

Chairman: Dr. Hosmani S. P 





Chilika Lake, ( ) on the Orissa coast, India, is one of the unique ecospheres in the world. It is the largest brackish water lagoon with estuarine character. On account of its rich biodiversity and socio – economic importance, it is designated as a ‘Ramsar site’ a wetland of international importance. Based on the circulation / hydrodynamics of the lake, the lake is divided into four sectors. The northern sector receives discharges of the floodwaters from the tributaries of the river Mahanadi. The southern sector is relatively smaller and does not show much seasonal variation in salinity. The central sector has features intermediate of the other sectors. The eastern sector, which is a narrow and constricted outer channel, connects the lagoon with the Bay of Bengal and the tidal effects are important in that area. Thus, due to its complicated geomorphology, the circulation in the lake corresponding to the different sectors is very complex. Interest in detailed analysis of the circulation, biotic and abiotic factors affecting the lake and its limnology is due to the threat to the lake from various factors – Eutrophication, weed proliferation, siltation, industrial pollution and depletion of bioresources. The present paper deals with the numerical simulation of seasonal circulation in the lake. The theoretical formulation leads to a vertically integrated nonlinear model, which includes the effects of wind in two different seasons on the circulation of the lake. In addition, the effect of the complicated boundary as well as the different type of circulation in different sectors of the lake are evaluated. The model is capable of accurate simulation of tidal elevations throughout the lake. A physico  biological model that incorporates the present dynamical model can be used to study the distribution of nutrients and chlorophyll in the lake.
Wetlands
play a central role in regional hydrologic and biogeochemical cycles, in
maintaining biodiversity and in a wide range of human activities. Over the past
two centuries, industrialization, urbanization and deforestation have led to the
wetland loss resulting in the extinction of countless species and alteration of
the relationship of wetlands with the regional environment. The physical
processes in large lakes are complicated due to the flow regime, effluent
discharge from urban runoffs and treated/untreated pollution sources.
It
is important to understand and analyze the individual contributory factors –
changes in the landscape, climate variability, eutrophication, effects of
species recruitment events etc – since the physical, biological and chemical
variability results from a combination of these effects and their interaction.
A longterm multi – disciplinary investigation of the lakes should
include the physico – chemical, hydrological and biological parameters.
The present study is concerned with the seasonal circulation in the Chilika lagoon – the largest brackish water lagoon in India situated along the East Coast in the state of Orissa. The interest and thrust in studying the ecology of the lake is due to the increasing threat to the lake in the form if siltation, choking of the mouth and outer channel, eutrophication, weed infestation, salinity changes and decrease in fishery resources. Description of our study area and its present status are given in detail in our companion paper (Mohanty et al, 2002) and we shall not go into those here. A comprehensive multidisciplinary approach based on modelling and observational studies is required to formulate realistic strategy towards protection and conservation of the lake. In the current study, we examine the basic physical processes in the lake controlled by seasonal variations. The objective is to prepare ground for formulating a physico – biological model to understand the seasonal cycle of the plankton productivity in the lake. The current profile developed in this model will be fitted into the biological model to study how the physical transport processes affect (i) the feeding or predator – prey interaction and (ii) carry passive organisms – eggs and larvae – into areas that are safer for survival. A brief introduction to the hydrology and the hydrodynamic model for the lake is given in section 2. Section 3 describes the grid generation for the numerical scheme used to handle the complicated Chilika topography. It also includes the results and discussions related to the seasonal circulation in the lake.
2.
HYDRODYNAMIC MODEL
The
water spread area of the Chilika lake varies between 1165 to 906 sq km during
the monsoon and summer respectively. A significant part of the fresh water and
silt input to the lake comes from Mahanadi and its distributaries. Direct
rainfall on the lake surface also makes a significant contribution to the fresh
water input to Chilika. The lake shows an overall increase in depth of about 50
cm – 1 m due to monsoon. The mouth connecting the channel to the sea is close
to the northeastern end of the lake. High tides near the inlet mouth drive in
salt water through the channel during the dry months, from December to June. The
lake area proper experiences ‘mean wind’ speeds ranging from 5 kmph in
winter to 10 – 15 kmph in summer. The coastal areas experience higher average
wind speeds up to 25 kmph. (Nayak et al, 1998; Chandramohan et al, 1998)
It
is important to study the seasonal circulation in the lake since the cyclic
variation is key to maintaining the high biodiversity of the area. A distinct
salinity gradient exists along the lagoon due to the influx of fresh water
during monsoon and due to the inflow of seawater through the outer channel. This
periodicity is responsible for maintaining the different species – marine,
estuarine and fresh water ones. Also, the currents regulate the supply of
dissolved inorganic nutrients to the surface layer where most of the
phytoplanktons are found. They also control the light levels experienced by
phytoplankton below the surface layer. Thus physical exchange process plays a
key role in the sustainability of the planktonic food web.
