The radial s and ridges, which extend for 200 km latitudinally and 90 km longitudinally in the South Yellow Sea, cover a large part of the offshore area along the Jiangsu coast in China(Fig. 1). There are more than 70 radiating s and ridges with Jianggang Town as their focal point distributed northward to the Sheyang River estuary and southward to the northern branch of Changjiang(Yangtze)River Delta(Ren, 1986). For such huge submarine s and bodies, the unique hydrodynamic conditions must prevail, among which the rotary tidal wave system and the radial tidal current field are of particular significance(Zhang and Zhang, 1996). As the M ₂tidal constituent is dominant in the South Yellow Sea, its co-tidal chart(Fig. 1)represents the main characteristics of the tidal system(Zhang et al., 2013). Along the troughs between the radial s and ridges, the tidal currents present a periodic convergence to and divergence from the focal point located at the Jianggang Town. Accordingly, these tidal currents with radiating features in the radial s and ridges area are known as the radial tidal currents.

Fig. 1 Location and distribution of the radial s and ridges in the South Yellow Sea(left), and the co-tidal chart of the M2constituent(right)(modified after Zhang et al., 2013)

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Many investigations have been conducted to ascertain the temporal-spatial distribution and variation of the tidal system in the “ridge-channel” offshore area. Several numerical studies using bathymetric data(Zhu and Chen, 2005; Wang et al., 2011a; Xing et al., 2011; Kang et al., 2013; Song et al., 2013; Zhang et al., 2013)confirmed that there is a stable radial tidal current field acting as the main dynamic factor in the formation and evolution of the radial s and ridges. Two large scale field surveys(Ren, 1986; Zhang, 2013)also proved the existence of this radial tidal current field. Some numerical studies obtained a radial tidal current field similar to that observed one by schematizing the topography into sloped(Xia and Wang, 1984; Zhang and Zhang, 1996; Zhu and Chang, 1997; Zhu and Chang, 2001; Ye, 2012; Qian et al., 2014) and stepped(Yao et al., 2013)configurations. Numerical results obtained from the schematized models further demonstrated that the existence of the radial tidal current field is independent of the “ridge-channel” submarine topography. Following Zhang et al.(1999), most researchers have generally described the genesis of the radial tidal current field in this manner: the counterclockwise rotating tidal wave interacts with the incident tidal wave, which forms the so-called moving stationary tidal wave. The radial tidal current field is generated by the convergence and divergence of the stationary tidal wave. Although the stationary tidal wave was successfully simulated, several investigators(Shen et al., 1993; Ye, 2012; Yao et al., 2013; Qian et al., 2014)failed to reproduce the radial tidal current field with flat bottom topography. This illustrates that our underst and ing toward the formation of the radial tidal current field might still be incomplete and most likely omitting some fundamental processes. Meanwhile, the significance of the Shangdong Peninsula to the formation of the radial tidal current field in the South Yellow Sea is still a matter of debate. Most researchers(Huang and Wang, 1987; Zhu et al., 1998; Zhang et al., 1999; Li et al., 2001; Wang et al., 2011b)speculated that the Shangdong Peninsula is pivotal to the formation and maintenance of the radial tidal current field. They suggested that, without the peninsula, the area comprised of the radial s and ridges off the central Jiangsu coast would be characterized by an entirely different tidal current field. In contrast, several researchers(e.g., Su et al., 2013)have performed numerical simulations over the whole East China Sea with the removal of the Shangdong Peninsula. Those studies indicated that despite the shift in positions of the focal point of the radial tidal current field as well as the amphidromic point, the radial tidal current field is still maintained. These results challenge previous studies indicating a critical function of the Shangdong Peninsula in the development and maintenance of the radial tidal current field.

