Internal Kelvin Waves Research Articles

Effect of an internal Kelvin wave on sound propagation in a coastal wedgea).

Spatiotemporal variability of the low-frequency sound field in a coastal wedge in the presence of an internal Kelvin wave (IKW) is studied both experimentally and theoretically. The experiments were carried out in Lake Kinneret, Israel (also known as the Sea of Galilee) in August 2021, with a wideband sound source deployed near the shore and receiving vertical line arrays located at the lake's center. Parameters of the IKW were obtained earlier from long-term thermistor string measurements combined with conductivity, temperature, and depth data. The IKW initiated range-dependent vertical displacements of the thermocline with a maximum amplitude near the shore and almost zero amplitude in the center of the lake. It corresponded to a thermocline inclination angle of ±0.08° with respect to the horizontal. Temporal variations in depth-averaged acoustic intensity, reaching almost 8 dB, and remarkable changes in the normal mode composition were registered. These effects are explained based on simulations using a parabolic equation and normal mode models. The role of mode coupling in acoustic intensity variations is assessed.

Sound field variability and mode coupling in the presence of internal Kelvin waves in Lake Kinneret, Israel

Spatiotemporal variability of the low- and mid-frequency sound field in the presence of internal Kelvin waves (IKWs) was studied theoretically and in experiment in Lake Kinneret, Israel. The experiments were done in 2021, where sound field was being recorded during two days (two periods of IKW) using two synchronized vertical line arrays (VLAs) of ten hydrophones each and 10 m between them, deployed in the center of the lake (depth ∼41 m). Wideband linearly frequency modulated sound signals (300Hz–7 kHz) were transmitted from the source deployed near the shore (depth ∼11 m, distance 5.5 km from VLA). IKWs were registered with thermistor strings together with CTD. Sound speed profile is characterized by the thermocline located between 15 and 20 m of the depth with sound speeds 1510 and 1480 m/s above and below the thermocline, respectively. The sound propagation modeling was done using a Parabolic Equation and Normal Modes approaches, considering the real parameters of the gas-saturated bottom and the bathymetry. Results show strong mode coupling along the acoustic track, initiating ∼12 dB variability of the sound intensity. Results of modeling are verified in the experiment. [This work was supported by RFBR, grant 20-55-S52005.]

Variability of the sound field in the presence of internal Kelvin waves in a stratified lake: The Sea of Galilee as a case study

The spatiotemporal variability of low- and mid-frequency sound field in the presence of internal Kelvin waves (IKWs) was studied in the Sea of Galilee. Experimental measurements of the sound field were carried out using a vertical line array (VLA) consisting of ten hydrophones with 3 m spacing. The VLA was deployed in the deepest (37 m) part of the lake. Signals were transmitted from the source deployed at the peripheral lake location at a distance of 5.5 km from the VLA at 8-m depth. Linear frequency modulation pulses (300–2000 Hz) were transmitted with 5 sec intervals during >24 h (the period of the IKWs). IKWs were registered using three thermistor chains (TCs) positioned along an offshore transect at 10-m, 20-m, and 37-m station depths. This setting allowed us to characterize the variations of the thermal structure and the corresponding sound speed profile along transect. The vertical structure of the sound field registered with the VLA shows connection with temporal variability of IKWs. The modeling of sound propagation was done using a Parabolic Equation (PE) method, taking into account the parameters of bottom and lake bathymetry. The PE results showed close agreement with our experimental measurements. [Work supported by Israel Science Foundation.]

Interference pattern of the sound field in the presence of an internal Kelvin wave in a stratified lake.

Internal Kelvin waves (IKWs) initiated by rotation of the Earth are one of the main hydrodynamic phenomena in large stratified lakes where baroclinic Rossby radius of deformation is smaller than the horizontal scale of the lake. IKWs can be identified using the spectra of internal waves, where in the presence of IKWs, the inertial frequency is at maximum. IKWs play a rather important role in the lake's dynamics for different processes, both in the water layer and sediment, especially at the periphery of lake. Due to influence of internal waves on the sound propagation, acoustical methods can be used for estimation of behaviour of IKWs. In this paper, the spatiotemporal variability of the mid-frequency (∼1 kHz) sound field in the presence of IKWs in a deep stratified Lake Kinneret is studied using numerical simulations based on normal-mode theory. Due to the specific character of perturbation of the water layer, IKWs can cause specific variations of interference pattern, in particular, a significant shift of the sound interference pattern both in spatial and frequency domain. These shifts can be easily measured and used for reconstruction of IKW parameters.

Fluctuations of arrival time and frequency shifts of a wideband sound signal in the presence of coastal internal Kelvin waves in shallow water

Internal Kelvin waves (IKWs) in a near shore area of shallow water with a curvilinear coastal line (gulf, lake, and channel) where the radius of curvature can be about 5–30 km are considered as a reason for the sound field variability. Amplitude of the thermocline vertical displacement due to IKW in such an area changes along the distance from the center of this circle (minimal value, about null) to the coast (maximal value, up to 5 m). Numerical simulations are implemented to study the effect of IKWs on the propagation of acoustic waves generated by a wideband (0.7 to 1 kHz) sound source. The results of the simulations show that the signal propagation time changes up to 1% following the thermocline displacement caused by IKW. Also, considerable shifts (more than 30% of the central frequency) of the interference pattern in the frequency domain are observed. The shifts change with distance from the shore and have opposite directions for positions of a single hydrophone receiver above or below the thermocline. Analytical estimates are obtained; experimental setup and a possible scheme of monitoring IKW are discussed. [Work was supported by RFBR and BSF.]