Simulation
of lagoon/estuarine processes may require detailed treatment of irregular
boundaries, complicated bottom topography, tidal effects, sediment transport,
chemical transformation, biological production etc. Knowledge of the circulatory
dynamics of the lake in general and seasonal circulation in particular is a
prerequisite to estimate the other events in the lake. For shallow lakes it is
appropriate to average all physical variables over the depth. Equations
describing the physical limnology are based on the hydrostatic equations of
motion and Boussinesq approximation and are known as the shallow water
equations. (Hutter et al, 1984)
2.2 Model simulation
For the formulation of the model, we use a system of rectangular Cartesian coordinates in which the origin O, is within the equilibrium level of the seasurface, Ox points towards the east, Oy points towards the north and Oz is directed vertically upwards. In the formulation, the sphericity of the earth’s surface is ignored, the displaced position of the free surface is given by and the position of the sea floor by The basic hydrodynamic equations of continuity and momentum for the dynamical processes in the water body are given by
where ( ) are the Reynolds averaged components of velocity in the direction of respectively. is the Coriolis parameter, g is the acceleration due to gravity, r is the density of the water supposed to be homogeneous and incompressible, are the x, y components respectively of the frictional surface stress, p is the pressure and t is the time. Molecular viscosity has been neglected. The terms in are included to model vertical turbulent diffusion. Denoting the wind stress and bottom stress components as and respectively and the surface pressure as , the boundary conditions become
The
last condition is the kinematic surface condition and expresses the fact that
the free surface is materially following the fluid. Since the main objective
lies in the prediction of long waves in shallow coastal waters, it is reasonable
to assume that the wavelength is large compared to the depth. With this
assumption, it may be shown that equation (4) reduces to hydrostatic pressure
approximation
The
principal equations (1), (2), (3), and (7) could be solved, but the procedure
would be laborious because of the presence of the vertical coordinate. Unlike
the problems of the atmosphere, a boundary layer would need to be designed both
at the top and bottom of the domain of integration. There is insufficient
knowledge about the flow in such boundary layers. To get over this difficulty, a
simplification is generally introduced by integrating vertically. The unknown
dependent variables are then
a) the water transport (or mean current) and
b) the surface height
A
parameterization of the bottom stress must be made in terms of the
depthaveraged currents. This is frequently done by conventional quadratic law.
where c_{f} = 1.25 10^{3} is an empirical bottom friction coefficient.
With this modification, the equations describing the flow are given by
where = and = are new prognostic variables and gives the total depth of the basin and where overbars denote depth averaged values, e.g.,
The equation of continuity (9) along with the two momentum equations (10) and (11) form three basic equations of the numerical model. It consists of a set of three coupled equations for the unknowns , ,z. The forcing terms in these three equations arise out of (i) the Coriolis term, (ii) the inverted barometric changes due to fall in atmospheric pressure, (iii) the component of wind stress and (iv) the bottom stress component. However, the forcing due to barometric changes is neglected, as its effect is negligible due to small variation of pressure over the region under study.
2.3
Boundary and initial conditions
In
addition to the fulfillment of the surface and bottom conditions (5) and (6),
appropriate conditions have to be satisfied along with the lateral boundaries of
the model area under consideration for all time. Theoretically the only boundary
condition needed in the vertically integrated system is that the normal
transport vanish at the coast, i.e.,
for all (13)
where a denotes the inclination of the outward directed normal to the  axis. It then follows that along the directed boundaries and along the directed boundaries. Assuming that the motion is observed from an initial state of rest, we get,everywhere for
Clearly,
these equations are nonlinear in nature and an analytical solution is not
possible without making major simplifying assumptions in which many important
parameters may have to be dropped. The best alternative is the numerical
solution. The numerical technique based on finite difference scheme consists of
solving the governing equations at a discrete set of points in space at discrete
instants of time. This method is also applicable when the forces and the
boundary conditions are described by very complicated functions, as is almost
always the case in reality. For practical forecasting, it is superior to the
analytical methods.
3. RESULTS AND DISCUSSIONS
Our preliminary results are based on our numerical experiments for the analysis area shown in Fig.1 covering an extent of about 60 km and 50 km in the eastwest and the northsouth respectively. In order to incorporate all the islands, the coastal boundaries and the openchannels, it is required at least a minimum grid interval of about 750m. Accordingly, the Chilika lake is approximated as closely as possible to the realistic boundary of the lake. The number of grid points in the  and  direction are 81 and 68 respectively and hence = =0.75 km approximately. With this grid specification, it was found that computational stability could be maintained with a time step of 60 sec. The manner of the boundary construction is illustrated in Fig. 1. The coastal boundary in the model is taken to be a vertical sidewall through which there is no flux of water. However, the lake is connected actually through two open channels. In the preliminary study, these open channels are not considered and the boundary is treated as a closed
one.
Address:
Center for Atmospheric Sciences
Indian Institute of Technology – Delhi
Hauz Khas, New Delhi – 110 016
†Department of Marine Sciences
Berhampur University, Berhampur – 760 007