TIDAL INLETS Natural of man-made cut through barrier island Allows for bay flushing Provides access for maritime traffic Normally migrate unless restrained by hard structures Puts system in an unnatural state and causes sediment to build up or be lost

TIDAL HYDRODYNAMICS Caused by differences in bay and ocean water levels. Assumptions: 1)Steep sided bay so the cross-section area is not a function of water level 2)The cross-sectional area of the channel changes as the water level moves up and down 3)Length and width of channel are fixed 4)Mean depth in the channel is h i 5)Bay depth is much greater than mean channel depth so wave travel times are not important 6)Assume only one tidal component driven by simple cosine wave ABAB ACAC L b ocean bay

TIDAL HYDRODYNAMICS Ocean tide with amplitude a 0, and frequency, σ Bay tide with different amplitude and phase shifted. Bay tide lags ocean tide. D&D

TIDAL HYDRODYNAMICS Mass Conservation: flow rate through the inlet, Q, assuming bays fills uniformly over plan area Q=velocity times width times mean depth plus the average tidal elevation Note that the flow rate can also be found from the time derivative of the volume in the bay as Assume that h i >> average tidal amplitude (i.e. linearize)

DYNAMIC EQUATION From Navier-Stokes along channel axis Assume P is hydrostatic, P=ρg(η-z) Integrate over depth Where U = depth-averaged velocity And the shears are denoted by at the surface and b at the bed

DYNAMIC EQUATION Define the bed shear stress using the quadratic drag law and assume no wind such that the surface shear is zero, and integrate along the channel to get Where L is the channel length and the water level elevations at location L and location I are just inside the channel on the bay and ocean side and are not typically equal to the tidal elevation in the bay and ocean respectively. Where K en is an entrance coefficient to account for losses due to the a velocity head in the inlet; typically 0.1 to 0.3 Where K ex is an exit coefficient to account for flow expansion losses; typically on the order of 1.0

DYNAMIC EQUATION Finally substitute for the bay and tidal amplitudes and integrate across the channel section to get Where R h is the wetted perimeter or hydraulic radius (part where water touches for frictional drag along walls This equation is the one that is often used to estimate things like maximum tidal velocities, channel widths etc after some additional assumptions are made. Typically used in an engineering fashion because one has to utilize coefficients like f, the K en and K ex and keep in mind the initial assumptions of bay geometries.

KEULEGAN METHOD Consider the intertial term to be small then Potential energy = allocation of energy losses through various means Solving for U

KEULEGAN METHOD Nondimensionalize and replace U by From mass conservation Leaves where K is called the repletion coefficient (filling coefficient). Signifies degree to which a bay will fill depending on bay, inlet and tidal parameters

KEULEGAN METHOD Increases in the numerator of K imply an increase in the relative tidal amplitude Increases in the denominator of K (increases in friction) decreases the relative tidal amplitude. Large bays likely have a small K because the area of walls is large Keulegan assumed that D&D Large bays Small bays

KEULEGAN METHOD Dimensionless maximum velocity can be found from conservation equation D&D

KEULEGAN METHOD Bay tide lags ocean tide by a phase shift defined by Note that as K gets large, implying a small bay, the phase shift approaches zero. As the bay gets very large (small K), the phase shift approaches but does not reach 90 degrees. All these types of analyses can be repeated for a Linear approach rather than Keulegan’s

TIDAL PRISM The tidal prism, Ω, is the volume of water flowing in or out during flood or ebb tide. Example: For a channel that is 120 m wide and 4 m deep, determine K, a B, U max and the tidal prism if L= 600m, a 0 =0.5m, A B =20x106 m 2, f=0.08, R h =3.75m and a tidal period of 12.4 hours. From figure 13.4, From figure 13.5,

INLET AREA RELATED TO TIDAL PRISM O’Brien and Jarret separately related the Ac to the tidal prism. For natural sandy inlets with Ac in ft 2 and Ω in ft 3 From After substituting for Ac Rough estimate of a max velocity for a natural inlet to be viable.

EBB TIDAL SHOALS Created by sediment being carried out of inlet and deposited offshore FLOOD SHOAL EBB SHOAL

EBB TIDAL SHOALS waves Ebb currents pushes seds offshore Waves pushing seds onshore Reach a dynamic equilibrium where shoals form Note that if the inlet was closed, the shoal would move shoreward under wave action and spread out along coast Large waves = small shoal Small waves = large shoal Some empirical relationships for shoal volume (Walton and Adams, 1976)