Water exchange and material exchange through a strait due to tidal flow

The process of material transport through a strait due to tidal flow is modeled, and then the differences between various concepts of tidal exchange which have been used hitherto are pointed out using this model. In particular, the exchange of water itself and the exchange of material should be distinguished even in the case where the material of interest is carried by the water,i.e., the material and water move as one body. Further, the physical meaning of “tidal trapping” (Fischeret al., 1979) is discussed by using the model in this paper. The relationship between the exchange ratio for the water itself (r) and the phase lag (δ) of material concentration to the tidal stream in a section of the strait, which is an important factor in tidal trapping, is obtained as follows: $$\delta = \tan ^{ - 1} \left( {\tfrac{1}{r} - 1} \right)$$ Observational results at Lake Hamana (Shizuoka Pref) and at Kabira Cove (Okinawa Pref.) support the validity of the above relationship.     

Year-to-year change in water exchange characteristics in a semi-enclosed bya,Lake Hamana

The year-to-year change in characteristics of water exchange between Lake Hamana, a semi-enclosed bya, and the adjacent open sea is investigated.The destruction of the bay mouth by a typhoon in 1953 and subsequent stabilization work on the bay mouth from 1954 to 1973 resulted in an increase in the tidal prism volume of the bay (Mazda, 1983). In the present paper, a simple model has been constructed in which the magnitude of water exchange depends on the tidal prism, and using this model, the year-to-year increase in salinity of the bay water after 1953 can be well explained. Consequently, it can be said that the salinity increase after 1953 is a result of a progressive increase in water exchange caused by successive changes in topography of the bay mouth.The extent of water exchange in Lake Hamana, which varies seasonally, has increased gradually since 1953, and became stable after about 1967. For instance, at present the turnover time of the bay for exchange with open sea water reaches a maximum (2.9 months) in January and a minimum (0.9 month) in October, while in 1955 it is estimated to have been about 2.5 times that at the present time.     

Water exchange in Kabira Cove,Ishigaki Island

The mechanism and rate of water exchange were investigated in Kabira Cove, Ishigaki Island, in the southernmost part of Japanese islands, near Taiwan. During observations in the summers of 1976 and 1977, a larger proportion of the salt transport into the bay was derived from the so-called “tidal trapping effect”. In the latter period of observation carried out after heavy rain brought by a seasonal typhoon under annual mean tidal conditions, the turnover time, i.e. the scale of replacement of the whole bay water with the open sea water, is estimated to be 3.6 days. Based on these observational results, a concept of the tidal trapping due to coupling of the actions of tides and buoyancy in a vertical two-dimensional field with a sill at the bay mouth is proposed. Considering the topographical, hydrometeorological and geographical conditions of the cove, it is inferred that this water exchange process tends to be formed in Kabira Cove in summer except during neap tides.     

The concept of tidal exchange and the tidal exchange ratio

The principal character of the tidal exchange process is neither diffusion nor advection, but a third category of transport, “Massenaustausch”, which appears in the space/time averaged transport. The exchange process can be divided into four fluxes: the flux of standing eddies, the flux of tidal exchange, the flux of tidal eddies and the flux of local eddies. The results of observations at the entrance channel of Kumihama-Bay show a typical example of transport dominated by tidal exchange. The tidal exchange ratio defined by Parkeret al. (1972) applies to the process of exchange between the outflowing watermass and the surrounding watermass outside of the bay mouth, but this should also be considered as being coupled with the ratio for the process of exchange between the inflowing watermass and the surrounding watermass inside of the bay mouth. These two exchange ratios can be combined into a single exchange ratio which describes the exchange process between the outer watermass and the bay water.     

