The objectives of cross-section analysis are to acquisition the understanding of the catchment management (Pen et al, 2001), flood frequencies (Grant et al. 1992). The form of the cross-section (A) of a river channel at any location has been formulated as, A = f (V. S. B), where V is flow, S is quantity and character of the sediment movement through the section and B is the character and composition of the materials making up the bed and banks (Leopold et al. 1964), the form of the cross section, A = f(X,Y), where X = the set of transverse series of points and Y = the set of longitudinal series of points (**Mondal and Satpati** 2019), is the product of surface width and mean depth (Knighton, 1998), equivalent to water volume per unit length of the concerned channel (Mosley, 1983), roughly parabolic in shape (Lane, 1955), characteristically irregular in outline and locally variable (Knighton, 1998) and the natural channel design involves dimension, pattern and profile of a stable cross section (Swamee et al. 2000). In the scientific context and also in river management, the stream cross-sectional geometry or hydraulic geometry has been treated as a key element (Lord et al. 2009). Hydraulic geometry is an empirical model to provide a quantitative description of stream behavior either at-a-station or along a particular stream (**Knighton**, 1977). In this model discharge is the dominant independent variable to which the dependent variables adjust and simple power functions are considered to be a suitable expression of the relationship between the dependant variables and discharge, w = aQb, d = cQf, v = kQm, where, w is width, d is mean depth and v are mean velocity (Knighton, 1998; Richards, 1982; Leopold et al. 1964; Leopold and Maddock, 1953). Hench, wdv = Q, sum of the exponent, b + f + m = 1, and product of the coefficient, ack = 1. The at-a-station model reflects the general cross-section shape, dependant on material properties and the parabolic channel-form is the outcome in the homogeneous non-cohesive sand environment (Richards, 1982).

The fluvial geomorphology has the brilliant experiences of the emergence of a large number of hypotheses, deployed for the analysis of hydraulic geometry of the cross-section. The chronological discussions of the hypothesis are the regime theory, which is based on analysis of data from stable canals on the Indian subcontinent. The summary of the hypothesis is, “given the design discharge and an accomplish amount of sediment is known to size, what will nature choose for the width, depth and bed slope of the channel to convey both the water and sediments from one point to another point”(Lindley, 1919) and followed by subsequent modifications (**Lacey, 1957;** Blench, 1957), the tractive force theory emphasis on the limiting force for a boundary of any given material under non-scouring condition. The lift and drag force are directly proportional to the tractive force and the theory tries to establish the relation between hydraulic geometry parameters and discharge (Lane, 1955), the power function theory is empirical and based on measurements of channel geometry and discharge, which is applicable for both at-a-station geometry and downstream geometry (Wolman, 1955; **Leopold and Maddock, 1953**), the least channel mobility theory hypothesized that for a given discharge and boundary condition, channel with different cross-sections will tend to attempt with minimum mobility **(**Dou, 1964), the fundamental postulate of the theory of minimum variance is that a change in stream power is adjusted by the channel change encompassing as equal a change of each component of power, the components of power being velocity, depth, width and slope (Langbein, 1964), the similarity principle theory is an energy deficiency model, advocated the alluvial stream tend to adjust the bed roughness with energy deficiency in similar manner (Engelund and Hansen, 1967), the theory of minimum energy degradation rate deals with the principle of minimum entropy production rate, that has been derived to generalized excess energy gradient equation which then yielded a set of hydraulic geometry relations (Brebner and Wilson, 1967), the hydrodynamic theory has been postulated based on the principles of conservation of mass and momentum for water and sediments, taking the form parameters as width, depth, velocity and slope (Smith, 1974), threshold channel geometry theory states that the formation of threshold channel and shifting from one threshold condition to another, is time being and heavy precipitation-guided and the theory deals with the parameters such as top width, cross sectional area, wetted perimeter, hydraulic radius, hydraulic depth (Li, 1975), the theory of minimum stream power advocated as, “ ..that a stable channel configuration corresponds to a minimum stream power per unit channel length and for small value of water