Chapter 13

Tidal Hydrodynamics and Inlets

Tidal Inlets

Hydraulically connecting lagoon

with ocean

Tides in lagoons

Navarre Pass, FL

Pensacola Bay, Santa Rosa Sound, and Choctawatchee Bay

Navarre Pass, FL

Tides

The tide in the lagoon lags and is smaller than thetide in the ocean

Tides in the ocean are predicted (except for storms)

Chapter 2

Conservation of Mass and Momentum

Mass:

Island

Linearize:

Planform area of bay

OceanBay

Conservation of Momentum

Add entrance and exit losses

Assume hydrostatic pressure

Integrate across channel

Hydraulic radius:

Note form of shear stress with abs value

Keulegan Method

Neglect inertial term as small

Solve for U

Using Conservation of Mass:

Non-dimensional forms:

Coefficient of Repletion

Nonlinear first order ODE

All of the parameters in $K$ can be determined from navigationalcharts, tide tables, and estimates of frictional losses. Examining theirinfluence on the repletion coefficient directly shows thatincreases in all of the parameters in the numerator (the inlet cross-section) will increase the relative filling of the bay, whereas increasing the parametersin the denominator (bay plan area, frictional lossesin channel) will decrease the relative filling in the bay. For large bays,then, the repletion coefficient is likely to be small.

Keulegan’s Solution

Keulegan’s Solution

Phase Lag Between Ocean and Bay

Bay Response

Linear Problem

From Conservation of Mass:

Conservation of Momentum (with acceleration):

Linear (Forced) Dynamics Equation:

Solution

Assume

Ratios of friction to inertial force

and hydrostatic to inertial force

\sigma_N is the natural frequency in absence of friction and tidal forcing (raise water level in bay and let go

F_0 is the Forcing Magnitude in figure.

Linear Solution

Large \phi_2 gives a_B/a_O of 1, small \phi_2 gives small tide in bay

Effect of Inlet Cross-section on Tidal Prism

Effect of Bay Area on Prism

Effect of Cross-sectional Area on Velocity

Nonlinearities in the Inlet Tides

Inlet Stability

Indian River Inlet, DEand

Ocean City Inlet, MD

Note the bay systems

Ocean City, MD

Ocean City Bathymetry

Why is the shoal asymmetrical? Why is there no connection of the shoal to the island on thenorth side?

Indian River Inlet, DE

Dredging

Bypassing

Cross-sectionalArea

Scour

Indian River Inlet Ebb Shoal

Tidal Prism versus Cross-Section

M.P. O’Brien (1931, 1969)

Tidal Prism versus Cross-section

Jarrett (1976)

Units: Ac [ft2] [ft3]

10^2 to 10^6

Ebb Tidal Shoal Volume

Sedimentary Stability

Bypassing at So.Lake Worth Inlet, FL

Schematic of Weir and Deposition Basin

Weir systems:

Hillsboro Inlet, Fl

Nerang Inlet, Australia