of governing internal waves In different vertical zones. Internal wave research by current measurement, an important method, can distinguish the Poincare waves from internal seiches. The earth rotation effects are responsible for the current rotation, as well as wind rotation phenomena. Thus, the important physical factors on internal wave dynamics during stratification period in the lake seem to he wind stress stratification, Coriolis force and shore constrained.

Internal waves were observed by measuring temperature variations of several subsurface layers at the innermost part of Suruga Bay from December 1968 to October 1971. Spectral energy densities of temperature fluctuations were computed from the records of the measurements. In the shorter period range from one minute to one hour, peaks of energy density were found occasionally in the range shorter than the minimum of VAisAlA periods computed from the vertical distribution of water density. It has been generally understood, however, that the periods of internal waves in a stable stratum should be within the range between the inertial and VAisAlA periods.

Lagrangian GPS drifter experiments, carried out in the surface layer of stratified Lake Kinneret (Israel), are presented. Differential kinematic properties and Lagrangian statistics were calculated and used to estimate the dominant mechanisms for horizontal dispersion. On time scales smaller than a few internal wave periods, internal waves lead to strong divergence and convergence events, causing instantaneous apparent horizontal growth rates that were larger, by up to an order of magnitude, than the actual mean dispersion coefficient. It is shown that the internal wave field modulated the vorticity field so as to satisfy conservation of potential vorticity. On time scales larger than a few internal wave periods, unbounded horizontal shear dispersion was of the same order as the actual mean observed dispersion coefficient (Kxy = 17.1 m2 s−1), while vertical shear dispersion was negligible.