Tidal residual circulation produced by a tidal vortex

“TIDAL VORTEX” is a term for a kind of starting vortex formed as a pair of vortices at the head of a tidal jet emanating from a narrow entrance into a bay. In this study, its formation and movement have been investigated by means of a hydraulic experiment and an analytical model. A tidal vortex is formed as a result of flow separation at the abrupt widening of a channel entrance followed by rolling up of the discontinuity surface around its free end. The vortex shows three types of life-history (type I, II and III), which are characterized by the Strouhal number and the aspect ratio of the horizontal shape of the entrance channel. In the case of type-I, the tidal vortex proceeds toward the inner region of the bay and there amalgamates with successive vortex cores into a core of tidal residual circulation. In the case of type-II, the tidal vortex core flows out into the entrance channel on the ebb but returns back into the bay on the subsequent flood. And, in the case of type-III, the tidal vortex core which was formed on the bay-side opening of the entrance channel flows out to the open sea and never comes back, whereas the core which was formed on the open-sea side of the entrance flows into the bay and never flows out. The circulation of a tidal vortex core is proportional to the reciprocal of the Strouhal number. The movement of the core near the bay entrance is determined by interaction between the cores and transportation due to the irrotational component of the tidal current. There are three types of tidal residual circulation, corresponding to three life-history types of tidal vortices. In the case of type-I, a strong tidal residual circulation is formed, but in type-II a small and weak circulation is formed. While, in type-III, the circulation having an inverse sense of rotation to that of type-I is formed.     

Tidal residual circulation produced by a tidal vortex

The role of the ‘tidal vortex’ in the mechanism of generation of tidal residual circulation is investigated for a bay with a narrow entrance channel. It is shown that the circulation of residual flow is produced not by the vorticity of the inflowing sidewall-boundary layer, but by a tidal vortex formed by rolling up of the discontinuity surface released from the flow separation point at the entrance. This tidal vortex is affected by the circulation of the inflowing water, that is the inflowing tidal vortex. A returning tidal vortex formed in the bay diminishes the circulation of the tidal vortex of the next generation, while the inflowing tidal vortex formed in the open sea increases it. These cases correspond to tidal vortex life-histories of type-II and type-III, respectively (Kashiwai, 1984a). Tidal vortices of each life-history type have different strength and produce residual circulation of different strength, corresponding to each type. The ratio of kinetic energy of residual flow to that of the tidal current through the bay entrance, that is to say the energy gain of the residual circulation, is proportional to the reciprocal of the Strouhal number, and its rate of increase depends on the life-history type of the tidal vortex. This explains the experimental observation reported by Oonishi (1977) and Yanagi (1978) that the energy ratio of residual flow to tidal flow increases with the Reynolds number not monotonously but goes through a maximum and a minimum at intermediate Reynolds number.     

象山港水交换特性研究

在验证良好的三维斜压潮流数学模型的基础上,以溶 解态的保守性物质为示踪剂,建立对流-扩散型的海湾水交换数值模型,计算了象山港水体半交换时间和平均滞留时间,并研究了斜压动力对湾内外水交换的贡献。研究结果表明,象山港水交换速度的区域性变化较大,水体半交换时间和平均滞留时间由象山港口门向湾顶逐渐增加,口门附近半交换时间在5d以内,平均滞留时间为5~10 d;湾顶水交换速度缓慢,水体半交换时间为30~35 d,平均滞留时间为35~40d。斜压动力对狭湾外段水交换影响较弱,对狭湾内段有较大的影响。     

A hydraulic experiment on tidal exchange

Tidal exchange through a narrow entrance channel was studied experimentally with the use of a simplified hydraulic model. The inflowing water mass, visualized with dye solution, exhibits the shape of a starting plume with a starting vortex pair at its head. Because of their periodical formation by the tide, these are called the tidal plume and tidal vortex pair. The axis of the tidal plume deflects and undulates with a period 2 to 9 times that of the tide. Together with this undulation, the vortex pair becomes asymmetric. A circulating flow is formed in the bay which affects the shape of the inflowing and outflowing water masses. A part of the inflowing water mass flows out during the subsequent ebb, and this outflowing portion can be divided into two parts. One is the water remaining in the entrance channel at high water which flows out during the first half of the subsequent ebb and the other is the water flowing round the bay in the circulating flow during flood that flows out during the latter half of the subsequent ebb. Both contribute to the exchange ratio, but we can estimate an upper limit for the exchange ratio by neglecting the latter outflow. This neglected portion is considered in the concept of the age composition of outflowing water. The age composition of the bay water shows the existence of intermittent effluence superposed on a trend in the age composition that is similar to that of the well-mixed case. From the analysis of a model consisting of a number of mixing tanks connected in series with a recycle flow, it is concluded that this intermittent effluence occurs in the case of weak mixing due to the effect of circulating flow in the bay but is negligible in the case of strong mixing.     

