Effects of longshore shelf variations on barotropic continental shelf waves,slope currents and ocean modes

Effects of continental shelf bends, converging depth contours and changing depth profiles are discussed. Some analysis is carried out for previously unstudied cases. Separate oceanic interior and shelf flow problems are formulated for a sufficiently narrow shelf. The ocean interior ‘sees’ only an integrated shelf effect, typically increasing shelf-edge amplitudes, retarding longshore Kelvin-wave propagation and increasing natural mode periods by 0 (10%). On the local shelf, the flow matches to the ocean interior and is nondivergent. Effects on shelf waves and slope currents depend subtly on the nature of the longshore variations. Curvature and contour convergence do not per se imply scaterring or generation of shelf waves. Indeed, any depth h(ξ) where ▽² ξ(x,y) = 0 (a condition approximating longshelf uniformity in the topography's convexity) supports essentially the same shelf waves as do straight depth contours (DAVIS, 1983), and slope currents follow depth contours. Scattering results rather from breaks in analyticity of the depth profile. Hence calculations for small isolated features (necessarily highly convex or concave) may overestimate scattering, and superposition for realistic topography may lead to much self-cancellation among scattered waves. Otherwise, examples show a strong preference for scattering into adjacent mode numbers and into any shelf wave mode near to its maximum frequency. A shelf sector, where the maximum shelf wave frequency maxω is less than the frequency ω of an incident shelf wave, causes substantial scattering unless maxω and ω are very close. Adjustment of slope currents to changed conditions takes place through (and over the decay distance of) scattered shelf waves.     

Propagating tsunami wave and subsequent resonant response signals detected by HF radar in the Kii Channel,Japan

Signals from the tsunami waves induced by the March 11, 2011 moment magnitude (M_w) 9.0 Tohoku-Oki earthquake and from subsequent resonances were detected as radial velocity variability by a high-frequency ocean surface radar (HF radar) installed on the eastern coast of the Kii Channel, at a range of about 1000 km from the epicenter along the eastern to southern coasts of Honshu Island. A time–distance diagram of band-passed (9–200 min) radial velocity along the beam reveals that the tsunami waves propagated from the continental shelf slope to the inner channel as progressive waves for the first three waves, and then natural oscillations were excited by the waves; and that the direction of the tsunami wave propagation and the axis of the natural oscillations differed from that of the radar beam. In addition, spectral analyses of the radial velocities and sea surface heights obtained in the channel and on the continental shelf slope suggest complex natural oscillation modes excited by the tsunami waves.     

Continental shelf waves off the Fukushima coast

Past observations and theories have indicated the importance of the constitution of the lowest-mode of shelf waves to the velocity field. However, significant contributions of the higher mode waves to current velocity fluctuations in the vicinity of the coast are suggested in observational results obtained along the Fukushima coast in Pt. I of this study (Kubota et al., 1981). To understand the importance of the higher modes, the generation of shelf waves is investigated theoretically by two methods. First, the generation of long shelf waves by monochromatic forcing is examined, and it is concluded that near the coast the second mode's contribution to the longshore velocity is the largest for the Fukushima coast. Second, the response of shelf waves to broad-band forcing is investigated by taking the dispersive characteristics of shelf waves into consideration. It is concluded that shelf waves with zero group velocity are selectively excited if the forcing has a broad-band spectrum. According to observational results obtained along the Fukushima coast, the wind spectrum has a broad peak at about 100 hours (Kubota et al., 1981). Since the third mode of shelf waves has zero group velocity around the period of 100 hours, the third mode can be selectively generated off the Fukushima coast. From this it is suggested that the Fukushima coast is in the forced region and that observed current fluctuations are motions associated with the second- and third-mode shelf waves.     

Diurnal shelf waves off Hamada on San'in Coast

The tidal current data observed off Hamada on San'in coast have shown the diurnal tidal currents to be larger than the semidiurnal ones by a factor of 5–8, although the ratio (K₁+O₁)/(M₂+S₂) for the tidal heights at Hamada is 1.3. Furthermore, the diurnal currents are found to be more remarkable on the shelf slope than on the shelf. We consider such diurnal current features as being due to the vortical mode waves, and show that the broad shelf and steep shelf slope off San'in coast allow 1st-mode interior shelf waves (ISWs) at a diurnal-period. Using a simple shelf model, it is shown that ISWs occur in response to the seaward component of diurnal tidal oscillations on the shelf and their propagation originates from the western entrance of the Tsushima Straits.     

