Contents preface (VII) introduction 1—37

Fig. 12.4 Movement of water at a bend
Joglekar (3) and other Indian engineers do not agree with the theory of excess energy. According to them (3), the primary cause of meandering is excess of total sediment load during floods. A river tends to build a steeper slope by depositing the sediment on the bed when the sediment load is in excess of that required for equilibrium. This increase in slope reduces the depth and increases the width of the river channel if the banks do not resist erosion. Only a slight deviation from uniform axial flow is then required to cause more flow towards one bank than the other. Additional flow is immediately attracted towards the former bank, leading to shoaling along the latter, accentuating the curvature of flow and finally producing meanders in its wake.
Meanders can be classified (4) as regular and irregular or, alternatively, as simple and compound. Regular meanders are a series of bends of approximately the same curvature and frequency. Irregular meanders are deformed in shape and may vary in amplitude and frequency. Simple meanders have bends with a single radius of curvature. In compound meanders each bend is made up of segments of different radii and varying angles.
The geometry of meanders can be described by the meander length M_L and the width of the meander belt M_B (Fig. 12.2), or by the sinuosity or the tortuosity. Many investigators have attempted to relate the geometry of meanders with the dominant discharge. The dominant discharge is defined (5) as that hypothetical steady discharge which would produce the same result (in terms of average channel dimensions) as the actual varying discharge. Inglis (2) found that for north Indian rivers, the dominant discharge was approximately the same as the bankful discharge and recommended that the dominant discharge be taken as equal to half to two-thirds of the maximum discharge.
Inglis (2) gave the following relationships for M_L and M_B (both in metres) in terms of the dominant discharge (or the bankful discharge) Q (in m³/s) for rivers in flood plains:

M = 53.6 Q^1/2	= 6.06 W	(12.1)
L		s
M = 153.4 Q^1/2	= 17.38 W	(12.2)
B		s

Here, W_s (in metres) is the bankful width of river (Fig. 12.1).

412 IRRIGATION AND WATER RESOURCES ENGINEERING
Agarwal et al. (6) have re-examined the laboratory and field data for discharges ranging from 9 × 10^–6 to 10⁴ m³/s and found that the following relationships proposed by them are better than Inglis’ relationships:


M_L = 29.70 Q^0.32 for Q < 9 m³/s
M_L = 11.55 Q^0.75 for Q > 9 m³/s

and M_B = 0.476 M_L

The sinuosity of a river is defined as the ratio of Joglekar (3) defines tortuosity as,
_{Tortuosity =} talweg length – valley length _{× 100} valley length
(12.3)
(12.4)
(12.5) talweg length to the valley length.

The sinuosity varies from 1.02 to 1.45 over 1500 km length of the river Indus. For the river Ganga, the sinuosity varies from 1.08 to 1.51 (3). Table 12.1 shows the extent of tortuosity of the river Ganga.