Internal Kelvin Research Articles

Internal seiches in the strongly stratified Dead Sea

and 15° due West of South, respectively. The waves propagate southward along the lake's western shore, and this cyclonic propagation sense, as well as their dispersion relation, are reminis- cent of internal Kelvin waves. The extremely large density jump at the pycnocline and the accurate determination of its depth yield a very precise fit of the measured period of the internal seiches to theoretical predictions. These data show, for the first time, that the widely used linear dispersion relation of internal waves is valid even at large reduced gravity of the order of 10 -1 m·s -2 .

Numerical Experiments on Stratified Wind-induced Circulation in Tokyo Bay, Japan

During summer in Tokyo Bay, the upwelling of the anoxic water strongly affects eggs and larvae of fish and shellfish. The northerly wind causes the upwelling along the eastern coast and near the bay head and downwelling along the western coast. Numerical experiments were carried with a three-dimensional model to explain the wind-induced circulation in Tokyo Bay. When a uniform north-easterly wind is imposed at the sea surface, the circulation almost reaches steady state, due to geostrophic adjustment, after one inertial period from the beginning of the computation. A forced internal Kelvin wave, propagating with the land on the right, is found to have a great effect on the development of the steady state. When the observed variable wind is given as the surface boundary condition, the results of the numerical experiment agree qualitatively with data from both the sea-surface temperature obtained by satellite images and field measurements at moored stations in the bay.

Surface Seiches and Internal Kelvin Waves Observed Off Zadar (East Adriatic)

Two campaigns, comprising the measurements of temperature, salinity, currents and sea level, were performed in the Zadar and Pašman Channels during summer 1994. Basic dynamics, including tidal, wind-driven and residual circulation, are briefly considered here, but the paper concentrates on the surface seiche and internal Kelvin wave analyses and modelling. Surface seiches are found to be excited by strong meteorological disturbances in the late summer of 1994, with a period of approximately 2·2h and a sea-level and current amplitude of approximately 10cm and 9cms−1, respectively. Internal Kelvin waves, having a period of approximately 4 days and maximum surface currents of approximately 8cms−1, appeared during July 1994. The energy loss at the head of the basin, occurring due to the basin bathymetry, is analytically modelled by imposing the radiation condition there, both for the surface seiches and internal Kelvin waves, while the nodal line is enforced at the basin mouth. The modelled periods of surface seiches and internal Kelvin waves are 2·1h and 94h, respectively. The currents and sea levels agree fairly well with the observed values. Furthermore, the Defant numerical procedure, which allows for a variable basin bathymetry, gives slightly lower periods (1·9h for the surface seiches and 91h for the internal Kelvin waves) and moves the maximum current amplitudes towards the head of the basin in agreement with the observations.

Propagation of Kelvin waves along irregular coastlines in finite-difference models

In this paper, we examine the behavior of internal Kelvin waves on an f-plane in finite-difference models using the Arakawa C-grid. The dependence of Kelvin wave phase speed on offshore grid resolution and propagation direction relative to the numerical grid is illustrated by numerical experiments for three different geometries: (1) Kelvin wave propagating along a straight coastline; (2) Kelvin wave propagating at a 45° angle to the numerical grid along a stairstep coastline with stairstep size equal to the grid spacing; (3) Kelvin wave propagating at a 45° angle to the numerical grid along a coarse resolution stairstep coastline with stairstep size greater than the grid spacing. It can be shown theoretically that the phase speed of a Kelvin wave propagating along a straight coastline on an Arakawa C-grid is equal to the analytical inviscid wave speed and is not dependent on offshore grid resolution. However, we found that finite-difference models considerably underestimate the Kelvin wave phase speed when the wave is propagating at an angle to the grid and the grid spacing is comparable with the Rossby deformation radius. In this case, the phase speed converges toward the correct value only as grid spacing decreases well below the Rossby radius. A grid spacing of one-fifth the Rossby radius was required to produce results for the stairstep boundary case comparable with the straight coast case. This effect does not appear to depend on the resolution of the coastline, but rather on the direction of wave propagation relative to the grid. This behavior is important for modeling internal Kelvin waves in realistic geometries where the Rossby radius is often comparable with the grid spacing, and the waves propagate along irregular coastlines.©1998 Published by Elsevier Science Limited. All rights reserved

