Coastal trapped waves in a two-layer ocean: Wave properties when the density interface intersects a sloping bottom

Properties of coastal trapped waves when the pycnocline intersects a sloping bottom are studied using a two-layer model which has slopes in both layers. In this system there is an infinite discrete sequence of modes, and four different sorts of waves exist: the barotropic Kelvin wave, the upper shelf wave, the lower shelf wave and the internal Kelvin-type wave. They all propagate with the coast to their right in the Northern Hemisphere. The upper and lower shelf waves are due to the topographic-effect on the upper-layer and lower-layer slopes, respectively. Their motions are dominant in the respective layers being accompanied by significant interface elevations. The properties of the upper (lower) shelf wave are almost unaffected by the existence of a lower-layer (upper-layer) slope. The motion of the internal Kelvin-type wave is confined to the region around the line where the density interface intersects the bottom slope.The modes, except that with the fastest phase speed (the barotropic Kelvin wave), are assigned mode numbers in order of descending frequency. Characteristics of Mode 1 change with wavenumber; the upper shelf wave for small wavenumbers and the internal Kelvin-type wave for large wavenumbers (high frequencies). The higher modes of Mode 2 and above can be classified into the upper and lower shelf waves.     

Parameterization of the dispersion relation of internal waves using the data of hydrological soundings in the Tropical Atlantic

Dependences have been determined which connect the parameters of the dispersion relation of the lowest mode of internal waves with the integral characteristics of the seasonal thermocline when 10 min30 min, 20 mh150 m, and 0·4 m²/s² Q5·2 m²/s².Translated by Mikhail M. Trufanov.     

Geostrophic response near the coast

Geostrophic response of a two-layer fluid near a straight coast is investigated for a successive disturbance by the use of the inviscid, reduced gravity model. Poincare waves, coastal motion (which is trapped by the coast) and a geostrophic eddy are created. The energy of these motions is obtained. The manner in which the ocean responds is found to depend considerably on the way the disturbance is applied. When the water is supplied continuously to a calm upper layer adjacent to the coast, a quasi-steady geostrophic eddy is formed and its energy increases in proportion toT ² (T is the duration for which water is supplied). The energy of the coastal motion increases in proportion toT. When the water is supplied continuously into the upper layer from a certain portion of the coast, a geostrophic eddy is not formed. The coastal motion has the same structure as in the former case and its energy increases in proportion toT.     

Response of a two-layer ocean with a baroclinic current to a moving storm,part I

A storm moves with a constant speed parallel to a stationary geostrophic current which flows only in the upper layer of a two-layer, infinite ocean. It is assumed that the lower layer is motionless. The quasi-geostrophic approximation is valid for a moving speed less than 4 ms^–1 for a storm radius of 100 km. The primary change of the upper layer thickness is caused by the wind stress divergence and the time integral of the wind stress curl. A cyclonic storm generates upwelling in its wake. The effect of the stationary flow similar to a western boundary current is minor by an order of magnitude and noticeable only on the left edge of the flow. Scaling of equations of motion and continuity for a more general upper geostrophic flow leads to expansion with a parametera ²=gH _m(fL)^–2, whereg is reduced gravity,H _m is the maximum thickness of the upper layer,f is Coriolis' parameter andL is the storm radius. The zeroth order perturbations of transport and thickness do not include the stationary flow which appears only in the first order perturbations ina ². When there is a coast, the change of the interface near the coast is dependent on the time integral of the wind stress component parallel to the coast, thus leading to upwelling or downwelling according to the center being to the left or right of the coastline.     

Onset of coastal upwelling in a two-layer ocean by wind stress with longshore variation

On the assumption that motions of the barotropic mode are horizontally nondivergent, action of the wind stress with longshore variation on a two-layer ocean adjacent to the meridional east coast is studied. Only the equatorward wind stress is considered. Along the east coast, upwelling is induced by the direct effect of the coast and is confined in a narrow strip with the width of the order of the internal radius of deformation. The upwelling propagates poleward with the internal gravity wave speed. Coastal upwelling induced by the wind stress with longshore variation may be interpreted as the generation and propagation of internal Kelvin waves. Associated with the coastal upwelling, the equatorward flow in the upper layer and the poleward flow in the lower layer are formed as an internal mode of motions. When the bottom topography with the continental shelf and slope is taken into account, occurrence of the poleward undercurrent is delayed by a few days because of the generation of continental shelf waves. And, after the forcing is stopped, the shelf waves propagate poleward away from the upwelling region and the poleward undercurrent fully develops. At the margin of the continental shelf, another upwelling region is induced and propagates poleward.     