A numerical investigation of western boundary currents in subtropical and subpolar gyres with a barotropic model

Dynamics of western boundary currents in the subtropical and subpolar gyres are studied as a source-sink flow of barotropic fluid by means of numerical integration of the time-dependent non-linear vorticity equation. The bottom topography consists of a continental shelf of uniform slope (120 km wide) parallel to the straight western coast and a flat bottom of uniform depth. The steady solution in the case of low Reynolds number (Re≦100) shows the vorticity balance of the western boundary current between theβ-, diffusion-, and bottom relief terms. The cuspidated flow of the western boundary current in the subpolar gyre is observed as a compensating flow for the subtropical western boundary current separating from the western coast. In the case of Re=350, the zonal current separating from the coast meanders with the wave length of the stationary Rossby waves. It is shown that in the present model the separation of the boundary current is controlled by the planetary vorticity (f) of the fluid particle in the boundary flow, with which the same particle flows out the eastern wall at the corresponding latitude. The decrease of the efflux width increases the intensity of the non-linear overshooting of the boundary current separating from the western coast.     

地形对陆架拦截波性质及机制的影响

陆架波的性质如频散关系、形成机制等受地形影响。研究地形对陆架波的性质影响具有重要意义。基于陆架拦截波理论,数值计算了分段线性地形下不同宽度陆架上陆架拦截波的频散关系、长波假设下波动的相速度、阻尼情况下的波动耗散率以及强迫波的外力影响因子。分析了陆架宽度及坡度对自由及强迫陆架拦截波性质的影响。陆架宽度影响陆架拦截波的频散关系。陆架变宽,使得长波频散曲线的斜率增大。陆架宽度的增加使第一模态陆架拦截波有明显的性质变化:相速度增大,波动受辐散影响的程度变大,摩擦衰减距离增大,且风应力旋度在波动的生成机制中起到的作用渐强。在宽的陆架上,研究陆架拦截波的生成及强迫波的振幅时,应充分考虑风应力旋度的作用。第二、三模态波动的相速度受陆架坡度的影响较大,但摩擦衰减距离基本都在200km左右,几乎不随陆架宽度改变,属于局地波。     

Anomalous amplifications of semidiurnal tides along the western coast of Taiwan

By compiling all the tidal data gathered from island-wide results of simple harmonic analysis, anomalous amplifications of semidiurnal tides along the western coast of Taiwan are illustrated. The mechanisms are investigated both theoretically and numerically by applying the linear shallow-water wave equations. Waves trapped by a continental shelf and resonance of tidal co-oscillation are identified theoretically. Numerically, a two-dimensional finite element model is applied to real topography for tidal computations. The co-range and equi-phase charts of three main semidiurnal constituents (M₂, S₂, and N₂) and one diurnal constituent K₁ are calculated. Anomalous amplifications of semidiurnal tides that appear as partially standing waves are demonstrated.     

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.     

Direct measurements of coastal currents around southern New Zealand

Results are presented from direct measurements of subsurface currents at ten coastal positions around the southern half of New Zealand, and from geomagnetic electrokinetograph measurements of surface currents between these positions. Currents on the continental shelf were predominantly tidal. Strongest mean flows were found on the continental slope adjacent to areas where the continental shelf is narrowest. The flow on the west coast of the South Island was southwards south of 44° S, with a maximum mean speed at a depth of 100 m of 0.64 m.s^‐1. On the east coast of the South Island the flow was generally towards the north, with a maximum speed at a depth of 100 m of 0.21 m.s^‐1 near latitude 42° 30’ S.     

Reflection of a long wave from an underwater slope

Reflection of long sea waves from an underwater slope described by a power law is studied within the shallow water theory. The slope is connected with the flat bottom. This model allows us to estimate the roles of a pointwise reflection from the inflection point of the bottom profile and distributed reflection at the underwater slope. The case of the underwater slope described by the so-called nonreflecting beach (h(x) ∼ x ^4/3, where h is the depth of the basin and x is the coordinate) when the wave is reflected only from the inflection point (pointwise reflection) is specially considered. The reflection and transmission coefficients over the bottom topography were calculated, and it was shown that the sum of the squared absolute values of these values differs from unity for all profiles except the nonreflecting one. This difference is related to the distributed re-reflections (resonances) over the underwater slope that lead to the deviations in the wave height from the known Green’s law.     

