PROPAGATION OF LONG-PERIOD WAVES INTO AN ESTUARY THROUGH A NARROW INLET

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1 PROPAGATION OF LONG-PERIOD WAVES INTO AN ESTUARY THROUGH A NARROW INLET Takumi Okabe, Shin-ichi Aoki and Shigeru Kato Department of Civil Engineering Toyohashi University of Technology Toyohashi, Aichi, JAPAN okabe@jughead.tutrp.tut.ac.jp ABSTRACT In order to estimate sediment exchange between an estuary and the open sea through a narrow inlet, it may be important to investigate the behavior of the long-period waves with periods of several minutes generated by wave groups in the sea. In this study, characteristics of the longperiod waves and associated flows outside and inside an inlet is discussed based on the field data. The results show that long-period waves are developed almost linearly to both significant wave heights and periods outside the inlet, but they are reduced about half in the inlet. The longperiod fluctuation in the flow velocity seems to consist of two components; one is associated with the long-period waves and the other is generated by tidal currents. INTRODUCTION In the vicinity of an inlet, tidal and wave actions and their interactions yield complex current fields. Hence the sediment transport and associated topographic change around an inlet are very complicated and little is known about them. For example, sediment exchange between an estuary and the sea through an inlet and influence of tidal currents on longshore sediment transport are difficult to estimate. External forces that induce sediment transport at around the inlet have wide range of periods from those of wind waves (seconds) to tides (hours). However, predominant factor or relative importance between the forces with different time scale has not been well investigated. In this paper, we focus on long-period components having periods of several minutes and investigate their characteristics based on the field data. Although previous research (eg. Sato, ) have shown that long-period waves with periods of several minutes can influence sediment transport, studies on long-period waves and associated flows near an inlet are very limited. It remains unclear either qualitatively or quantitatively whether long-period waves influence on sediment transport near the inlet. Detailed investigations of behavior of the long-period waves generated by wave groups in the sea may be necessary in order to estimate influences of the long-period waves on sediment transport near the inlet. 15

2 In this study, characteristics of the long-period waves and associated flows inside and outside the inlet channel where tidal current is predominant are discussed based on the field data. We focus on wave components with periods larger than 3s. We discuss the relations between long-period waves and significant wave heights and periods, and propagation properties of the long-period waves into the inlet. Generations of long-period fluctuations in the currents induced by tidal action are also shown in the paper. FIELD OBSERVATIONS Field measurements were conducted at two stations outside and inside the inlet of Hamana Lake, Japan, for about two months from August to November 6. Figure 1 and Photo 1 show the locations of the inlet and the observation stations. In the figure, Stn-in denotes the station inside the inlet, where two-dimensional horizontal flow velocities and water pressure were measured at the bottom. At the station Stn-out located outside the inlet, twodimensional bottom velocities, water pressure and water surface elevation were measured. All the data were recorded continuously at sampling rate of.5s except for the data loss occurred in the period of maintenance of the equipments. Mean water depths during the measurements were 5.6m at Stn-in and.8m at Stn-out, respectively. As Stn-out was sometimes in the surf zone due to high waves (Photo ), water surface elevation measured by the ultrasonic wave gauge could not be used because of noisy signals under storm conditions. The details of the field measurements are shown in Table 1. Photo 1. Aerial view of Hamana Lake inlet 153

3 Hamana Lake JAPAN m m Stn-in N Hamana Lake the Pacific Ocean 6m Stn-out m m 6m 8m 1m 1m (a) Location of Hamana Lake in Japan (b) Inlet of Hamana Lake Figure 1. Location of inlet of Hamana Lake and observation stations Photo. Surf zone near Stn-out under storm conditions Table 1. Summary of field measurement Station Stn-in Stn-out Mean Water depth 5.6(m).8(m) Equipment WaveHunter- WaveHunter- Σ Sampling Frequency (Hz) (Hz) Measurement Items Water Pressure, Two dimensional Flow Velocity Water Surface Elevation, Water Pressure, Two dimensional Flow Velocity Height of Sensors from sea bottom.7 to.9 (m).7 to.9 (m) 15