Evolution of an isolated eddy near a coast and its relevance to the “Kyucho”

The evolution of an isolated meso-scale eddy near a coast is studied numerically. In particular, it is found that the translation speed of the adjusted eddy is estimated well by the mutual induction mechanism adapted to a rotating stratified fluid. The nonlinear Kelvin wave excited during the adjustment process is also discussed in connection with the Kyucho, the sudden warming of coastal waters associated with swift currents.     

Transmission and reflection of planetary and topographic Rossby waves in a two-layer ocean

Transmission and reflection problems when kissing≓ occurs among planetary and topographic Rossby waves in a two-layer ocean are studied. The slope parameterS(=dh ₂/dx, whereh ₂is the thickness of the lower layer) is assumed to have constant values in the regionsx 0 andxL and to vary linearly with the increase ofx in the region0xL (refer to Fig. 2 in the text). Furthermore, a wave is entered fromx=– and kissing is assumed to occur in the region (0<)x _axx_b(<L).It is found that a wave of the same type as the incident wave is mainly transmitted when the width of the region in which kissing occurs,L _kiss(=tx _b–x_a), is smaller than _kiss=2/(¦K¦+ _y/2), whereK is a representative wavenumber in the regionx _ab, _y is they-component of , and is the frequency. WhenL _kiss is larger than _kiss, on the other hand, the main wave transmitted is of a different type to the incident wave. As an application, transmission and reflection problems of planetary Rossby waves are considered, and it is shown that when an external (internal) planetary Rossby wave is entered, an internal (external) one can be transmitted due to the effect of kissing.     

The generation of coastal undercurrents

Equilibrium conditions in anf-plane ocean evolve as follows after the sudden onset of winds parallel to a coast. At first the flow is two-dimensional-spatial variations are confined to a plane perpendicular to the coast-and the salient features in the forcing region are acceleration of a coastal jet in the surface layers in the wind direction, and offshore Ekman drift that causes coastal upwelling. Kelvin waves excited at the edge of the forced region establish equilibrium conditions by creating an alongshore pressure gradient that balances the wind so that the acceleration stops. The vertical structure corresponding to each vertical mode differs from that of the wind-driven coastal jet so that the arrival of the barotropic Kelvin wave starts to accelerate a coastal undercurrent in a direction opposite to that of the wind. Subsequent baroclinic Kelvin waves modify the vertical structure of the coastal current so that the undercurrent in the subsurface layer is accelerated. In an inviscid model there is a singularity in the surface layers at the coast ast→∞ because the Kelvin modes with small offshore and vertical scales travel slowly and take a very long time to make their contribution to the establishment of equilibrium conditions. A modest amount of friction eliminates this problem. Nonlinearities are important in the heat equation and affect sea surface temperatures significantly but their effect on the momentum balance is secondary.     

The mechanism of the development of wind-wave spectra

The mechanism of the development of wind-waves will be proposed on the basis of the observed wave spectra in the wind tunnels and at Lake Biwa (Imasato, 1976). It consists of two aspects: One is that the air flow over the wind-waves transfers momentum concentratively to the steepest component waves and the other is that the upper limit of the growth of a wave spectral density is given by the ultimate value in the slope spectral density. The first aspect means that the wave field has the momentum transfer filter on receiving the momentum from the air flow. Wind-waves in the stage of sea-waves receive the necessary amount of momentum by the form drag,e.g. according to the Miles' (1960) inviscid mechanism, through a very narrow frequency region around a dominant spectral peak. On the other hand, wind-waves in the stage of initial-wavelets receive it according to the Miles' (1962a) viscous model through a fairly broad frequency region around the peak. The upper limit ofS _max developing according to viscous mechanism is given byS _max =6.40×10^–4 k _max ^–2cm²s andS _max =2.03C(f _max )^–2cm²s(S _max is the power density of the wave spectral peak with the frequencyf _max ,k _max is the wave number corresponding to the frequencyf _max andC is the phase velocity).From the second aspect, the upper limit of the growth of wave spectral density is given by 33.3f ^–4cm²s in the frequency region of late stage of sea-waves. Therefore, the spectral peak, which has the largest value in the slope spectral density in the component waves of the wave spectrum, rises high over the line 4.15f ^–5cm²s. The energy is transported from the spectral peak to the high frequency part and to the forward face of a wave spectrum by nonlinear wave-wave interaction. This nonlinearity is confirmed by the bispectra calculated from the observed wind-wave data. In the stage of sea-waves, nonlinear rearrangement of the wave energy comes from a narrow momentum transfer filter, and, in the stage of initial-wavelets, it comes mainly from small corrugations and small steepness of the wave field.     