Distribution,reproduction, and feeding of West African shrimp <Emphasis Type="Italic">Plesionika carinata</Emphasis> Holthuis, 1951 (Decapoda,Pandalidae)

Plesionika carinata is endemic in the West African tropical biogeographical realm and is distributed from the western Sahara coast (23°35′ N) to southern Namibia (29° S). A total of 263 individuals with a total carapace length of 31 to 71 mm have been studied. P. carinata juveniles are pelagic and occur over depths from 340 to 2000 m or more, mainly over the lower part of the continental slope in summer and over the upper part of the continental slope in autumn. Adults are mainly benthic and occur on the edge of the shelf and the upper part of the continental slope (at depths of 300 to 880 m). Ovigerous females have 750 to 3330 eggs 0.45–0.5 × 0.5–0.65 mm in size on pleopods. Plesionika carinata feeds on abundant micronectonic and macroplanktonic crustaceans (euphausiids and pelagic shrimps) at earlier pelagic stages; it is detritophagous/necrophagous and predatory near the bottom when adult.     

Correlation between the intensity of tsunami in the Black Sea and the magnitude of underwater earthquakes

We perform the analysis of tsunami waves in the shelf zone of the Crimean peninsula generated by underwater earthquakes whose epicentres are located near the lower boundary of the continental slope. For this purpose, we use a one-dimensional nonlinear dissipative numerical model of long waves. The investigated distributions of the depth of the basin correspond to four points of the south coast of the Crimean peninsula. We use the empirical dependences of parameters of the sources of tsunami waves on the magnitude of the earthquake obtained earlier for the Pacific Ocean. It is shown that the height, vertical climb, and duration of tsunami waves increase with the magnitude of the earthquake. For equal magnitudes of the earthquake, the highest tsunamis on the south coast of the Crimea are observed between Alushta and Yalta. We also deduced a generalized regression dependence of the height of tsunami waves near the coast on the magnitude of the earthquake. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Investigation of transformations of barotropic tides in the coastal zone

Within the framework of the linear theory of long waves, we perform the numerical investigation of transformations of a barotropic diurnal tide in the process of its motion from the deepwater region of the sea into the region of continental slope and shelf zone at any angle to the coast line. For a linear profile of the bottom of the continental slope and shelf, we establish dependences of the amplitudes and velocities of waves on the direction of propagation of the tidal wave and the latitude of the place. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Modelling tidal currents on the coast of Portugal

A tide circulation model of the Atlantic coast of the Iberian Peninsula has been constructed. This regional numerical model covers the whole continental shelf. The finite element computational grid is made of some 16,300 triangular elements with sizes ranging between 13 km (on the offshore boundary) and 1 km (near the coast), with local refinements on the continental shelf and in the area of Figueira da Foz. This site was selected as experimental site for the study of waves and currents in the frame of the MAST2/WAVEMOD research project.Boundary conditions along the three oceanic limits of this widely open domain are obtained from the North-Atlantic component of a World Ocean tidal numerical model known as FES94 [Le Provost, C., Genco, M.L., Lyard, F., Vincent, P. and Canceil, P. (1994) Spectroscopy of the world ocean tides from a finite element hydrodynamic model, Journal of Geophysical Research, Topex-Poseidon Special Issue]. A new radiation-like boundary condition has been introduced in the modelling system used (Telemac-2D), which solves the Shallow Water Equations (SWE), in order to interface the two models and to allow for the tidal wave to leave the northern limit without reflection. Model calibration has been performed on the dominating M₂ constituent. The introduction of the astral static potential generating the tide in the SWE improved this regional model.A long duration run (1 month) has been performed, the model being forced by the eight major tide constituents. Harmonic analysis of results has been performed on 17 tide constituents, due to non-linear interactions of constituents on the continental shelf. Comparisons with the FES94 model on one hand, and with a set of coastal tide gauges on the other hand, are good. A database of tidal harmonics is now available for forecasting sea levels and currents in this area.This work has shown that diurnal shelf trapped tide waves exist in some places along the Portuguese continental shelf, which induce diurnal dominant tidal currents in these places (North of Figueira da Foz).     