TIDICS—Control of tidal residual circulation and tidal exchange in a channel-basin system

A self-excited oscillation of tidal flow occurs in a tidal channel-basin system with a narrow and high speed inflowing tidal jet. The mechanism of this oscillation was examined through hydraulic experiments. Results show that the oscillation is caused by alternation in the strength of asymmetric residual circulation caused by a biased supply of vorticity by asymmetric tidal vortex pairs, and that the mechanism of alternation also depends on negative feed-back between the residual circulation and the vorticity supply.The unstable state of the flow suggested the possibility of controlling the tidal current and tidal exchange in the channel-basin system and this was confirmed experimentally. Under fixed tidal conditions and with fixed basin dimensions, the tidal residual circulation was controlled to form two strong clockwise and anticlockwise circulations or a single circulation by changing the shape of the bay entrance.     

Study of internal wave generation by tide-topography interaction

The generation mechanism of internal waves by a relatively strong tidal flow over a sill is clarified analytically. Special attention is directed to the role of the tidal advection effect, which is examined by use of characteristics. An internal wave which propagates upstream is gradually formed through interference of infinitesimal amplitude internal waves (elementary waves) emanating from the sill at each instant of time. In the accelerating (or decelerating) stage of the tidal flow, the effective amplification of the internal wave takes place as the internal Froude number exceeds (or falls below) unity because during this period the internal wave slowly travels downstream (or upstream) while crossing over the sill where elementary waves are efficiently superimposed. In fact, the variability in the internal wave field actually observed in a realistic situation (Stellwagen Bank in Massachusetts Bay) is shown to be satisfactorily interpreted in terms of this mechanism. Furthermore, by using this analytical model, the relation between the strength of the tidal advection effect and the resulting internal waveform is clarified. This theory is easily extended to include a vertically sheared steady flow. In this case, although the fundamental generation mechanism is the same as above, the amplitude of the elementary wave varies with time depending on the relative direction of the tidal flow and steady shear flow, so that the internal wave field over the sill differs markedly between the ebb and flood tidal phases. As an example, the internal wave generation process over the sill in the Strait of Gibraltar is qualitatively discussed on the basis of this analytical model. The effect of vertical mixing caused by breaking of these large-amplitude internal waves on the coastal environment is also pointed out. In particular, a brief discussion is made on the control of water exchange by the fortnightly modulation of tidal mixing processes at the sills and constrictions in channels connecting freshwater sources with the ocean.     

Fortnightly shifts of intrusion depth of oceanic water into Ise Bay

To clarify the time change in water exchanges between Ise Bay and the adjacent ocean, repeated hydrographic observations were conducted along the longitudinal section in Ise Bay. The results show that the mixing condition at the bay mouth (Irago Strait) changed fortnightly in summer. During the spring tides, the strait water below the pycnocline was well-mixed and nearly homogeneous. By contrast, it was weakly stratified during the neap tide. There is a strong negative correlation between the tidal range and the density difference between the upper and lower layers at the strait. In summer, the intrusion depth of oceanic water into the bay and consequent hydrographic conditions inside the bay changed frequently according to the tidal strength. During the spring tides a prominent bottom front was created at the bay mouth, indicating that the strait water, which is a mixture of oceanic and bay waters, intruded through the middle layer. On the other hand, during the neaps, cold and saline oceanic water intruded through the bottom layer into the bay. The intrusion depth is significantly correlated with the tidal range. It is considered that the wellmixed strait water, which has a density equivalent to the middle layer inside the bay, is lighter than the bottom bay water and thus intrudes through the middle layer during the spring tides, while insufficient mixing makes the bottom water at the strait heavier than the bay water, leading to the bottom intrusion during the neap tides.     