Current knowledge is thus still incomplete in explaining how the radial tidal current field emerges over the actual l and form, a schematized shelving slope, and a stepped topography. Also, the exact significance of the Shangdong Peninsula in the formation of the radial tidal current field has yet to be determined. Besides, the environmental variations such as coastline changes(Zhang et al., 2011; Wang et al., 2011c; Song et al., 2013) and bottom erosions(Chen et al., 2009; Huang et al., 2009; Zhou et al., 2014)have been occurring in the South Yellow Sea, and might have profound effects on the existing tidal system. This also leads to a critical question: what are the effects of the coastline changes and bottom erosions on the existing tidal system, especially with respect to the displacement of the amphidromic point and the focal point of the radial tidal current field? All these questions regarding the hydrodynamics and geomorphology in the radial s and ridges area were investigated in this study, using a semi-enclosed rectangular basin with and without a coastal barrier as a simplified representation of the Bohai Sea and Yellow Sea(Fig. 2). A 2D tidal model was set up using the DELFT3D-FLOW open source software. Several numerical experiments(Table 1)were carried out using various water depth and coastline advances. The results were comparatively analyzed to indicate the formation of the radial tidal current field and its possible changes under similar natural and anthropogenic impacts.

Fig. 2 Semi-enclosed rectangular basins schematized from the Bohai Sea and Yellow Sea a. without the Shangdong Peninsula; b. with the Shangdong Peninsula represented by a coastal barrier.

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Table 1 Conditions for the various numerical experiments

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The radial tidal current field in the South Yellow Sea was studied using a depth-averaged 2D tidal model in a semi-enclosed rectangular basin. The numerical model is based on the DELFT3D-FLOW open source software. The governing equations including one continuity equation and two momentum equations are described in the Cartesian curvilinear coordinates as follows:

The schematized semi-enclosed rectangular basin is 1 000 km long and 500 km wide(Fig. 2a). The coastal barrier, located at a distance of 450 km from the bay head, perpendicularly protrudes into this basin for 300 km(Fig. 2b). The average latitude of the basin was set to be 51.6°N. Rectangular grids with uniform size of 5 km×5 km were arranged in the Cartesian coordinates. Since the M ₂tidal constituent is dominant in the South Yellow Sea(Zhang et al., 2013), the open boundary can be approximately prescribed with analytical solutions(Fang and Wang, 1966)of the spatially and temporally varying water levels of the M ₂constituent as the driving force for the water body in the basin. In the numerical model, month-long water levels were specified at distance intervals of 50 km and at time intervals of 15 min for each location along the entrance of the basin. The bottom of this basin was considered to be impermeable and nonerodible. For the purpose of model intercomparison, parameters adopted in the present model were set to match the analytical solutions(Fang and Wang, 1966). Hence, a uniform depth of 68.4 m was employed for the basin. The horizontal eddy viscosity coefficient was set to nil and the Chezy coefficient to 50.6 m ^1/2/s . For initial conditions, a cold boot with initial water levels and flow velocities equaling zero was set in the computational domain. The tidal system in this basin was simulated for one month with the time step of 5 min. 2.2 Model intercomparison

Numerical results of the M ₂tidal constituent for case C1(Table 1)in the semi-enclosed rectangular basin with uniform water depth( d=68.4 m)were compared with the analytical solutions(Fang and Wang, 1966). The convection and diffusion terms were neglected in the analytical solutions, and the bottom frictional term and continuity equation were linearized. Figure 3 shows that the amphidromic system as well as the tidal current field simulated by the schematized model generally agree with the analytical solutions. The deviations of co-amplitude lines, co-phase lines, and current velocity vectors are mainly due to the differences between the numerical and analytical models in coping with the frictional term. The analytical model simplified the problem by defining the frictional term as proportional to the tidal current speed, while in the numerical model it was proportional to the square of the tidal current speed to account for its non-linear effect. The difference in the frictional term induces the time lags in the co-phase lines as well as smaller tide amplitudes and current velocities in the numerical solutions. The above analysis generates confidence that the numerical model is capable of producing reliable results and therefore can be employed to investigate the tidal wave system and the tidal current field within the semi-enclosed rectangular basin.