A numerical experiment of the M2 tide in the Yellow sea

Semi-diurnal tides in the Yellow Sea are calculated by integrating the shallow water wave equations with frictional and inertial terms.It is found that the results depend on the bottom friction. In the frictionless case the tidal range is unstably amplified because of the occurrence of resonance of the semi-diurnal tidal component in Inchon Bay. When the bottom friction is in the form of the square of velocity, the results agree fairly well with the observations.The following results are obtained. First, the tidal range is larger at the coast of the Korean Peninsula than at the China Coast. Second, resonance of the semi-diurnal tide occurs in Inchon Bay. Third, bottom friction is very important in the shallow ocean,i.e., when the bottom friction become large, the phase lag is retarded and the tidal range decreases.The amplitude and the phase lag calculated in this study agree well with the observations in the case of _b =_b ² V¦V¦, _b ²=0.0026, especially in the coast of the Korean Peninsula.     

Tides and tidal currents in the Tusima Strait

Tides and tidal currents in the Tusima Strait are described, and cotidal charts are re-edited on the basis of intensive analysis of observed data. Some remarkable features are revealed as follows;

Effects of longshore variation of coastline geometry and bottom topography on coastal upwelling in a two-layer model

Effects of the longshore variation of the coastline geometry and the bottom topography on coastal upwelling are discussed. Longshore variations of the topography cause local enhancing or weakening of upwelling in the process of the generation and propagation of internal Kelvin and the shelf waves.     

Response of a two-layer ocean with a baroclinic current to a moving storm,part II

A circular storm moves with a constant speedc along a geostrophic flow similar to a western boundary current in the upper layer of a two-layer ocean with the motionless lower layer. The linear inertia terms are retained. Effects of the current becomes more conspicuous for smallerc and insignificant forc above 10 m s^–1. The inertia effects are manifested in cellular patterns of the interface perturbations with cell lengths of(c–vf ^–1 in a wake of the storm with a radius of an order of 100 km, wherev is the current velocity. On the left hand edge where the flow has a strong shear, the interface displacements have large amplitudes which increase with a distance along the path in a wake of the storm. These disturbances propagate to the left of the edge within an angle of cot^–1 (c ²/gH₀–1), whereg is the reduced gravity andH ₀ is the depth of the interface at the edge of the current. Comparison with the observations during Typhoon Trix in 1971 south of Japan suggests that fluctuations of the daily mean sea level with several days' periods observed along the southern coast of Japan may be due to the stationary oscillations of the Kuroshio caused by the inertia undulations along its left edge or due to the propagating perturbations to the left.     

Numerical experiment on <Emphasis Type="Italic">Kyucho</Emphasis> around the Tango Peninsula induced by Typhoon 0406

A numerical experiment using a three dimensional level model was performed to clarify the mechanism generating a strong coastal current, Kyucho, induced by the passage of Typhoon 0406 around the tip of the Tango Peninsula, Japan in June 2004. Wind stress accompanied by Typhoon 0406 was applied to the model ocean with realistic bottom topography and stratification condition. The model well reproduced the characteristics of Kyucho observed by Kumaki et al. (2005), i.e., the strong alongshore current with maximum velocity of 53 cm s⁻¹ and its propagation along the peninsula with propagation speed of about 0.6 m s⁻¹ one half-day after the typhoon’s passage. Coastal-trapped waves (CTW) accompanied by downwelling were induced along the northwest coast of the peninsula by the alongshore wind stress. The energy density flux due to the CTW flowed eastward along the coast, and indicated scattering of the CTW around the eastern coast of the peninsula. In addition, significant near-inertial internal gravity waves were also caused in the offshore region from the west of the Noto Peninsula to the north of the Tango Peninsula by the typhoon’s passage. The energy flux density of the near-inertial fluctuations flowed southward off the Fukui coast, and part of the energy flux was trapped on the tip of the Tango Peninsula, flowing with the coast on its right. It was found that the strong current, Kyucho, at the northeastern tip of the Tango Peninsula was generated by superposition of the near-inertial internal gravity waves and subinertial CTW.     