湾口建闸海湾水体交换及景观水位数值模拟

大幅度的潮位变动对近岸景观和亲水性有较大影响,为此往往在湾口建闸控制湾内潮位变动,通过设置景观水位改善以上问题,但这将带来湾内的水动力及水体交换条件下降。本研究以马銮湾为例通过潮流数学模型模拟,研究湾口开闸孔数、开闸位置及不同景观水位与湾内水动力和水体交换的关系。利用湾口闸门调度,在湾内形成大尺度环流提高水体交换效率,对马銮湾景观水位和闸门调度方式提出了建议,有效地解决了湾内潮差减小引起水体交换效率减低的问题。     

Particulate matter exchange across a Rjord sill

Recent studies have indicated the existence of a considerably higher planktonic biomass in the deep waters of the Saguenay Fjord as compared to corresponding depths in the adjacent St Lawrence Estuary on the other side of a shallow sill. The hypothesis that has been put forward to explain this phenomenon is related to the advection of near surface estuarine waters, at times very rich in particulate matter, over the entrance sill into the deeper waters of the fjord. Mixing processes associated with the development of a density flow, the presence of a hydraulic jump or other mechanisms are assumed to be responsible for the common occurrence of lower density subsurface water within the basin as compared to that penetrating over the sill.The exchange processes between the estuary and the fjord are described and an estimate made of the estuarine water volume that penetrates into the lower layer of the fjord over a semidiurnal tide cycle. From these calculations, the replacement time for the outer basin was estimated to range between one and four days. The biological characteristics of this water were used to establish a budget for particulate matter exchange which showed, in early August, a typical net input of ? 188 t of particulate organic carbon into the deep waters of the fjord over one tide cycle.     

胶州湾潮余流和物质输送之间的关系

基于MIKE21的HD模型,通过模拟得到胶州湾的潮流场,胶州湾在涨急时最大流速1.04m/s,落急时最大流速约为0.96m/s。胶州湾余流总体较小,平均为0.03m/s左右。并在湾内不同位置释放自由粒子,以MIKE21的Particle tracking模型计算出其在潮流作用下的运移轨迹,结果表明粒子大多数运移到湾内近岸区域,少部分在湾口区域附近;在潮流场基础上计算了欧拉余流场,并和粒子运移结果进行对比,表明欧拉余流场在区域流向比较一致时可以表示粒子运动的趋势,为物质迁移、控制污染等方面提供了一定的参考借鉴意义。     

A numerical study of a tide with four harmonic constituents at the open boundary

The tidal current in Kagoshima Bay is simulated by the two-dimensional subdomain finite-element method. At the open boundary, the sea level is forced to be oscillatory with a linear combination of the four harmonic constituents (M2, S2, K1, O1) of the tide. A calculation having only M2 sea level at the open boundary is also performed and the harmonic constants of M2 are compared with those calculated by the four components.In the calculated velocity vector, a large difference between the two maxima or the two minima in one day appears when the vector is directed to the open sea. On the other hand, when it is directed into the bay, the two extreme velocities are almost equal. In tide-killer residual flow, the flow pattern is almost independent of the tidal age; however, the absolute value of the current velocity depends on the tidal age. The pattern is nearly the same as that calculated by giving only M2 sea level at the open boundary.In relation to the nonlinear interaction, the kinetic energy ratio KER is defined by the ratio of kinetic energy of the induced harmonic components to that of harmonic constituents given at the open boundary. KER is large where the tidal current is disturbed by obstacles,e.g. along the west coast at the mouth of the bay and in the southern sea of Mt. Sakurajima. The distribution of KER seems to be independent of the number of harmonic constituents (one or four) given at the open boundary. The difference of kinetic energy of the M2 tidal constituent between the two calculations.i.e. with the open boundary conditions of four components (M2, S2, K1, O1) and of a single component (M2), is found to be large where the current velocity is large.     

Water exchange in a time-varying transport field

The average residence time and the remnant function which are quantitative expressions of water exchange in coastal waters are investigated in a timevarying transport field by using a simple model. It is shown that the influence of temporal variation on the average residence time and concentration is small, when the ratio of the period of variation to the average residence time in the average state is small, and the influence is large when the ratio is large. The results are applied to the Seto Inland Sea, Lake Hamana, and Osaka Bay.     

