The Korea Strait (KS) is a major navigation passage
linking the Japan Sea (JS) to the East China Sea and Yellow Sea. Almost all
existing studies of the tides in the KS employed either data analysis or
numerical modelling methods; thus, theoretical research is lacking. In this
paper, we idealize the KS–JS basin as four connected uniform-depth
rectangular areas and establish a theoretical model for the tides in the KS
and JS using the extended Taylor method. The model-produced

The Korea Strait (KS, also called the Tsushima Strait) connects the East China Sea (ECS) to the southwest and the Japan Sea (the JS, also called the East Sea, or the Sea of Japan) to the northeast. It is the main route linking the JS to the ECS and the Yellow Sea and is thus an important passage for navigation. The strait is located on the continental shelf, and it has a length of approximately 350 km, a width of 250 km and an average water depth of approximately 100 m. The JS, which is adjacent to the KS, is a deep basin that has an average depth of approximately 2000 m and a depth of more than 3000 m at its deepest part. A steep continental slope separates the KS and the JS, and it presents abrupt depth and width changes (Fig. 1). Such topographic characteristics create the unique tidal waves that occur in the KS.

Ogura (1933) first conducted a comprehensive study of the tides in the seas
adjacent to Japan using data from the tidal stations along the coast and
gained a preliminary understanding of the characteristics of the tides,
including amphidromic systems in the KS. Since then, many researchers have
investigated the tides in the strait via observations (Odamaki, 1989a;
Matsumoto et al., 2000; Morimoto et al., 2000; Teague et al., 2001; Takikawa
et al., 2003) and numerical simulations (Fang and Yang, 1988; Kang et al.,
1991; Choi et al., 1999; Book et al., 2004). The results of these studies
show consistent structures of the tidal waves in the KS. Figure 2 displays the
distributions of the

However, almost all previous studies have employed either data analysis or
numerical modelling methods; thus, theoretical research is lacking. In
particular, the existence of amphidromic points in the northeast KS for both
diurnal and semidiurnal tides has not been explained based on geophysical
dynamics. In this paper, we intend to establish a theoretical model for the

Map of the Korea Strait and its neighbouring areas. (TTS: Tartar Strait; SYS: Soya Strait; TGS: Tsugaru Strait; KS: Korea Strait; ECS: East China Sea). Isobaths are in metres (based on ETOPO1 from US National Geophysical Center).

Tidal charts of the KS and its neighbouring areas based on
DTU10 (Cheng and Andersen, 2011) for the

The Taylor problem is a classic tidal dynamic problem (Hendershott and Speranza, 1971). Taylor (1922) first presented a theoretical solution for tides in a semi-infinite rotating rectangular channel of uniform depth to explain the formation of amphidromic systems in gulfs and applied the theory to the North Sea. The classic Taylor problem was subsequently improved by introducing frictional effects (Fang and Wang, 1966; Webb, 1976; Rienecker and Teubner, 1980) and open-boundary conditions (Fang et al., 1991) to study tides in multiple rectangular basins (Jung et al., 2005; Roos and Schuttelaars, 2011; Roos et al., 2011) as well as to solve tidal dynamics in a strait (Wu et al., 2018).

The method initiated by Taylor and developed afterwards is called the extended Taylor method (Wu et al., 2018). This method is especially useful in understanding the tidal dynamics in marginal seas and straits because the tidal waves in these sea areas can generally be represented by combinations of the Kelvin waves and Poincaré waves/modes (e.g. Taylor, 1922; Fang and Wang, 1966; Hendershott and Speranza, 1971; Webb, 1976; Fang et al., 1991; Carbajal, 1997; Jung et al., 2005; Roos and Schuttelaars, 2011; Roos et al., 2011; Wu et al., 2018).

A sketch of the model geometry is shown in Fig. 3, and it consists of a
sequence of

Model geometry.

Consider a tidal wave of angular velocity

Provided that the

Along the cross sections, such as

Equation (9) is matching conditions accounting for sea level continuity and
volume transport continuity. The individual Eqs. (6) to (9), or their
combination, may be used as boundary conditions for the cross sections. The
relationship between

For the

The collocation approach was first proposed by Defant in 1925 (see Defant,
1961) and is convenient in determining the coefficients
(

For

As noted by Odamaki (1989b), the co-oscillating tides are dominant in the JS, which is mainly induced by inputs at the opening of the KS rather than those through the Tsugaru Strait (TGS) and Soya Strait (SYS). Furthermore, our study focuses on the KS, in which influences of the tide-generating force and the inputs from the TGS and SYS are negligible. Therefore, we idealize the KS–JS basin as a semi-enclosed basin with a sole opening connected to the ECS and study the co-oscillating tides generated by the tidal waves from the ECS through the opening.

To establish an idealized analytical model for the KS–JS basin, we use four
rectangular areas as shown in Fig. 4 to represent the study region. The
first rectangle, designated as Area1, represents the KS, which is our focus
area. According to the shape of its coastline, we use three rectangles
designated as Area2 and Area3 to represent the JS. We place the

Idealized model domain fitting the Korea Strait and Japan Sea. The dashed line represents an open boundary, and the solid lines represent closed boundaries. A, B, …, M indicate the localities of the points used in Fig. 6 for model–observation comparison. Numbered red dots are tidal gauge stations where the observed harmonic constants are used for model validation in Table 2.

Based on the depths listed in Table 1, the wavelengths of the

Parameters used in the model.