4 CHARACTERISTICS OF LONG-PERIOD WAVES In this study, long-period waves are classified into two categories that have different nature in generation mechanism: wave-group-induced long-period waves and meteorologically-generated long-period waves. Judging from the power spectra under high wave conditions, we defined the frequency range of wave-group-induced waves as 3s 3s. Wave components that have larger periods than 3s are classified as meteorologically-generated long-period waves. These longperiod wave components were extracted from the raw wave data by the numerical filtering using FFT. Development of long-period waves Figure shows time series of significant wave height, significant wave period, and root mean square (RMS) value of long-period water surface elevation. In the period of measurement, some low-pressures passed near the coast and high waves were observed. From the comparison between the figures, the wave-group-induced long-period waves (3s 3s) clearly developed under high wave conditions. Although similar trend can be seen for the meteorologically-generated long-period waves with periods over 3s, the increase in the amplitude was smaller than the wave-group-induced long-period waves. H η L 1/3 (m) RMS (cm) (m) Stn-in Stn-out 3-3s 3s (s) (s) (cm) s 3s- 6/9/11 6/1/ 6/1/3 Date Figure. Time series of significant wave height, significant wave period and RMS value of longperiod waves at Stn-out and Stn-in Figure 3 plots the RMS values of the long-period waves as functions of the product of the significant wave heights and periods observed at Stn-out. The RMS values of the wave-group- 155

5 induced long-period waves (3s 3s) increase almost linearly to except for large values, while those of the meteorologically-generated long-period waves seem (3s ) to have little relation with wave heights and wave periods of short waves. Aoki () and Aoki et al.() show that the linear relationship is seen in the wave data obtained on the mild-slope sandy coast with wide surf zone. Propagation of long-period waves into an inlet.15 Stn-out 3-3s Stn-out 3sη L RMS =.3 =1.5*1- ( ) (m) (m*s) 5 Figure 3. Relationship between RMS values of long-period waves and products of significant wave heights and periods at Stn-out Figure shows relationship between the RMS values of long-period waves observed inside and outside the inlet, Stn-in and Stn-out, in which the broken lines indicate that the same values were observed both inside and outside of the inlet. For the wave-group-induced long-period waves (Fig. (a)), the RMS values in the inlet show almost half of those measured outside. On the other hand, the meteorologically-generated long-period waves (Fig. (b)) were not reduced in the inlet and even amplified for some data. 156

6 (cm) : Stn-in s (cm) : Stn-in (cm) : Stn-out 1 3 (cm) : Stn-out over 3s (a) Wave-group-induced long waves (b) Meteorologically-generated long waves Figure. Relationship between long-period waves inside and outside the inlet The transmission of waves into an infinitely-long narrow channel with no reflection is theoretically given by Mei (1989) as A B = (1) [1 + ka + ( ika / π )ln( γka / πe)] where A is complex amplitude of the incident waves from the ocean, B is complex amplitude of waves in the narrow channel, k is wave number, γ is the Euler s constant (approximate value is ) and a is width of the channel. The inlet of Hamana Lake can be assumed to be narrow but there should be some reflection from the lake. The transmission coefficient is given as B/A. Figure 5 shows B/A as functions of ka. In the case of 5m water depth (h=5m) and m channel width (a=1m), Eq.(1) gives the transmission coefficient.98 for the wave with period of 3s, which corresponds to the point P-1 (Fig. 5). For the wave with period of 3s, the transmission coefficient yields 1.7 as indicated by P-. The bar charts show results estimated from field data, which is calculated from the ratio of the energy spectra, for calm and high wave conditions, Figures 5(a) and (b) respectively. Under calm wave conditions, observed transmission coefficients show closer values to the theoretical ones while factors show smaller values under high wave conditions. One of the reasons why the transmission becomes small may be that longperiod free waves generated near the surf zone tend to be reflected offshore in storm conditions. 157