Fig. 3 Comparison of(a)iso-amplitude, (b)co-phase, and (c)instantaneous tidal current field(t=0.147 14T)charts for the numerical and analytical models of uniform depth The red lines/arrows denote the analytical solutions and the blue lines/ arrows represent the numerical results

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In this paper, we have concentrated on further explaining the formation of the radial tidal current field, and evaluating its possible responses under similar natural and anthropogenic impacts. Because of the complexity of the real submarine conditions in the Bohai Sea and Yellow Sea, we simplified the bottom topography into several continental shelves with various slopes(Fig. 4) and stepped topographies differing in water depth over the step(Fig. 5). We also schematized the coastal l and reclamations and subaqueous slope erosions into several seaward coastline protrusions(Fig. 6) and continental shelves with various slopes(Fig. 4). Specifically, several schematizations used in the following simulations of the tidal phenomena in the semi-enclosed rectangular basin were specified as follows:

Fig. 4 Three types of schematized cross-basin depth profile for the semi-enclosed rectangular basin

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Fig. 5 Location of the stepped topography in the semienclosed rectangular basin

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Fig. 6 Schematized coastline changes a. three new coastline positions from the coastal barrier to the bay entrance; b. localized protrusion from the focal point ofthe radial tidal current field in front of the coastal barrier.

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The underwater topography of the South Yellow Sea(Lin and Mao, 1989; Lin, 1989)can be schematized as an inclined ramp from both coasts towards center of the sea area(Fig. 4). When facing the bay head, we defined the left h and side as the left coast(China’s coast) and right h and side as right coast(Korean Peninsula’s coast). The slope off the right coast was constantly set to be 1:1 462, and the one off left coast 1:5 848(Fig. 4a), 1:3 500(Fig. 4b), and 1:1 462(Fig. 4c), respectively. The maximum water depth was 68.4 m with the slope off China’s coast being gentler than that off the Korean Peninsula’s. In addition, we schematized another three different stepped topographies differing in the water depth over the step into the semi-enclosed rectangular basin(Fig. 5). The three cases of water depth over the step were 35 m, 25 m, and 15 m, respectively. Uniform water depth of 68.4 m was set for the remaining areas within the bottom topography.

Three new coastline positions from the coastal barrier to the bay entrance and one local protrusion from the focal point of the radial tidal current field in front of the coastal barrier(Fig. 6)were schematized. The three new positions of the coastlines were 20 km, 40 km, and 60 km offshore away from the original coastline(Fig. 6a). The localized protrusion extended 30 km into the sea and at a distance of 240–310 km from the bay entrance(Fig. 6b).

Based on the above schematizations, several numerical experiments were carried out using various cross-basin water depth profiles and coastline advances. The locations of the amphidromic point and the focal point of the radial tidal current field are of particular interest. All the cases are listed as above(Table 1).

Poincaré waves might exist if the Kelvin waves cannot be perfectly reflected in this semi-enclosed rectangular basin, and perfect reflection of the Kelvin waves can take place when the following relationship is satisfied(Taylor, 1922; Fang and Wang, 1966):

From above relation, we can easily find that perfect reflection of the Kelvin waves can take place when the average water depth of the basin is greater than 17.1 m. For all the cases listed in Table 1, case C13 has the shallowest average water depth of 33.6 m in front of the coastal barrier, which is approximately two times larger than the critical depth of 17.1 m. Therefore, only Kelvin waves exist in the semienclosed rectangular basin for all the listed cases(Table 1). 3 MODEL RESULT 3.1 Formation of the radial tidal current field 3.1.1 Formation mechanism of the radial tidal current field