Fluctuations of the sound field in the presence of internal Kelvin waves in a stratified lake

In stratified lakes internal waves has great ecological significance since they affect mixing, resuspension, material transport, chemical regime and ecosystem productivity. Reconstruction of spatio-temporal heterogeneity of the basin scale internal waves and their accurate parameterization are important tasks. The effect of internal Kelvin waves (IKWs) on spatiotemporal variability of the mid-frequency (1 kHz) sound field in a deep lake using geoacoustic modeling is studied. It is demonstrated that IKWs cause significant fluctuations of the sound field, such as horizontal shift of interference structure. This shift can be easily measured in situ and used for practical reconstruction of IKW parameters. Overall, it is suggested implementing the low-cost geoacoustic methodology for accurate parameterization of the basin scale internal waves and studying their dynamics.

A numerical study of water circulation in a thermally stratified embayment

Princeton Ocean Model is used to study the response of Jervis Bay, NSW, Australia, to the local wind and remote shelf coastal trapped wave (CTW) forcings in summer seasons when the water column is stratified by the water temperature. The study has revealed that the response of bay to the wind forcing is the generation of the wind driven currents and the internal Kelvin waves (IKW). However, both temperature and flow sub-inertial oscillations in the bay are weaker than those from the observations and the correlation between the modeled and observed low frequency currents is low. In response to the forcing of CTWs on the adjacent shelf, IKWs are also established in the bay and amplitudes of sub-inertial oscillations of temperature and currents agree better with the observations. It can be concluded that sub-inertial baroclinic flows in the bay is dominantly forced by remote CTW on the shelf adjacent to Jervis Bay during thermally stratified summer seasons.

The Baroclinic Response of Straits and Bays to Coastal-Trapped Wave Scattering

Abstract A result for the conservation of bottom pressure along coastal isobaths is used to show how coastal-trapped wave (CTW) energy may be scattered into baroclinic and barotropic motions within straits and bays. Central to this scattering problem is the decoupling of CTWs and internal Kelvin waves (IKWs) for broad flat shelves where the former are shown to be either barotropic at the coast or trapped out on the shelf slope and break. In this case, the horizontal gradients of incident CTW bottom pressure that map into vertical gradients at the strait or bay mouth may be represented as a set of IKWs. A pair of decoupled long-wave equations are derived to describe the approximate baroclinic and barotropic response of the strait or bay to forcing by these IKWs as well as the scattered CTWs on the adjacent shelf. The results are applied to Bass Strait where about 1% of the energy of a mode 1 incident CTW is shown to force a 10-day period IKW, with temperature and velocity oscillations of about 1°C and 20 c...

On Vertically Propagating Coastal Kelvin Waves at Low Latitudes

Abstract Vertically propagating coastal internal Kelvin waves (IKWs) forward by the alongshore component of the wind at the coast are studied, utilizing an f-plane model of a continuously stratified ocean with a vertical eastern boundary. With an infinitely deep ocean, several initial value problems that illustrate the basic properties of the forced flow are presented. For a wind stress at the surface that is localized in time and space, changes in amplitude and frequency with depth are predicted. Far from the forcing region, the response represents a non-uniform wavetrain of free IKWs characterized by local frequencies and wavenumbers. The group velocity vector is directed downward and poleward while the phase propagation is upward and pole-ward. For forcing by a traveling wind with fixed frequency σ and horizontal wavenumber l and with step functions at an alongshore location y = 0 and at t = 0, the response near and far from y = 0 has a different qualitative behavior. Near y = 0 a maximum in alongshore...

Some results of observation of the long-period internal seiche in Lake Biwa.

Seasonal change of the internal seiches' period will be treated by the spectrum analysis of the continuous temperature records which were obtained from the thermistor-buoy stations in Lake Biwa.The dominant period almost coincides with theoretical one which can be derived from a longitudinal internal seiche in a two-layered rectangular lake, but the observed spatial phase difference and amplitude cannot be explained reasonably by the concept of a simple longitudinal internal seiche. They rather correspond to the rotating internal KELVIN wave, which was found out from the numerical experiments in the preceding paper (6). The results of the “Round Cruise Survey” of the thermocline of Lake Biwa, which was carried out during the period from Aug. 9 to Aug. 13, 1973 shows that the dominant internal oscillation has a rotatory nature, that is, the high water region rotates along the lake shore in the anticlockwise direction with an apparent phase velocity of 2.2km/hr (in August). Such a rotatory behavior of the internal oscillation enables us to interpret reasonably the results of the spectrum analysis of the temperature records.