Introduction

The dynamics of the flow in the inlet are described by the equation for uniform unsteady open channel flow. Variations in depth with tidal stage are neglected. The dynamic equation is complemented with a continuity condition that assumes a pumping mode for the back-barrier lagoon, i.e., the water level in the back-barrier lagoon fluctuates uniformly. Although these are simplifications, the advantage is that they allow relatively simple analytical solutions that are helpful in identifying mechanisms responsible for phenomena such as resonance, tidal choking and generation of (odd) overtides. As examples, analytical solutions by Keulegan (1951, 1967) and Mehta and Özsoy (1978) are presented. Results of the analytical solutions are applied to a representative inlet and compared with numerical results.

Inlet Schematization

The tidal inlet system is schematized to an inlet and a back-barrier lagoon (Fig. 6.1). The inlet connects the back-barrier lagoon and the ocean. Its geometry is simplified to a prismatic channel with diverging sections at both ends. The backbarrier lagoon is schematized to a basin with uniform depth. Referring to Chapter 2, in the real world inlets have varying widths and depths and back-barrier lagoons are characterized by tidal flats and marsh areas. Therefore, the schematization presented in Fig. 6.1 is only a rough representation of an actual inlet.

Governing Equations and Boundary Condition

Dimensional Equations

In deriving the governing equations, the major assumptions are 1) one-dimensional unsteady uniform flow in the inlet, 2) a uniformly fluctuating water level in the basin (pumping or Helmholz mode) and 3) negligible variations in cross-sectional area of the inlet and basin surface area with tidal stage. With these assumptions, the equation for the flow in the inlet is (Appendix 6.A):

In this equation u is the cross-sectionally averaged velocity, positive in the flood direction, L is length of the prismatic part of the inlet, g is gravity acceleration, t is time, F = f /8 where f is the Darcy–Weisbach friction factor, R is hydraulic radius, m is entrance/exit loss coefficient, η0 is the ocean tide and ηb is the basin tide.