The co-tidal and tidal ellipse charts of the M ₂constituent for case C2 in the semi-enclosed rectangular basin are shown in Fig. 7, in which Fig. 7a shows that, considering the Coriolis force, the counterclockwise rotating tidal wave is caused by the superposition of the tidal wave reflected by the bay head onto the incident tidal wave. The radial tidal current pattern off the left coast, formed due to the confluence of the rotary and progressive tidal waves, can also be easily observed in Fig. 7b. The above findings are consistent with the literature(Zhang et al., 1999)regarding the formation of the amphidromic system in the South Yellow Sea. Nevertheless, how the radial tidal current field emerges over the actual l and form(Fig. 1), a schematized sloped shelf(Fig. 4), and even the stepped topography(Fig. 5)remains an open question. Wave theory(Shepard and Inman, 1950)indicated that if a harmonic wave approaches the coast with oblique incidence, the wave crest can be treated as a special iso-phase line which will slowly change its position to be parallel to the coastline. This refraction phenomenon is due to the depth-variationinduced alteration in phase speed along the wave crest. In order to further underst and the formation mechanism of the radial tidal current field, the concept of tidal wave refraction will be introduced by means of drawing an analogy with the offshore wave refraction. If the M ²tidal constituent obliquely propagates toward the coast, the co-phase lines will also deflect to be parallel to the water depth contours. Using the concept of tidal wave refraction, the formation mechanism of the radial tidal current field over the sloped shelf can be explained as follows: taking the Coriolis force into account, the counterclockwise rotating tidal wave results from the superposition of the reflected tidal wave onto the incident tidal wave. Using the submarine topography shown in Fig. 4a, the co-phase lines of the counterclockwise rotary tidal wave will present clockwise refraction, while those of the incident tidal wave take on counterclockwise refraction(Fig. 7a). Due to depth-variation-induced clockwise refraction of the counterclockwise rotary tidal wave and the counterclockwise refraction of the incident tidal wave, the two tidal wave systems will simultaneously converge to and diverge from the same focal point on the left coast, thus forming the radial tidal current field.

Fig. 7 Results of(a)co-tidal and (b)tidal ellipse charts of the M 2constituent for case C2

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The formation of the radial tidal current field over the stepped topography(Fig. 5)can also be explained using the concept of tidal wave refraction. The cotidal and tidal ellipse maps of the M ²constituent for cases C8, C9, and C10 are displayed(Fig. 8). Due to the abrupt changes in water depth induced by the stepped topography, the tidal wave refraction phenomenon can be observed by the distinct co-phase line deflection of both the rotary and incident tidal waves, thereby forming the radial tidal current field. It can also be found that the shallower the water depth over the step, the more distinct the radial tidal current pattern will be.

Fig. 8 Results of co-tidal(left panels) and tidal ellipse(right panels)maps of the M 2constituent for cases C8(a1, b1), C9(a2, b2), and C10(a3, b3)

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Figure 9 shows the co-tidal and tidal ellipse charts of the M ₂constituent for case C3 in the semi-enclosed rectangular basin. Both the amphidromic point induced by superposition of the reflected and incident tidal waves and the radial tidal current pattern resulting from tidal wave refraction, which resemble those in front of the Shangdong Peninsula, can be easily observed in front of the coastal barrier. In contrast, Fig. 7 shows results without coastal barrier, and neither the amphidromic point nor the radial tidal current field is found in the corresponding sea area. This may indicate that if the coastal barrier does not exist, the rotary tidal wave and radial tidal current systems might not emerge in front of it. To address this conjecture, two more submarine topographies were designed(Fig. 4b, c). The co-tidal and tidal ellipse charts of the M ₂constituent for cases C4, C5, C6, and C7 are presented in Fig. 10.

Fig. 9 Results of(a)co-tidal and (b)tidal ellipse charts of the M 2constituent for case C3

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Fig. 10 Results of co-tidal(left panels) and tidal ellipse(right panels)charts of the M 2constituent for cases C4(a1, b1), C5(a2, b2), C6(a3, b3), and C7(a4, b4)