Wind‐forced upwelling and internal Kelvin wave generation in Mackenzie Canyon, Beaufort Sea

Low‐frequency current, temperature, and salinity variations over the shelf break in the southeastern Beaufort Sea (Mackenzie Shelf) are examined to determine the response of seasonally ice‐free waters to wind forcing and the role of submarine canyons in upwelling events and shelf circulation. Upwelling events were found to be statistically correlated to northeasterly winds, which transport surface waters offshore and draw up water from deeper layers. The response to alongshore wind stress is significantly amplified in Mackenzie Canyon, where isopycnal displacements of over 400 m are observed. Such displacements are then observed to propagate eastward at a phase velocity near 0.6 m s−1. The canyon is thus a site of intense upwelling, while the collapse of displaced isopycnals subsequent to cessation of wind forcing creates a disturbance propagating northeast along shelf as a free internal Kelvin wave.

SDP and LP fluctuations observed along the coast of Sagami Bay

Episodic and subtidal variations of current velocity and temperature are found in the mooring data obtained at seven stations in Sagami Bay during the summer-fall period, 1991. A detailed description of the episodic variation, which occurred from late July to 1 August, shows the intrusion of warm and saline water into Sagami Bay through Oshima east-channel, which causes the rise of sea level along the coast. The power spectra of the current and temperature records in the subtidal frequency range show that significant energy is found at the period of 2–7 days (SDP) and longer than twenty days (LP). The phase relation between eastward current and temperature fluctuations for SDP is different from that for LP. At the bay head, the temperature rise for LP is accompanied by a westward current in the surface layer. For SDP fluctuation, the phase relation between the near-surface, alongshore current and subsurface temperature implies the westward propagation of internal gravity waves. The SDP temperature fluctuations are larger along the bay coast than in the center of the bay, which is a characteristic of internal Kelvin waves. The SDP fluctuations propagate from east to west with the speeds of 0.32–1.16 m s−1, the propagation speed being larger at the eastern corner of the bay head than in the other area. A cross-correlation analysis between the local wind and temperature and/or current at the bay head show that the SDP fluctuations of temperature and current are induced by the local wind. The wind leads the temperature and/or current by about 12 h for the 2–3 day period (SDP2) fluctuations, and by about 2.5 days for the 5–6 day period (SDP5) fluctuations. A theoretical analysis using a two-layer model has been conducted to clarify the response of these SDP fluctuations to the periodic wind forcing. The SDP2 fluctuations observed in Sagami Bay are considered to be mostly generated along the east coast of the bay as a forced internal Kelvin wave by the local wind. In contrast, most of SDP5 fluctuations are caused by internal Kelvin waves propagating into Sagami Bay from outside, having an amplitude 2.5 times that of the forced internal Kelvin wave under local wind forcing.

Vertical Structure of Internal Waves in Lake Biwa, Japan

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.

Numerical Simulation of Internal Kelvin Waves and Coastal Upwelling Fronts*

Two three-dimensional primitive equation numerical ocean models are applied to the problem of internal Kelvin waves and coastal upwelling in the Great Lakes. One is the Princeton Ocean Model (POM) with a terrain-following (sigma) vertical coordinate, and the other is the Dietrich/Center for Air Sea Technology (DIECAST) model with constant z-level coordinates. The sigma coordinate system is particularly convenient for simulating coastal upwelling, while the z-level system might be better for representing abrupt topographic changes. The models are first tested with a stratified idealized circular lake 100 km in diameter and 100 m deep. Two bottom topographies are considered: a flat bottom and a parabolic depth profile. Three rectilinear horizontal grids are used: 5, 2.5, and 1.25 km. The POM was used with 13 vertical levels, while the DIECAST model was tested with both 13 and 29 vertical levels. The models are driven with an impulsive wind stress imitating the passage of a weather system. In the case of the flat-bottom basin, the dynamical response to light wind forcing is a small amplitude internal Kelvin wave. For both models, the speed of the Kelvin wave in the model is somewhat less than the inviscid analytic solution wave speed. In the case of strong wind forcing, the thermocline breaks the surface (full upwelling) and a strong surface thermal front appears. After the wind ceases, the edges of this thermal front propagate cyclonically around the lake, quite similar to an internal Kelvin wave. In the case of parabolic bathymetry, Kelvin wave and thermal front propagation is modified by interaction with a topographic wave and a geostrophic circulation. In both models, higher horizontal resolution gives higher wave and frontal speeds. Horizontal resolution is much more critical in the full upwelling case than in the Kelvin wave case. Vertical resolution is not as critical. The models are also applied to Lake Michigan to determine the response to strong northerly winds causing upwelling along the eastern shore. The results are more complex than for the circular basin, but clearly show the characteristics of cyclonically propagating thermal fronts. The resulting northward warm front propagation along the eastern shore compares favorably with observations of temperature fluctuations at municipal water intakes after a storm, although the model frontal speed was less than the observed speed.

