# Subtidal Dynamics in a Tidal River with Limited Discharge

^{1}

^{2}

^{*}

## Abstract

**:**

^{3}/s) leads to the vertical variability of subtidal friction contributions from subtidal flow and subtidal-tidal interaction, as well as Eulerian return flux, and (ii) the vertical variability of the aforementioned terms can be associated with the existence of influential longitudinal subtidal density gradients along the tidal river. We believe that these findings advance our understanding of subtidal dynamics in tidal river systems, particularly those with limited discharge.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Field Site

^{3}during summer and 20–30 m

^{3}during winter [25]. Approximately 10–20% of the total discharge flows to the Ota Diversion Channel, depending on the flow condition, whereas the remaining streams flow into the bifurcating eastern branch [27].

^{3}[23]. The Gion Floodgate, a flood control structure at the upstream end of the Ota Diversion Channel consisting of three sluice gates, was built to regulate the amount of river flow to the channel. When the gauging station at Yaguchi reports a discharge of greater than 400 m

^{3}/s, the Gion Floodgate is fully opened. Xiao et al. [29] classified the Ota Diversion Channel as having moderate estuarine circulation because it is influenced by limited runoff and mesotidal flow from Hiroshima Bay.

#### 2.2. Data Acquisition

#### 2.3. Data Processing

#### 2.3.1. Tidal Frequency Domain Analysis

- Spectral Analysis

- Harmonic Analysis

_{0}(t) is the mean water level; and A, ω, and Φ are the tidal amplitude, frequency, and phase, respectively, of tidal constituents n (n = 1, 2, ..., N), and r(t) represents the residual components. The short-term tidal harmonic analysis in this study utilized a short data sequence of a 25 h depth-averaged velocity to provide a time series of tidal outputs for the six tidal constituents. Three of these tidal constituents, K1, M2, and M4, were used to represent diurnal, semidiurnal, and quarterdiurnal velocities, respectively.

#### 2.3.2. Subtidal Friction Decomposition

_{m}), and a and b are two constant coefficients set to 0.3395 and 0.6791, respectively, based on the work of Godin [8]. The dominant velocity components over a diurnal period occur at diurnal, semidiurnal, and quarterdiurnal frequencies. Hence, the nondimensional current velocity can be approximated as [12]

#### 2.3.3. Stokes Fluxes Analysis

_{0}is the subtidal elevation, and ƞ″ denotes the zero-mean variation in the water surface elevation during a tidal cycle. Subsequently, by assuming a constant channel width, the subtidal flux can be expressed as

## 3. Results

#### 3.1. Time and Frequency Variation of Water Level, Near-Bottom Density, and Current Velocity

^{3}at both stations, whereas during the spring tide, the water densities dropped to 1010 kg/m

^{3}and 1001 kg/m

^{3}at Stations A and C, respectively.

^{3}/s to 130 m

^{3}/s. Since, at most, the Ota Diversion Channel only received one-fifth of the total discharge from the Ota River, it can be said that during the observation period, the channel was under the limited influence of freshwater runoff. The subtidal velocity ranges from 0.05 m/s to 0.2 m/s at the surface, −0.025 m/s to 0.025 m/s at the mid-depth, and −0.05 m/s to −0.01 m/s at the lower depth. The subtidal velocity represents a distinct vertical variability from the seaward subtidal velocity at the upper depth. Vertically, the magnitude of the subtidal velocity gradually diminished from the upper depth to mid-depth before changing in a landward direction at a lower depth.

#### 3.2. Subtidal Friction

#### 3.3. Stokes Fluxes

^{2}/s to 0 m

^{2}/s) throughout all depths, except for relatively minor positive values in the upper depth of Station C (~0.01 m

^{2}/s) during the second phase of spring tide (Figure 9a,d,g). The time series of Stokes fluxes shows temporal variation due to the spring-neap tidal cycles, with greater values further upstream. Because Stokes flux is affected by the phase difference between the current velocity and water level instead of merely the tidal magnitude, its values will be greater when the diurnal-semidiurnal inequality is at its maximum and lower when the tidal asymmetry is at its minimum [36]. The return flux shows temporal patterns that do not clearly resemble the variation due to the spring-neap tidal cycles. The values of the return flux, which are higher than those of the Stokes flux, vary with both positive and negative signs (Figure 9b,e,h). In the upper depth, the return flux varies in positive values from 0.04 m

^{2}/s to 0.2 m

^{2}/s, with greater values observed farther upstream. At mid-depth, the return flux varies from −0.025 m

^{2}/s to 0.045 m

^{2}/s. During spring tide, the return flux at Station A was predominantly negative, whereas a positive return flux was more apparent at Stations B and C. At neap tide, the values of the return flux at all stations were relatively close to zero. At lower depths, the return flux induced negative values at all stations, ranging from −0.06 m

^{2}/s to 0 m

^{2}/s. Subsequently, the total flux at all stations had non-zero values and was clearly modulated by the return flux because its magnitude was greater than that of the Stokes flux.

## 4. Discussion

^{2}), A is vertical eddy viscosity (m

^{2}/s), ρ is water density (kg/m

^{3}), and x is longitudinal distance (m). However, in this study, we could not estimate the eddy viscosity because of the limited density data in the vertical distribution and the insufficiencies of the temporal and spatial resolutions of the current data in calculating the Reynolds shear stress. The return flux pattern shows the seaward surface and landward bottom fluxes. This vertical variability closely resembles the two-layer circulation flow of gravitational circulation. Additionally, Geyer and Macready [38] indicated that subtidal velocity, which is the influential driver of Fr, Frt, and return flux, can be associated with gravitational circulation. Hence, because we could not quantify gravitational circulation, and density stratification data were not available, we opted to use the near-bottom longitudinal density gradient term ($\partial \mathsf{\rho}/\partial \mathrm{x}$) as a proxy to show the influence of gravitational circulation.