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Figure 10 shows that two amphidromic systems and their corresponding radial tidal current fields appear within the semi-enclosed rectangular basins. Herein, the amphidromic point which is closer to the bay head represents the inner amphidromic point and correspondingly inner radial tidal current field, and those closer to the bay entrance represent the outer amphidromic point and outer radial tidal current field. The outer amphidromic system as well as outer radial tidal current field still exists without the coastal barrier. If the coastal barrier does not exist, the outer amphidromic point is induced by the superposition of the incident tidal wave onto the bay-head- reflected tidal wave, which propagates toward the outer sea area. This represents the second rotary tidal wave system reflected by the bay head. When the coastal barrier exists, the outer amphidromic system is induced by the superposition of the tidal wave reflected by the coastal barrier onto the incident tidal wave, and it is the first rotary tidal wave system reflected by the coastal barrier(Qian et al., 2014). Correspondingly, the radial tidal current field will arise under the effect of tidal wave refraction. To conclude, regardless of whether the coastal barrier exists or not, the outer radial tidal current field might emerge due to the tidal wave refraction phenomenon over the sloped or stepped submarine topography, and including the coastal barrier is crucial to get it at the correct along-basin position. 3.1.3 Applications in the South Yellow Sea

The above mechanisms obtained from the schematized model can also be applied to explain the appearance of the radial tidal current field in the South Yellow Sea area off the Jiangsu coast. Also, they provide a more comprehensive underst and ing of the significance of the Sh and ong Peninsula in the formation of the rotary tidal wave system and the radial tidal current field.

On the one h and , considering the Coriolis force, the counterclockwise tidal wave system in the South Yellow Sea is formed by the superposition of the tidal wave reflected by the Sh and ong Peninsula onto the following incident tidal wave. Due to the simultaneous tidal wave refraction of both the rotary and progressive tidal waves over the gently sloping continental shelf, the radial tidal current field off the Jiangsu coast emerges. On the other h and , if the Sh and ong Peninsula did not exist, the rotary tidal wave system and theradial tidal current field might still emerge as a result of the particular submarine topography. Herein, with the influence of the Coriolis force, the rotary tidal wave system is formed by the superposition of the tidal wave reflected by the bay head. The wave then travels to the South Yellow Sea adjacent area onto the progressive incident tidal wave, and afterwards the radial tidal current field arises off the Jiangsu coast. 3.2 Evolution of the radial tidal current field 3.2.1 Response to coastline changes

In recent years, the large scale reclamations along the Jiangsu coast(Wang et al., 2011c; Zhang et al., 2011 ;Song et al., 2013)have been taking place in the South Yellow Sea, which will move the coastline forward to the offshore direction. Accordingly, we schematized three new coastline positions from the coastal barrier to the bay entrance(Fig. 6a) and one local protrusion from the focal point of the radial tidal current field(Fig. 6b)in front of the coastal barrier to study the influence of the coastline changes on the existing tidal wave system. The location of the amphidromic point and the focal point of the radial tidal current field in the semi-enclosed rectangular basin were of particular interest.

Figure 11 shows the co-tidal and tidal ellipse charts of the M ₂constituent for cases C11, C12, and C13 in the semi-enclosed rectangular basin. Despite great variations of the coastline, the overall patterns of the rotary tidal wave and radial tidal current field systems in the semi-enclosed rectangular basin remain similar.

Fig. 11 Results of co-tidal(left panels) and tidal ellipse(right panels)charts of the M 2constituent for cases C11(a1, b1), C12(a2, b2), and C13(a3, b3)in the semi-enclosed rectangular basin

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Figure 12 compares the movement of the outer amphidromic points and their corresponding focal points of radial tidal current field(represented by the variations of mean velocity contour lines)for different coastline positions. From Fig. 12, we can observe that the outer amphidromic point for case C3 has a distance of 189 km from the coastal barrier, and 81 km from the original coastline. For cases C11, C12, and C13, the distance of the outer amphidromic point from the coastal barrier and that from the original coastline will keep increase. For case C13, the distance of the outer amphidromic point from the coastal barrier increases to 192 km and that from the original coastline 146 km. Because of the significant enlargement of averaged water depth induced by the protruding coastline, the bottom frictional effect is weakened and the tidal wave length increased. As a consequence, the outer amphidromic point will simultaneously shift toward both the central axis and entrance of the semi-enclosed rectangular basin, and its corresponding focal point of the radial tidal current field will move toward the entrance of the bay.

Fig. 12 Comparison of the movement of(a)outer amphidromic points and their corresponding(b)focal points of the radial tidal current field(represented by the mean velocity contour lines)in the semi-enclosed rectangular basin The red, blue, black, and green lines represent cases of C3, C11, C12, and C13, respectively.