Patterns of K1 and M2 internal tides and their seasonal variations in the northern South China Sea

Seasonal variations of baroclinic tides for K₁ and M₂ constituents were separately studied using two-dimensional numerical simulations along the 21°N section of the northern South China Sea (SCS). Results show that the continental slope of the northern SCS and the west ridge of the Luzon Strait are supercritical to K₁ internal tides, which may be trapped in the deep basin of the SCS and form standing or partial standing waves. Meanwhile, these areas are sub-critical to M₂ internal tides, which can transmit onto the shelf and are seldom reflected back into the basin. The trapped K₁ internal tides are dominated by mode-2 and mode-3 in summer and by mode-1 and mode-3 in winter. Moreover, high mode K₁ internal tides account for nearly 20–40 % of the total energy density in winter and 15–20 % in summer. The pattern of K₁ internal tides in the basin is mainly determined by the percentage of reflected energy from the continental slope. The phase difference between the incoming mode-1 and mode-2 K₁ internal tides near the continental slope are nearly out of phase in winter, which means that the percentage of reflection of the K₁ internal tide is larger than that in summer. Both the convergence and high mode K₁ internal tides can enhance the vertical shear. The above results indicate that, in the deep basin of the SCS, water mixing potentially induced by internal tides in winter is stronger than in summer.     

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.     

Origin of theAbiki phenomenon (a kind of seiche) in Nagasaki Bay

Large oscillations of water level in Nagasaki Bay are calledAbiki and are most frequently observed in winter. The largestAbiki recorded in the past 20 years at the tide station at Nagasaki occurred on March 31, 1979. Simultaneously, a distinct atmospheric pressure disturbance of solitary type with an amplitude of about 3 mb was recorded at several neighbouring stations in Kyûshû, which indicated the pressure disturbance probably travelled eastward with an average speed of about 110 km h^–1.The quantitative relation between this pressure disturbance and notable seiches observed in Nagasaki Bay is examined by means of numerical simulation, and it is confirmed that the exceptionally large range of oscillations in the bay, which reached 278 cm at the tide station, was indeed produced by this travelling pressure disturbance.The leading part of shallow water waves induced by the atmospheric pressure disturbance was amplified up to about 10 cm in amplitude, over the broad continental shelf region off China, because of near resonant coupling to the pressure disturbance. After leaving this continental shelf region, the amplified water wave converged into the shelf region (Gotô Nada) surrounded by the north-western coast of Kyûshû and the Gotô Islands and excited eigenoscillations on the shelf. A train of waves thus formed with a period of about 35 min entered Nagasaki Bay and was resonantly amplified at periods of 36 min and 23 min which are the eigen periods of the bay. Besides resonance, the combined effects of shoaling and reflection inside Nagasaki Bay also enhanced the amplification.     

Downflow of the Antarctic shelf water at the shelf and continental slope of the Commonwealth Sea in the summer season and its effect on the bottom water formation in the Southern Ocean

In the summer seasons of 2004–2007, the intensive runoff (cascading) of the Antarctic shelf water (ASW) down the shelf and continental slope was revealed thanks to the recording of numerous thermohaline profiles across the shelf and continental slope of the Commonwealth Sea and Prydz Bay. The quickly executed profiles (4–10 h) with submesoscale resolution (near the shelf’s edge, the scale was even eddy-determinative, i.e., within 1.9–5.6 km), in combination with the fine-structure sounding and fine vertical resolution of the near-bottom boundary layer, provided a qualitatively new level of understanding the natural data. The detailed analysis of the temperature, salinity, and density patterns revealed the regularities and peculiarities of the ASW shelf and slope cascading. The intensive ASW cascading near the shelf break and lower part of the slope can be forced (appearing as discrete frontal meanders) or free (appearing as discrete plumes) and often has a wave-eddy character. The field observational data confirmed the obtained representative estimates of the elements of the ASW slope cascading. The basic area of the ASW formation is near the Amery Shelf Ice, from where the ASW spreads to the northwest, goes around the Fram Bank, and flows down the continental slope. The evaluative contribution of the ASW slope cascading to the ventilation of the deep and slope water of the Southern Ocean (near the shelf break 70 km long where the ASW cascading was observed) is Q _K = 0.04–0.24 Sv, which agrees well with the analogous estimates obtained in other regions of the Antarctic.     

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.     

Numerical experiment on the circulation in the Japan Sea

By using a two-dimensional barotropic model on a-plane, the effect of the bottom topography on the path of the Tsushima Current is investigated. The rectangular model ocean with continental slopes has two openings: one is located at the southern boundary and the other at the eastern boundary. In a steady state, most of the water supplied into the model ocean through the inflow opening, flows along the continental slope with the coast to the right. Continental shelf waves play an important role in the process of adjustment to a steady state. It is suggested that the nearshore branch of the Tsushima Current might be largely topographically controlled.