  In this work, we consider the two dimensional tidal dynamics equations in a
bounded domain and address some optimal control problems like total energy
minimization, minimization of dissipation of energy of the flow, etc. We also
examine an another interesting control problem which is similar to that of the
data assimilation problems in meteorology of obtaining unknown initial data,
when the system under consideration is the tidal dynamics, using optimal
control techniques. For these cases, different distributed optimal control
problems are formulated as the minimization of suitable cost functionals
subject to the controlled two dimensional tidal dynamics system. The existence
of an optimal control as well as the first order necessary conditions of
optimality for such systems is established and the optimal control is
characterized via adjoint variable. We also establish the uniqueness of optimal
control in small time interval.