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Figure 13 shows the co-tidal and tidal ellipse charts of the M ₂constituent for case C14 in the semienclosed rectangular basin. Despite the large protrusion of coastline, the overall patterns of the rotary tidal wave and radial tidal current systems in the semi-enclosed rectangular basin appear to be stable and consistent. Figure 14 shows a comparison of the movement of outer amphidromic points and their corresponding focal points of the radial tidal current field(represented by the variations of mean velocity contour lines)with and without localized protrusion. From Fig. 14, we can observe that the outer amphidromic point for both cases of C3 and C14 has almost the same distance of 189 km from the coastal barrier, and 81 km from the original coastline. The results demonstrate that this protrusion has very little influence on the location of the amphidromic point or the focal point of the radial tidal current field. Only the mean current velocity in the adjacent area of the protrusion was slightly changed.

Fig. 13 Results of(a)co-tidal and (b)tidal ellipse charts of the M 2constituent for case C14 in the semi-enclosed rectangular basin

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Fig. 14 Comparison of the movement of(a)outer amphidromic points and their corresponding(b)focal points of the radial tidal current field(represented by the mean velocity contour lines)in the semi-enclosed rectangular basin The red and blue lines represent cases of C3 and C14.

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Since the Huanghe(Yellow)River is pouring into the Bohai Sea and the Changjiang River Mouth shifting toward the southeast, the amount of sediment supplied for the Jiangsu coast is significantly declining, which directly leads to the erosion of the submarine topography in the radial s and ridges area(Chen et al., 2009; Huang et al., 2009; Zhou et al., 2014). To determine the effect of the bottom erosion with different intensities on both the rotary tidal wave system and the radial tidal current pattern, three inclined continental slopes(Fig. 4a, b, c)from the coastal barrier to the bay entrance were configured to study the impact of the continental shelf erosion on the distributions of the rotary tidal wave and radial tidal current systems in the semi-enclosed rectangular basin. And the slope from the bay head to the coastal barrier is set to be the same as Fig. 4a shown.

Figure 15 shows the co-tidal and tidal ellipse charts of the M ₂constituent for cases C15, C16, and C17 in the semi-enclosed rectangular basin. Despite the significant changes in the continental slopes ahead of the coastal barrier, the overall patterns of the rotary tidal wave and the radial tidal current systems in the semi-enclosed rectangular basin are similar to each other. A comparison of the movement of outer amphidromic points and their corresponding focal points of the radial tidal current field(represented by the variations of mean velocity contour lines)are shown in Fig. 16. From Fig. 16, we can observe that the outer amphidromic point for case C15 has a distance of 189 km from the coastal barrier, and 81 km from the coastline. For cases C16 and C17, the distance of the outer amphidromic point from the coastal barrier and that from the coastline will keep increasing. For case C17, the distance of the outer amphidromic point from the coastal barrier increases to 225 km and that from the coastline 130 km. Because of the significant enlargement of the averaged water depth induced by different intensities of bottom erosion, the bottom frictional effect is weakened and the tidal wave length increased. Therefore, the outer amphidromic point will simultaneously shifts toward both the central axis and entrance of the semi-enclosed rectangular basin and the focal point of the radial tidal current field moves toward the entrance of the bay.

Fig. 15 Results of co-tidal(left panels) and tidal ellipse(right panels)charts of the M 2constituent for cases C15(a1, b1), C16(a2, b2), and C17(a3, b3)in the semi-enclosed rectangular basin

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Fig. 16 Comparison of the movement of(a)outer amphidromic points and their corresponding(b)focal points of the radial tidal current field(represented by the mean velocity contour lines)in the semi-enclosed rectangular basin The red, green, and blue lines represent cases of C15, C16, and C17, respectively.