Study on the chemical forms of radionuclides in seawater-III complexes of60Co with amino acids

Stability constants were determined for⁶⁰Co (II)-amino acid complexes in sodium perchlorate media at an ionic strength=0.67, using cation exchange resins. Stability constants were, for Co(II)-phenylalanine, log ₁=4.4, log ₂=8.2, log ₃=11.7, for Co(II)-histidine, log ₁=7.4. for Co(II)-valine, log ₁=4.3, log ₂=8.5, for Co(II)-proline, log ₁=4.1, and for Co(II)-tyrosine, log ₁=7.2, respectively. The abundance of Co(II)-amino acid complexes in seawater was calculated from these stability constants on the basis of chemical equilibrium, assuming the concentration of individual amino acid to be 10^–7 to 10^–8 mol l^–1. It was inferred that the Co(II)-amino acid complexes are probably not formed abundantly in seawater while inorganic species of⁶⁰Co(II) may still be dominant for a short period of time after discharge into seawater as liquid waste.     

Response of a two-layer ocean to typhoon passage in the western boundary region

Effect of the typhoon passage on the western boundary region of a two-layer ocean with bottom topography is studied. The ocean is initially at rest and is set in motion by a typhoon passing parallel to the west coast. Equations that represent barotropic and baroclinic modes of motions are solved numerically by means of the method of finite differences. Motions of the barotropic mode are assumed to be horizontally non-divergent. In this mode, an elongated vortex is produced by the typhoon and propagates toward the south after passage of the typhoon. Behavior of the vortex may be interpreted as continental shelf waves. It is found that the formation and propagation of continental shelf waves are hardly affected by the density stratification. As for the baroclinic response, the typhoon causes considerable interface displacements along its track. The interface displacements are associated with geostrophic motions and remain for long time, though they are formed on the continental slope. Besides the large scale baroclinic response, internal Kelvin waves are induced along the artificial east wall.     

Bispectra of spike-array type time series and their application to the analysis of oceanic microstructures

Bispectral analysis is applied to records of the vertical profile of the vertical temperature gradient in the oceanic thermocline in the San Diego Trough. The bispectra exhibit three notable features; (1) bispectral peaks at the points (0.2 m^–1, 0.2 m^–1) and (0.2 m^–1, 0.1 m^–1), (2) bispectral ridges along the lines ( ₁= ₀, ₂= ₀ and ₁+ ₂= ₀ corresponding to peak wavenumbers ₀ in power spectra, and (3) array of bispectral peaks of interval of 0.2 m^–1 The results are compared with the bispectra of several modeled time series of spike-array type. The periodicity of 5 m found in the records seems to have two meanings: spacing of predominant spikes and wavelength of predominant sinusoidal wave. If this indicates the existence of internal waves having a vertical wavelength the same as the scale of homogeneous layers, it would suggest the possible importance of internal waves in the formation and maintenance mechanisms of oceanic microstructure.     

On the relation between the growth rate of water waves and wind speed

Various wind velocitiesu _*,U _/2,U andU ₁₀ are correlated to the measured growth rate of water waves , whereu _* is the friction velocity of the wind, andU _/2,U andU ₁₀ are the wind speeds respectively at the heights /2, and 10m above sea surface (: wave length). It is shown that within a range of the dimensionless wind speed, 0.1<u _* /C<0.6, there are no appreciable differences in the correlations, whereC is the phase velocity of water waves. The present relation between andU shows qualitatively similar properties as the one obtained by Al'Zanaidi and Hui (1984); the growth rate for waves with rough surface is larger than that with smooth surface. However, our present relations give, for the both waves with different surface roughness, larger values by factors 1.71.8 than those given by Al'Zanaidi and Hui's relation.     

A field study of physico-chemical states of artificial radionuclides in seawater

The physico-chemical states of artificial radionuclides,⁹⁰Sr,¹³⁷Cs and¹⁴⁴Ce in seawater were investigated by radiochemical analysis of filtered and unfiltered seawater. The difference of radionuclide concentrations between unfiltered and filtered seawaters was defined as the particulate form radioisotope and its particle ratio was discussed.Practically no particulate⁹⁰Sr, greater than 0.22 in size, was observed in both coastal and open seawaters, but some of¹³⁷Cs seemed to be insoluble in some circumstances, especially in coastal waters. A considerable amount of¹⁴⁴Ce was found to be particulate.An estimation of the radionuclides in particulate form was made for Kashima-nada seawaters collected in 1970 to 1972, and it was shown that the possible occurrence of particulate radionuclides, greater than 0.22 in size, were 1% or less for⁹⁰Sr and 6% for¹³⁷Cs. In the coastal water, 80 % of¹⁴⁴Ce were seemed to be in particulate form, but in the open seawater only a few%. The influences of suspended materials to¹³⁷Cs and¹⁴⁴Ce concentration levels in seawater were not negligible and further investigations are desirable.