4.2.1 Mixing Index (MI)
To classify the mixing condition in the estuary a new index is proposed in this study namely mixing index (MI) which is defined as the ratio of average tidal flux per unit width to the gravitational flux per unit width of the channel.
The tidal and gravitational fluxes are the major factors that influence the salinity distribution in the estuary. In order to reach a detailed understanding about the effect of these fluxes on the mixing type using mixing index, a diagram showing the relationship between tidal flux (TF) and gravitational flux (GF) was created (Fig. 4.17).
Even though the present diagram might be limited to the present simplified estuary, there was a clear separation of the mixing types. The estuaries having low TF and GF are tend to have well mixed condition in the estuary, generally these estuaries are very
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shallow in nature and dominated by the freshwater discharges. Estuaries with low TF and high GF tend to have the stratified type, this type of estuaries are with micro tidal and deep estuaries, such as Fjord type. The estuaries with high TF and GF tend to have the well mixed conditions, since these estuaries are generally macro tidal to hyper tidal.
For the better classification of estuaries using basic parameters, MI can be used effectively. In this study quantified the MI by considering the seawater salinity of 30 and freshwater salinity of 0. The mixing can be classified using these limits, if MI <
0.6 then the estuary is classifies as stratified type, if the MI is between 0.6 to 1 then the estuary is partially mixed, and the estuary is well mixed for the MI greater than 1.
4.2.2 Application of MI to Estuaries in Japan and around the World
The MI was applied to the some of the estuaries in Japan and the world to check the applicability. The data of the 105 estuaries were collected from the report
Fig. 4.17 Relationship between tidal flux and gravitational flux.
0 2 4 6 8
0 2 4 6
8 Well Mixed Partially Mixed Salt Wedge
Tidal flux per unit width (m2 /s)
Gravitational flux per unit width (m2/s)
MI=1.0
MI=0.6
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published by the Ministry of Land, Infrastructure, Transport, and Tourism. Bed elevation data was available for the 82 estuaries out of 109 estuaries (Table A1). The average bed elevation around the river mouth and bed slope was given in the report.
Average depth of the estuary was calculated using these two parameters. Fig. 4.18a shows the classification of estuaries in Japan using MI. The colour of the symbols show the region in which estuary located in Japan, which are given in Fig. 4.20. 52 estuaries were exactly classified out of 82 which are 63.4%. The error in classification mainly due to the estuary depth, since only average depth around estuary mouth was available.
The MI is more sensitive to the estuary depth. The mixing condition of Japan estuaries strongly depends on the ocean to which it flows. For example, the estuaries in Region C (Hokuriku), flow into the Japan Sea, which have very low tidal ranges and all are partially, mixed type. Whereas the estuaries flowing into the Pacific Ocean showed the partially mixed to well mixed conditions. The estuaries which are flowing into the Ariake Sea (I10-I8) are have well mixed conditions, which are macrotidal estuaries.
The mixing index was also applied to the some of the estuaries in the world available in the literature which is shown in Fig. 4.18b. The details of collected data and source are given in Table A2. The estuaries are ranging from macro tidal to micro tidal as well as from well mixed to salt wedge type. The mixing condition of the estuaries are classified well using the mixing index, except the Weser River estuary in Germany, Seine River estuary in France ,and Sebou River estuary in Morocco. These three estuaries are the partially mixed type. Whereas, these estuaries are fall under well mixed type estuaries when classified using the mixing index. Because the mixing index increases with increase in estuary length and decreases with increase in depth.
Fig. 4.19 shows the classification of each mixing type individually for the estuaries around the world including Japan. 29 (71%) of 41 estuaries were exactly fall into the zone of well mixing (Fig. 4.19a), whereas 9 estuaries were classified as partially mixed and the remaining were salt wedge type. 15 (41%) of 36 estuaries exactly fall into the zone of partially mixed type (Fig. 4.19b) and 30 (91%) of 33 estuaries were exactly fall into the zone of salt wedge type (Fig. 4.19c). Overall, 74 estuaries out of 110 estuaries were exactly fall into the respected mixing zones, which are 67%. The partially mixed type is a transition between the salt wedge and well mixed
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type. There could be chance of wrong classification with the manual observation of contour maps. From the Fig. 4.19b, it is clear that the estuary classified as partially mixed type is actually classified as the salt wedge type. From the observed tidal data
Fig. 4.18 Classification of estuaries in (a) Japan (color of symbol corresponds to the color of the region in Fig. 4.20) and (b) around the world other than Japan based on mixing index.
0.01 0.1 1 10 100
0.01 0.1 1 10
100 A1 A2 A3
A4 A5 A6 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 D1 D2 D3 D4 D5 D6 E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 F1 F2 F3 F4 F5 F6 F7 F8 G1 G2 G3 G4 G5 G6 G7 G8 G9 H1 H2 H3 H4 H5 H6 I1 I2 I3 I4 I5 I6 I7 I8 I9 I10 I11 I12 I13 I14
Tidal flux per unit width (m2 /s)
Gravitational flux per unit width (m2/s) PM WM
SW
Well mixed Partially mixed Salt wedge
(a)
(b)
0.01 0.1 1 10 100
0.01 0.1 1 10 100
SW PM
Hudson, US Pamilco, US Chesapeake, US Delware, US Snohomish, US Lynher, UK Tavy, Uk Humber, UK Tamar, UK Tweed_S, UK Tweed_N, UK Taf , UK Brisbane, Australia Ojiang, China Jiaojiang, China Gironde, France Seine, France Charente, France Mekong, Viatnam Guadiana_N, peninsulia Guadiana_ S, peninsulia Hoogly, India Weser, Germany Elbe, Germany Scheldt, Belgium Incomati, Mozambique Sebou, Morocco
Tidal flux per unit width (m2 /s)
Gravitational flux per unit width (m2/s) WM
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Fig. 4.19 Individual classification of (a) well mixed, (b) partially mixed and (c) salt wedge estuaries around the world including Japan.
0.01 0.1 1 10 100
0.01 0.1 1 10 100
0.01 0.1 1 10 100
0.01 0.1 1 10 100
Tidal flux per unit width (m2 /s) (a)
(b)
(c)
WM PM
SW
WM PM
SW
WM PM
SW Tidal flux per unit width (m2 /s)Tidal flux per unit width (m2 /s)
Gravitational flux per unit width (m2/s)
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(Table A1), most of the estuaries are in the microtidal (< 2 m) estuaries, which are salt wedge type estuaries normally. The MI gives the advantage of exact classification of estuarine mixing type even with the limited data.
Fig. 4.20 Regions of the Japan.