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The counterclockwise rotary tidal wave system and the radial tidal current field are prominent hydrodynamic characteristics in the radial s and ridges area of the South Yellow Sea. Their formation and redistribution, especially with respect to the amphidromic point and the focal point of the radial tidal current field, have attracted the interest of many researchers(Ren, 1986; Zhang, 2013). In this study, the formation and evolution of the radial tidal current field were investigated using a strongly schematized semi-enclosed rectangular basin to represent the topography of the Bohai Sea and Yellow Sea based on a 2D tidal model(DELFT3D-FLOW).

However, the present work may have a number of limitations. We have strongly schematized the coastal lineament and bottom topography into the semienclosed rectangular basin from the Bohai Sea and Yellow Sea(Fig. 2). We also strongly schematized the coastal l and reclamations and subaqueous slope erosions into several seaward coastline protrusions(Fig. 6) and continental shelves with various slopes(Fig. 4). All these generalizations cannot perfectly reflect the real coastline and submarine conditions in the Bohai Sea and Yellow Sea, and the modelling results of the tidal wave/current systems based on these schematizations also cannot be obtained accurately(Fig. 1), especially the tidal phenomena in the Bohai Sea. Nevertheless, we have clearly reproduced the rotary tidal wave system and the radial tidal current field with inclined and stepped slopes, which are the main tidal dynamic characteristics in the South Yellow Sea area and thus of particular interest in this work. The successful reproduction of the rotary tidal wave system and the radial tidal current field within the semi-enclosed rectangular basin is sufficient to guarantee the qualitative analysis of their formation mechanisms. Besides, the exaggerated seaward coastline protrusions and submarine erosions can provide the displacement trend of the amphidromic point and the focal point of the radial tidal current field under extreme circumstances, from which we can also qualitatively predict their potential evolution trend under different intensities of the real coastal l and reclamations and submarine slope erosions in the South Yellow Sea area.

In addition, when establishing the 2D tidal model based on the DELFT3D-FLOW module, we approximately adopted the water levels along the basin entrance of M ₂tidal constituent from the analytical solutions(Fang and Wang, 1966), which doesn’t take into account the nonlinear and frictional interaction between various tidal constituents. This is because of the fact that the M ₂tidal constituent is dominant in the South Yellow Sea area(Fig. 1), and this approximation exerted limited impact on the generation of satisfactory results. Since the analytical solutions(Fang and Wang, 1966)were obtained with the linearization of the bottom friction as well as the continuity equation and the disregard of the convection and diffusion terms, we set the horizontal eddy viscosity coefficient as zero to neglect the diffusion term in the Delft3D flow model. However, we just retained the convection term and the non-linear frictional term in the Delft3D flow model, which will lead to some deviations of the co-amplitude lines, cophase lines, and current velocity vectors between thenumerical and analytical models(Fig. 3). Obviously, these slight differences can only quantitatively affect the modelling results, and we can still employ the established model to qualitatively illustrate the formation and evolution of the rotary tidal wave system and the radial tidal current field. 5 CONCLUSION

A semi-enclosed rectangular basin was schematized to represent the topography of the Bohai Sea and Yellow Sea, and a coastal barrier as a representation of the Shangdong Peninsula. The radial tidal current field in this basin was successfully reproduced based on a 2D tidal model(DELFT3D-FLOW). Tidal wave refraction was demonstrated to be one of the critical mechanisms contributing to the appearance of the radial tidal current field. Regardless of whether the coastal barrier exists or not, the outer radial tidal current field can independently emerge over a certain topography. Significantly increased water depth induced by either natural evolution or anthropogenic impact will lead to the movement of the amphidromic point toward the entrance and central axis of the basin and the focal point of the radial tidal current field toward the bay entrance. Although the results arising from the schematized semi-enclosed rectangular basin cannot perfectly reflect the real situation, they can still provide meaningful insights for the analysis of the emergence and evolution of the rotary tidal wave system and the radial tidal current field in the South Yellow Sea. 6 ACKNOWLEDGEMENT

The authors are grateful to Profs. ZHANG Dongsheng and ZHANG Junlun at Hohai University, and Prof. Giovanni COCO at the University of Auckl and for their useful comments and suggestions. We would also like to thank two anonymous reviewers for their constructive critique.