In addition to the parameters listed in Table 1, we need to estimate the
parameters

For the collocation approach, we take 10 km as the spacing between
collocation points. Thus in this model, a total of 198 collocation points
are used to establish 256 equations, and the parameters of 3 pairs of Kelvin
waves and 125 pairs of Poincaré modes can be obtained. Along the open
boundary of the KS, the open-boundary condition Eq. (8) is employed, with
the value of

The obtained analytical solutions of the

Comparison of tidal system charts.

Comparison of model results (blue) and observations based on DTU10
(orange) along the coasts.

The maximum amplitude of the

To quantitatively validate the model results, we first extract the data
along the solid boundary of the model for comparison as shown in Fig. 6. For
the

For further validation, we select 16 tide gauge stations where harmonic
constants are available from the International Hydrographic Bureau (1930).
The station locations are shown in Fig. 4. The result of the comparison is
given in Table 2, which also shows that the model results are consistent
with the data obtained from gauge observations: the RMS (root mean square)
differences of amplitudes of

Comparison between harmonic constants from the observations and models at coastal tide gauge stations.

Although the theoretical model greatly simplifies the topography and boundary, the amplitude and phase-lag differences of these two tidal constituents are very small in the KS and its surroundings, and the basic characteristics of the tidal patterns are well retained (Fig. 5). These findings show that the simplification of the model is reasonable and the extended Taylor method is appropriate for modelling the tides in the KS–JS basin. Therefore, it is meaningful to use the model results for theoretical analysis.

To reveal the relative importance of the Kelvin waves versus Poincaré
modes in the modelled Korea Strait, the superposition of Kelvin waves and
that of the Poincaré modes are given in Fig. 7a–b for

For the

For the

The above results show that the Poincaré modes only exist along the open boundary and the connecting cross section and their amplitudes quickly approach zero away from these cross sections. In fact, these properties of the Poincaré wave are inherent in any narrow strait. Therefore, in the following, we will focus on Kelvin waves and analyse the characteristics of the incident (northeastward) and reflected (southwestward) Kelvin waves.

The incident and reflected

The incident and reflected

The above results indicate that the relation of the amplitudes and phase
lags of the reflected Kelvin wave with the incident wave plays a decisive
role in the tidal system in the KS, especially in the formation of
amphidromic points, for both the

Decomposed charts for the model-produced

Same as in Fig. 7 but for

To explore the tidal dynamics of the KS–JS basin, especially the formation
mechanism of amphidromic points, we consider the simplest case: a
one-dimensional tidal model in channels. In the one-dimensional case, the
amphidromic point is equivalent to the wave node. As previously mentioned,
an important feature of the topography of the KS–JS basin is that there is
a steep continental slope between the KS and JS, and to the northeast of this
slope, the JS is much deeper and wider than the KS. Thus, the channel is
idealized to contain two areas, with the first one (Area1) having uniform
depth

If the second area is semi-infinitely long, allowing for the wave radiating
out from the second area freely, then a part of the wave is reflected at the
connecting point and another part is transmitted into the second area. The
amplitude of the transmitted wave is (see for example Dean and Dalrymple, 1984)

The complete solution for this case is as follows (see also Dean and
Dalrymple, 1984):

However, Sect. 3.3 shows that the phase-lag changes of the reflected waves
relative to the incident waves are not exactly equal to 180

The complete solution for this case is as follows:

Amplitude distribution along the channel.

Phase-lag increase of the reflected wave relative to the incident wave as a function of the angular velocity at the connecting point. See the text for details.

Equation (35) indicates that the amplitude of the reflected wave in the
first area is equal to that of the incident wave. This result is natural
because friction is not considered and no dissipation is present during wave
propagation. Equation (35) also indicates that the phase lag of the
reflected wave at the connecting point is greater than that of the incident
wave at the same point by

In this paper, we establish a theoretical model for the KS–JS basin using
the extended Taylor method. The model idealizes the study region as three
connected flat rectangular areas, incorporates the effects of the Coriolis
force and bottom friction in the governing equations, and is forced by
observed tides at the opening of the KS. The analytical solutions of the

The theoretical model results are consistent with the satellite altimeter
and tidal gauge observations, which indicates that the model is suitable and
correct. The model reproduces well the

The model solution provides the following insights into the tidal dynamics
in the KS. (1) The tidal system in each rectangular area can be decomposed
into two oppositely travelling Kelvin waves and two families of Poincaré
modes, with Kelvin waves dominating the tidal system due to the narrowness of
the area. (2) The incident Kelvin wave from the ECS through the opening of
the KS travels toward the JS and is reflected at the connecting
cross section between the KS and JS, where abrupt increases from the KS to
JS in water depth and basin width occur. (3) The phase lag of the reflected
wave at the connecting cross section increases by less than 180

The ETOPO1 data (

The supplement related to this article is available online at:

GF conceived the study scope and the basic dynamics. DW performed calculation and prepared the draft. ZW and XC checked model results.

The authors declare that they have no conflict of interest.

We sincerely thank Joanne Williams for handling our paper and thank David Webb and Kyung Tae Jung for their careful reading of our paper and constructive comments and suggestions which were of great help in improving our work.

This research has been supported by the National Natural Science Foundation of China (grant nos. 41706031 and 41821004).

This paper was edited by Joanne Williams and reviewed by Kyung Tae Jung and David Webb.