Fundamental study on the tidal residual circulation,II

The tidal residual circulation in a bay was investigated by means of a hydraulic model experiment. In addition to the experiment in the previous paper, some other experiments were carried out to study the effect of external parameters to the tidal residual flow. The ratio of the kinetic energy of tidal residual flows to that of tidal currents in the bay depends on the Reynolds number. With the training wall at the mouth, the vorticity transfer from the tidal current to the tidal residual flow sharply decreases. As a result the remarkable tidal residual circulation in the bay does not occur.     

Transport of suspended matter in a bar-built Danish estuary

The river Varde Å discharges into the bay of Ho Bugt on the western coast of Jutland forming a small, bar-built estuary. This paper deals with tidal fluxes of water and sediment in the Varde Å estuary.The inflowing water at flood tide is part of a turbidity maximum in the northern part of the bay. At high tide slack water the suspended material deposits inside the estuary. During ebb-tide it is resuspended, and the estuary bottom is washed clean coinciding with the influx of relatively pure freshwater from the drainage area.From one station in the estuary mouth, current velocities and concentrations of suspended material have been measured during 10 tidal periods covering all four seasons. It is shown how these data can be used in a quantitative calculation of the transport of water and suspended material through the cross-section of study.A model has been formulated which—based on half-tidal periods—quantifies the transport of water and suspended material through the estuary mouth.The model is calibrated on the basis of measurements made during the above-mentioned 10 tidal periods. The rather small number of measurements is to some extent compensated for by a carefully pre-arranged selection of tidal periods.The model is discussed in relation to the prediction of net suspended transport through the estuary mouth in different weather and tidal situations.     

Fundamental study on the tidal residual circulation—I

The tidal residual circulation in a bay was experimentally investigated with use of a hydraulic model. The model basin is a square bay of 5 m sides with a one-sided mouth of 1 m wide. The depth of the basin is 0.1 m. The tide of a six-minute period was provided by a tide generator of plunger type through the mouth. Tidal currents in the bay always flow in one direction though its strengths change according to the tidal phase, that is, a strong tidal residual circulation occurs in the bay. A similar flow pattern was observed to occur in a field with a horizontal boundary geometrically similar to the present model. The vorticity transfer from tidal current to residual flow is balanced with the vorticity advection of residual flow and the dissipation due to the viscosity.     

Stability analysis of a two-inlet bay system

The stability analysis for a double-inlet bay system is applied to an inlet system resembling Big Marco Pass and Capri Pass on the lower west coast of Florida. Since the opening of Capri Pass in 1967, the length of Big Marco Pass has increased from 2000 m in 1967 to 3000 m in 1988 and the cross-sectional area has decreased from 1200 m² in 1967 to 1000 m² in 1988. Since 1967, the cross-sectional area of Capri Pass has steadily increased and in 1988 was 700 m². Tides off the inlets are of the mixed type with a diurnal range of 1 m. The gross littoral transport rate in the vicinity of the inlets is estimated at 150,000 m³ yr⁻¹.For each inlet the maximum tidal velocities are calculated as a function of the gorge cross-sectional areas using a lumped-parameter model to describe the hydrodynamics of the flow. In the model it is assumed that the bay level fluctuates uniformly and the bay surface area remains constant. The velocities are used to calculate the tidal maximum of the bottom shear stress in each inlet as a function of the cross-sectional areas of the two inlets (=closure surface). Values of the equilibrium shear stress are derived from an empirical relationship between cross-sectional area and tidal prism for stable inlets along the west coast of Florida. Closure surfaces and equilibrium stress values are calculated for values of friction factors ranging from F=4×10⁻³ to F=6×10⁻³. Using the closure surfaces and equilibrium stress values, the equilibrium flow curve for each inlet is determined. The equilibrium flow curve represents the locus of the combination of cross-sectional areas for which the actual bottom shear stress in the inlet equals the equilibrium shear stress.Based on the equilibrium flow curves and the known values of the cross-sectional areas of the two inlets in 1988, it is expected that, ultimately, Big Marco Pass will close and Capri Pass will remain as the sole inlet with a cross-sectional area of 1250 m² and a maximum tidal velocity pertaining to a diurnal tide of 0.85 m s⁻¹.