The method of extracting current profiles from layered ocean models, applied to an oscillatory internal Kelvin wave with friction damping along the coast

The method of extracting current profiles from vertically integrated hydrodynamic models for fluids with uniform density is extended and formulated for a multi-layered ocean model with constant density in each layer. Current profiles are extracted from an oscillatory internal Kelvin wave with friction damping along the coast, and the influence of eddy viscosity with geographical latitude is investigated. The critical latitude singularity of the oscillatory equations of motion, where the inertial frequency equals that of the oscillatory motion, has no apparent effect on the horizontal distribution of the two-dimensional current. The current profile becomes extremely sensitive to the magnitude and the vertical variation of the eddy viscosity. The constant eddy viscosity in each layer produces most inaccuracy near the sea bed and across the internal interface, but can satisfy current consistency far from the critical latitude. At the critical latitude a linear increase of the eddy viscosity with height above the sea bed is essential in the near bed region in order to obtain depth-averaged currents consistent with the two-dimensional current. © 1997 Elsevier Science Ltd

Relationship of Internal Waves with Tide and Wind Drift Effects and Propagation of Internal Kelvin Waves in Brackish Lake Nakaumi.

An internal wave with an amplitude of about 2 m driven by tidal and wind drift effects is frequently observed in Lake Nakaumi. Highly saline water of the lower layer creeps up toward the lake coast driven by the internal waves, greatly affecting the general water quality and biological environment not only of Lake Nakaumi but also of the Ohashi River and Lake Shinji because of the upstream flow of highly saline water. In this paper, the effects of tides and wind drift on the internal waves were evaluated with the results of observations made with neutral buoys.Tides appear to clearly affect the internal oscillations only at the observation point near the Nakaura water gate ; the internal oscillation near the gate occurs with a phase lag of 1 hr after a water level change. The effect of wind drift on internal oscillation is clearly apparent near the upwind and downwind coasts. The halocline in the eastern littoral region of the downwind coast descends about 2.5 hr after a westerly wind starts to blow, while the halocline in the western littoral region of the upwind side rises about 3 hrs after the wind comes up.These phenomena agree well with the relationship between wind drift and inclination of the halocline in a two-layer lake model. The effect of wind drift on internal oscillation is greater than tidal effects, except for the observation point near the Nakaura water gate, because a dominant wind usually blows toward the east in Lake Nakaumi during summer. Cross correlation of observed displacement of the halocline between neighboring points and internal phase speeds calculated from density stratification conditions in Lake Nakaumi suggest that an internal Kelvin wave propagates counterclockwise along the coast.

Low‐frequency fluctuations in the Indonesian throughflow through Lombok Strait

A significant component of the Indonesian throughflow, apparently about 25%, passes through the Lombok Strait. Direct observations in 1985 reported a ∼2 Sv annual average, with an annual cycle of amplitude ∼2 Sv. There are also significant fluctuations in this transport in the 0.01–0.1 cpd frequency band. Shallow pressure gauge data (sea level) inside the strait during the current meter observations were of limited use in explaining the large fluctuations in currents. Sea level data at Cilacap, 720 km west (upcoast), however, overlap the current observations for 5 months and correlate exceedingly well (r = 0.87) with the observations inside the strait at these frequencies. These sea level oscillations in the Indian Ocean force fluctuations in the Lombok throughflow that reach 50–70 cm/s, equivalent to 2–3 Sv. Lagged regression analysis indicates Cilacap sea level leads Lombok currents by 1–2 days, suggesting a low‐frequency, progressive wave. Simultaneous data in 1989 from four stations extending from the near‐equatorial station at Padang at 1°S to Benoa in the Lombok Strait (2000 km downcoast) clearly show the persistent propagation of low‐frequency waves of 20‐ to 40‐cm range along this coast. Lagged correlation on station pairs indicates a phase speed consistent with coastally trapped internal Kelvin waves. We speculate that further eastward progression of these waves to the Timor Passage of Ombai Strait will further modulate the throughflow. The forcing of these waves is not yet identified, but it appears likely that intraseasonal oscillations in the equatorial Indian Ocean winds, as demonstrated by Enfield [1987] for the Pacific, are a probable mechanism. Improved wind data quality in 1991 due to the assimilation of satellite data (special sensor microwave/imager) will allow investigation of remote forcing on more recent data sets.