discharge..”, and the parameters are width, depth, slope (**Channg**, 1979b), six variables were applied to formulated the maximum sediment transport theory which stated that the alluvial channel adjust its slope and geometry to minimize its transport capacity (White et al. 1982),the theory of maximum friction factor hypothesized that the deformation of channel shape depend on the rise of local maximum friction factor (**Davis and Sutherland**, 1983), the theory of minimum energy dissipation rate conveys that a channel in equilibrium somehow attain a minimum energy expenditure mode through a justified boundary condition (Yang, 1987; Yang and Song, 1986; **Yang and Song, 1981)**, theory of minimum froude number concerns with the channel stability as well as equilibrium condition that condition has been measured by froude number and also closely related to the bed material movement (Jia, 1990), theory of maximum entropy employed a morphological equation based on a given discharge the flow depth and width were independent variables among five hydraulic variables and the adjustment among the variables are seldom (**Dang and Zhang**, 1994), the thermodynamic entropy law states that under a given discharge, the three geometric characters of a channel i.e. width, flow depth and slope are adjusted in such a way that the system maintain the second law of thermodynamic (Yalin and Ferreire Da Silva, 1999), the theory of maximum flow efficiency advocated that natural channel adjust their form with the available maximum flow efficiency and in such a condition river exhibits a regular hydraulic geometry **(Huang and Nanson**, 2000). The other notable findings are Lovric and Tosic (2016), NEH (2007), Hey (2006), Darus et al (2005), Sinha-Roy (2001), Rosgen (1994), etc.

The present paper deals with the character of the cross-section of the Ichamati river, an important distributary and also meandering river-system of the western part of Ganga Delta **(**Rob, 1991) has been studied in recent time (**Mondal, 2011a ; 2012**; Mondal and Satpati, 2019a, b; 2017; 2016; 2015; 2014; 2013; **Mondal and Bandhyapadhyay**, 2014a, b). The river is anthropogenically delinked (the off take point at Majdia, Nadia, India; Rudra, 2014) from the Mathabhanga river (Sarkar, 2004). After traversing a length of 19.5 km in India, the Ichamati river enters Bangladesh. It flows for 30 km in Bangladesh and again enters in India. The Ichamati river did not get any water from the Mathabhanga river and remain dry throughout the year except the rainy season (Bandyopadhyay et al. 2015) and seems to in a waning condition due to degeneration (**Bandopadhyay et al. 2015**). The river acts as a connecter between the ‘Nadia group of river’ and Sunderban, in the south (**Mondal and Bandopadhyay**, 2014a, b), which did not permit to increase the salinity in the southern regions being carried the freshwater from the apex. The decaying of the river creates hydro-geomorphological as well as geo-environmental problems in the study area. The northern limit of tidal propagation of the river is to be found, at a place called Tipi, some 11km away downward from the study area. In the study area, the river is characterized only by the tidal-push water (which has been discussed in the later section) and the velocity is hardly measurable even by a current meter. This scenario may be treated as a given discharge or a constant velocity or a steady-state non-uniform flow (dv/ dx = 0) (CIVE2400, 2014). The river has experienced frequent floods (1802, 1823, 1838, 1857, 1859, 1867, 1871, 1885, 1890, 1936, 1938, 1952, 1955, 1959, 1966, 1970, 1971, 1978, 1984, 1999, 2000, 2004 (**Mondal et al**, 2019; Fenton et al. 2017; Basu and Howlader, 2008), bank erosion (Sarkar, 2004), prolong water logging condition at some pocket areas both in India and Bangladesh (District Statistics-Satkhira, 2013).To minimize these problems a holistic river– management program should be lunched through the stretch of the river. But the selected reach of the river, lying on the international boundary, does not permit to do so, so far. The introspection of fluvial geomorphology is to impose the vivacious spirit on the landform evaluation (Leopold, 1953), but the concentrated focus of a hydraulic engineer is the formulation of the basic equations and implementation of them. The basic attitude of this paper is formulating an index; bring these two views into a perfect agreement. And for doing that the arrangement of the study has been set up as (1) general discussion about the geometric character of the channel with respect of symmetrical assessment (**Forthingham and Brown**, 2002), (2) Justification the cross section with the present discharge, (3) to formulate the Stable Cross Section Index (SCSI), (4) ascertain the validity of the SCSI and (5) ascertain of the state of the stability of the channel under the existing discharge.