7 Eq.(1) : Mei(1989) Eq.(1) : Mei(1989) B/A, ( I in / I out ) 1/ P- ( I in / I out ) 1/ P-1 9/1 1:-13:1 =.77m 1/1 5:-6:1 =.67m B/A, ( I in / I out ) 1/ P- ( I in / I out ) 1/ 9/18 1:3-13: =.9m 9/ :-1:3 =.76m P ka 3 1 ka 3 (a) Calm wave condition (b) High wave condition Figure 5. Transmission coefficient in the inlet comparison with the theory LONG-PERIOD VELOCITY FLUCTUATION Figure 6 shows power spectra of the east-west-ward horizontal velocities measured at Stn-out under calm and high wave conditions. Under high wave conditions, not only the energy in the frequency range of wind waves (less than 3s in wave period), but also low-frequency range, especially between 3s and 3s in the period, were increased s 3s 1 Stn-out: V E 1 3 S(f) (cm /s) / :-1:3 =3.m 1/5 :1-1: =.m F (Hz) Figure 6. Power spectra of bottom velocities for calm and high wave conditions 158

8 In Figure 7, the RMS values of long-period north-south-ward velocities observed at Stn-out are plotted as functions of mean current velocities obtained by averaging the velocity data over 7 minutes. Figures 7(a) and (b) correspond to frequency ranges 3s 3s and 3s 1s, respectively. The size of the circle markers represents the magnitude of RMS value of longperiod waves discussed above. Two data groups are indicated in Figure 7(a): G-1 and G-. The group G-1 is comprised of small RMS values of long-period waves and the long period velocity components seem to be generated by tidal currents because the RMS values of long-period velocity increase as the mean velocities increase. On the other hand, the group G- consists of large RMS values of long-period waves and shows no correlation with mean velocities. This shows that there seem two different sources for the generation of long-period velocity fluctuations around an inlet with strong tidal current. V N LRMS (cm/s) = 1 (cm) G- G-1 Stn-out (N-S) Mean:7min-data RMS: 3s-3s V N - MEAN (cm/s) (a) Velocity components in the range between 3s to 3s 1 8 Stn-out (N-S) Mean:7min-data RMS: over 3s-data = 1.5 (cm) V N LRMS (cm/s) V N - MEAN (cm/s) (b) Velocity components in the range between 3s to 1s Figure 7. Relationship between mean velocities and RMS values of long-period velocities at Stn-out 159

9 Figure 8 shows an example of time series of the RMS value of the long-period velocity comparing with tidal fluctuation of water surface at Stn-out. Increase in the long-period velocity appears at the phase of ebb tide indicated by ellipses in the figure, which implies that the strong tidal current has some influence on the generation of long-period velocities under calm wave conditions. 1 Stn-out Tide Level V N LRMS : 3-3s. Tide Level (cm) V N LRMS (cm/s) 6/11/ 6/11/5 6/11/6 6/11/7 Date Figure 8. Time series of tide level and RMS value of the long-period velocity at Stn-out CONCLUSION The conclusions obtained in the study are summarized as follows: 1) Outside the inlet, the RMS values of the wave-group-induced long-period waves (3s 3s) are increased almost proportionally to the products of the significant wave heights and periods. ) The RMS values of wave-group-induced long-period waves are reduced half in the inlet. The transmission coefficients of the long-period waves into the inlet show good agreement with the theory under calm wave condition, while show smaller values under high wave conditions. 3) The long-period velocity components are increased corresponding to the development of long-period waves. Under calm wave conditions long-period velocity fluctuations seem to be caused by strong tidal currents. 16

10 ACKNOWLEDGMENTS This study was carried out as a part of research project Dynamic sediment management and coastal disaster prevention by advanced technologies supported by the Special Coordination Funds for promoting Science and Technology of Ministry of Education, Culture, Sports, Science and Technology. The authors are grateful to the financial support and collaboration with the project team. REFERENCES Aoki, S.. Generation and Propagation of Coastal Long Waves. Proceedings of Civil Engineering in the Ocean VOL.18, pp (in Japanese) Aoki, S., T. Okabe and I. Deguchi.. Characteristics of Long Wave Generation and Secondary Oscillation in a Harbor:Comparison between Two Coasts with Different Wave Conditions. Proceedings of Coastal Engineering, JSCE, Vol.9, pp (in Japanese) Mei, C.C The Applied Dynamics of Ocean Surface Waves. Singapore:World Scientific Publishing. pp Sato, S.. Interaction between Infragravity Waves and Coastal Sedimentary Processes. Proceedings of Civil Engineering in the Ocean VOL.18, pp (in Japanese) 161

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