Internal Surge in Lake Biwa Induced by Strong Winds of a Typhoon

The detailed structure and evolution of current and hydrography after a wind storm, typhoon T9313, is described from an intensive field study. The study was done using current meters deployed at 8 stations, as well as 15 thermistor chains, in the southern part of the North Basin of Lake Biwa in summer of 1993. In the morning of 4 September, strong southerly winds with the maximum speed of more than 20 m ⋅see-1 blew over the lake. After the wind speed peaked, the cold water in the thermocline of the North Basin intruded into the South Basin. This intrusion of cold water was induced by the surface seiche which was generated by the winds of the typhoon. Then a large amplitude internal surge (a steepfronted depression wave on the thermocline) traveled from north to south along the west coast of the North Basin as an internal Kelvin wave. The internal surge shoaled over the southern slope of the North Basin and finally collided against the slope. When the surge shoaled over the slope, a strong jet of over 60 cm⋅s-1 was generated in the lower benthic layer (benthic jet). Assuming the internal surge as a moving internal jump, we explain the mechanism which induced the benthic jet. When the surge collided against the slope, a homogeneous mixed water mass was generated in the thermocline. After the collision, the internal surge was reflected to travel north along the east coast of the North Basin.

TOGA COARE IOPに赤道圏界面付近で見られた東進擾乱について

The three eastward-moving disturbances localized near the tropopause during January and February 1993 were investigated using JMA (Japan Meteorological Agency) global analysis data and the rawinsonde data at some stations during the TOGA COARE IOP (November 1992-February 1993). These events are considered to be part of the equatorial trapped internal Kelvin waves with upward energy propagation. These waves have large amplitude only in the several ten degree longitudes around the western Pacific. In January, the wave form is far from a sinusoidal one when the amplitude becomes very large. Change from the easterly to the westerly is much more rapid than change from the westerly to the easterly.

Difference in the prevailing periods of internal tides between Sagami and Suruga Bays: Numerical experiments

Current measurements in the surface layer in Sagami and Suruga Bays showed existence of significant tidal currents which are considered to be mainly due to internal tides (Inaba, 1982; Ohwaki,ea al., 1991). In addition, the prevailing period of the tidal currents is semidiurnal in Sagami Bay, but diurnal in Suruga Bay. To explain this difference in the prevailing, periods, numerical experiments were carried out using a two layer model. The internal tides are generated on the Izu Ridge outside the two bays. The semidiurnal internal tide propagates into Sagami Bay having characteristics of an internal inertia-gravity wave, while it propagates into Suruga Bay having characteristics of either an internal inertia-gravity wave or an internal Kelvin wave. The diurnal internal tide behaves only as an internal Kelvin wave, because the diurnal period is longer than the inertia period. Thus, the diurnal internal tide generated on the Izu Ridge can be propagated into Suruga Bay, while it cannot propagate into the inner region of Sagami Bay, though it is trapped around Oshima Island, which is located at the mouth of Sagami Bay. The difference in the propagation characteristics between the semidiurnal and diurnal internal tides can give a mechanism to explain the difference in the prevailing periods of the internal tides between Sagami and Suruga Bays.

Physical Limnology and Water Quality Modeling of North American Great Lakes

Abstract Physical limnological research relevant to large lake water quality issues conducted in the Laurentian Great Lakes over the last two decades is presented. Particular attention is given to Lake Ontario. Persistent boundary currents are observed near the north and especially the south shore. The coastal boundary layer characteristics are defined as well as coastal upwelling and coastal circulation characteristics, including the occurrence of internal Kelvin wave propagation following major upwelling events. In addition, fundamental turbulent diffusion characteristics, based on large scale experiments and specialized studies, are described.