^{2}and p-values at each station. The Frt and density gradients were correlated at each station. On the other hand, although Fr and the density gradient are found to be highly correlated in the Stations A and C, more than with Frt, the R

^{2}value in Station B indicates poor correlation between both terms. Because the magnitude of the subtidal density gradient is significantly affected by the spring-neap tidal cycle, the low correlation of Fr at Station B could be attributed to the phase difference between the subtidal velocity at Station B and the other stations (Figure 5d). These results suggest that the subtidal density gradient indeed modulates both Frt and Fr through the subtidal velocity, with a greater modulation potential in the latter.

^{2}, and p-values between the return flux and longitudinal subtidal density gradient. Similar to the subtidal friction terms, the return flux tended to increase with increasing density gradient magnitude. Likewise, the return fluxes at stations A and C were found to be finely correlated with the density gradient, whereas Station B showed a poor correlation between both terms. The low correlation at Station B was likely caused by a greater value of return flux than that at the other stations during the period between the peak of the first spring tide and the lowest neap tide (Figure 9h). As the difference in the subtidal range between Station B and the other stations was not significant (Figure 3), the higher value of the return flux could be attributed to the phase difference in the subtidal velocity at lower depths at Station B (Figure 5d). This phase difference can be attributed to the bathymetry effect because Station B is situated in a small trough within the longitudinal orientation of the channel. Subsequently, this phase difference led to a relatively higher subtidal velocity at Station B than that at the other stations, which induced a higher return flux.

_{0}in high-discharge tidal rivers. More importantly, for subtidal friction, the product of the constant coefficient (a) and subtidal velocity (U

_{0}) has the potential to be the mechanism makes the greatest contribution to subtidal friction [12]. However, the effects of high river discharge on the subtidal dynamics may not stop there. Studies in the Qiantang River, China [42,43,44] revealed that the interaction of high river discharge and tides could generate seasonal and interannual variations in bed morphology due to sediment erosion and accumulation. Although we did not focus on the effects of bathymetry on subtidal dynamics, our study indicates that bed morphology could affect the longitudinal variation of subtidal fluxes, particularly the Eulerian return flux. The relationship between bed morphology evolution and subtidal dynamics may provide significant information; however, owing to the time span of our data, this will be considered in future studies.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The observation sites in the Ota Diversion Channel, Hiroshima, Japan. Red diamonds show the location of instrument deployment. Insets show a cross-sectional view (seaward) of each station.

**Figure 2.**Time series plot of observed water depth (

**a**), near-bottom salinity (

**b**), and current velocities in station A (

**c**), station B (

**d**), and station C (

**e**).

**Figure 5.**River discharge at the Yaguchi Gauging Station (

**a**) and subtidal velocities at the upper depth, (

**b**) mid-depth (

**c**), and lower depth (

**d**) at Stations A, B, and C.

**Figure 6.**The power spectrum of water elevation (

**a**) and current velocity in upper (

**b**), mid-depth (

**c**), and lower (

**d**) depths at Stations A, B, and C.

**Figure 7.**The diurnal velocity (

**a**,

**d**,

**g**), semidiurnal velocity (

**b**,

**e**,

**h**), and quarterdiurnal velocity (

**c**,

**f**,

**i**) at upper (top row), mid- (middle row), and lower depth (bottom row) at Stations A, B, and C.

**Figure 8.**Frt (

**a**,

**d**,

**g**), Ft (

**b**,

**e**,

**h**), and Fr (

**c**,

**f**,

**i**) at upper (top row), mid (middle row), and lower depth (bottom row) in Stations A, B, and C.

**Figure 9.**Stokes flux (

**a**,

**d**,

**g**), return flux (

**b**,

**e**,

**h**), and total flux (

**c**,

**f**,

**i**) at upper (top row), mid- (middle row), and lower depth (bottom row) at Stations A, B, and C.

**Figure 10.**The longitudinal gradient of near-bottom density between Stations C and A. The red line depicts subtidal density gradient, while the black line depicts 10 min interval density gradient.

**Figure 11.**The longitudinal subtidal density gradient vs. Fr (blue triangles) and Frt (red dots) at Stations A (

**a**), B (

**b**), and C (

**c**). The trendlines denote the linear relationship between the density gradient with Fr (blue lines) and Frt (red lines).

**Figure 12.**The longitudinal subtidal density gradient vs. return flux at Stations A (blue triangles), B (red dots), and C (black plus). The trendlines denote the linear relationship between the density gradient with return flux in each respective station.

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**MDPI and ACS Style**

Gusti, G.N.N.; Kawanisi, K.; Sawaf, M.B.A.; Khadami, F.
Subtidal Dynamics in a Tidal River with Limited Discharge. *Water* **2022**, *14*, 2585.
https://doi.org/10.3390/w14162585

**AMA Style**

Gusti GNN, Kawanisi K, Sawaf MBA, Khadami F.
Subtidal Dynamics in a Tidal River with Limited Discharge. *Water*. 2022; 14(16):2585.
https://doi.org/10.3390/w14162585

**Chicago/Turabian Style**

Gusti, Gillang Noor Nugrahaning, Kiyosi Kawanisi, Mohamad Basel Al Sawaf, and Faruq Khadami.
2022. "Subtidal Dynamics in a Tidal River with Limited Discharge" *Water* 14, no. 16: 2585.
https://doi.org/10.3390/w14162585