GenCade:Representation of Inlets

GenCade employs the Inlet Reservoir Model (IRM) as first presented in Kraus (2000) and further developed by Larson et al. (2003, 2006). Each inlet is represented by six morphological elements (shoals and bars) plus the inlet channel (Figure 1). Each morphological element is, in turn, represented by an actual sand volume Vx and an equilibrium volume $V_{xq}$, where the subscript x is a placeholder for subscripts a (attachment bars), b (bypass bars), e (ebb shoal), or f (flood shoal). Each morphological element is assumed to have a certain equilibrium volume for fixed hydrodynamic and sediment conditions. The flux of sediment out of each morphological element is given by:

$Q_{ox}=Q_{ix}{\frac {V_{x}}{V_{xq}}}$

where $Q_{ox}$ represents the flux out of the element x and $Q_{ox}$ is the flux into the element. The attachment and bypass bars also have a third index, l or b, in front of the other two, where index l stands for the left side of the inlet and index r stands for the right side when looking seaward from land. When the sediment transport goes from left to right, the attachment and bypass bars on the left-hand side of the inlet are not active, as the sediment is assumed to be transferred from the beach on the left-hand side onto the ebb shoal without passing through the attachment and bypass bars on that side. The corresponding situation occurs as sediment is moving from right to left.

In Figure 1, the transport goes from left to right. A transport rate $Q_{lst}$ is moving alongshore towards the inlet, which may or may not be stabilized by a jetty. If there is a jetty, a portion of this sediment $Q_{j}$ will be trapped by the jetty (thus, when no jetty, $Q_{j}=0$) whereas the remaining part $Q_{in}$ will enter into the inlet system. A part of this rate may go to the ebb shoal, $Q_{ie}$ , depending on how full the ebb and flood shoals are with respect to the equilibrium volume, while the other portion, $Q_{ic}$ , will go into the inlet channel. This will, in turn, feed the ebb and flood shoals in proportion to their relative volumes.

Unless the system is completely full at equilibrium, only a portion $Q_{out}$ of the incoming rate $Q_{in}$ will leave the inlet system and be transported further along the beach. Initial and equilibrium volumes of the respective morphological elements are specified as input values to the model as are the respective locations of the attachment bars.

Figure 1. Interactions between the morphological elements of an inlet

Walton and Adams (1976) derived empirical equations for the equilibrium ebb shoal volume based on field data from 43 United States inlets. Walton and Adams’ definition of the ebb shoal approximately corresponds to the sum of the IRM’s volumes of the ebb shoal and bypass bars. To employ these equations for computing $V_{xq}$ of the different morphologic units, some assumptions must be made concerning the size relationship among them. Historical aerial photographs or bathymetric surveys can be employed to determine the relative proportions of the morphological elements. To represent an inlet that does not have ANY impact on adjacent beaches the inlet needs to fulfill ALL the three conditions below:

1. Have no jetties on either side of the channel;
2. Have all morphological units completely full where the initial volume of the morphological elements is equal to the equilibrium volume;
3. $Q_{out}$ on either side is released only to the first cell adjacent to the inlet.

[[[ Ocean City, MD Example ]]]

As an illustration of the use of the inlet module in GenCade, an example from Ocean City, MD, will be briefly presented. Beaches south of Ocean City Inlet have experienced long-term shoreline recession caused by impoundment of southerly-directed longshore transport by the north jetty and capture of additional sand by the ebb tidal shoal complex. The sediment trapping capacity of the north jetty has effectively reached its maximum, with most of the sediment transported southward bypassing the jetty (Stauble et al. 1993). This sediment deposits in the entrance channel of the inlet, settles on the ebb-tidal shoal, or bypasses the inlet and supplies Assateague Island south of the inlet with material.

Since the Ocean City Inlet opened in 1933, the evolution and migration of the ebb-tidal shoal, the bypass bar, and the attachment bar have been monitored. In this particular study, only the volumetric evolution was considered to validate the IRM.

The net sediment transport $Q_{lst}$ at the site is estimated at some $150,000{\frac {m^{3}}{year}}$ from north to south (Stauble et al. 1993). Equilibrium volumes of the morphological units at the inlet are estimated to be $3Mm^{3}$ for the ebb-tidal shoal, $7Mm^{3}$ for the bypass bar, and $0.5Mm^{3}$ for the attachment bar.