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...

Trapped internal gravity waves in a geostrophic boundary current

The effect of a geostrophic boundary current on internal gravity waves is studied with a reduced-gravity model. We found that the boundary current not only modifies the coastal Kelvin wave, but also forms wave guides for short internal gravity waves. The combined effects of current shear, the boundary, and the slope of the interface create the trapping mechanism. These trapped internal gravity waves appear as groups of discrete zonal modes. They have wavelengths comparable to or shorter than the internal Rossby radius of deformation. Their phase speeds are close to that of the internal Kelvin wave. However, they can propagate both in, or opposite to, the direction of the Kelvin wave. The results of the present work suggest the possibility of finding an energetic internal gravity wave phenomenon with near-inertial frequency in a broad geostrophic boundary current.

The Scattering at Low Frequencies of Coastally Trapped Waves

The scattering of coastally trapped waves is described in a particular low frequency limit where the fundamental results are independent of the relative importance of stratification and rotation in the dynamics. Progress is made possible by restricting attention to frequencies small compared to a “profile” frequency, N0H/L that estimates the combined effect of the density and shelf profiles through the product of a typical buoyancy frequency N0 and the average shelf slope (for ocean depth H and shelf width L. Combined with results on the scattering of barotropic shelf waves, the present results describe scattering irrespective of the strength of any stratification provided solely that the frequency of the motion is small compared to either the inertial frequency or the profile frequency. In all cases the transmitted wavefield follows directly by tracing an incident pressure field along coastal isobaths. Strong notification is shown to suppress scattering at all subinertial frequencies, leading to particularly simple flow fields. At moderate stratification all energy is scattered forwards. An example is given where isobath tracing determines explicitly the amount of internal wave energy that passes over a ridge abutting a coastal wall. Various flows are possible if stratification is weak. In each flow the transmitted field is given by the barotropic connection formula. If the scatterer is conservative, this is the whole field. If the scatterer is nonconservative and the incident frequency is small compared to the profile frequency, so stratification dominates locally, then energy is carried forward in a narrow, intense boundary current. Over larger distances the current disperses into an internal Kelvin wave field. If the scatterer is nonconservative but the incident frequency is large compared to the profile frequency, then energy is dissipated or reflected as short barotropic waves. It is noted briefly that the results describe how coastal energy can split at the mouths of bays and straits and may be relevant to observations of long period motions near the Gulf of California and energy propagation through Bass Strait.

Coastal-trapped waves in elliptical lakes and around elliptical islands

Abstract The propagation of low-frequency waves, trapped around the shelves of lakes and islands, is investigated. A two-layer model with a simple step topography is used to study the combined effects of depth changes and stratification. The lake or island boundary and corresponding shelf break are modelled as confocal ellipses and analytical solutions for the barotropic streamfunction, interface displacement and dispersion relation are found. Results show the presence of a topographically modified internal Kelvin wave and a stratification-modified topographic Rossby wave. The model is applied to the small, elongated northern basin of Lake Lugano. Although the Rossby wave frequency is close to its barotropic value the two mode 1 dispersion curves “kiss” for very weak stratification with important effects on the wave structures and velocities. The velocity field of the observed 74th oscillation more closely resembles that of an internal Kelvin wave than a topographic Rossby wave.

On the generation of nonlinear internal Kelvin waves in a rotating channel

Recent observations have shown that islands and constrictions may be the sites of significant internal wave activity in sea straits. In this paper we examine one generation mechanism: resonant forcing by transcritical flow past topography. Experiments were conducted on the large rotating platform at the Coriolis Laboratory, Institut de Mécanique de Grenoble, Grenoble, France. A slender body was towed through a two‐layer stratified rotating channel, simulating the flow past an island or constriction in a strait. For a range of Froude numbers, blockage coefficients, and rotation rates, nonlinear internal Kelvin waves were generated upstream. The dependence of the wave parameters on the Froude number, Rossby number, and blockage coefficient was measured. The transition between subcritical and supercritical flow is found to occur at Froude numbers greater than unity, to depend on the blockage, but to be essentially independent of the internal Rossby radius of deformation. The results are compared with recent similar measurements of single‐layer flows in nonrotating channels, and good agreement is obtained. The nonlinear Kelvin waves which are generated upstream are found to be similar in all respects to those described by Renouard et al. (1987).