Small-Scale Inlets as Tidal Filters

Abstract

The tidal distortion by small-scale tidal inlets has been investigated at six locations on or near Cape Cod, Mass. For these inlets the ratio of the inlet cross-sectional area, a, and the surface area of the adjoining estuary, A, ranged from 0.36 × 10^-5 to 111 × 10^-5, while the length of the inlets, ranged from 42 m to ~380 m.

The amplitude of the semidiurnal M₂ tide on the ocean side of the inlets varied from 18 cm to 98 cm with corresponding M₄/M₂ ratios of 0.28 and 0.01. The response function L² (the squared ratio of the basin tide amplitude, 03B7;_b, to the ocean tide amplitude, 03B7;_o), for the semidiurnal tides (N₂, M₂, and S₂) was 0.35 for six inlets, reflecting the constricted nature of these inlets.

Three approximations are made to simplify the equations of motion for constricted inlets (a/A<2.0 × 10^-5) and as a result the response function is proportional to a $Q = \frac{g} {{\eta _0 }}\left( {\frac{a} {{\omega A}}} \right)^2$, dimensionless number where g is the acceleration of gravity and ω is the frequency of the tidal constituent. The logarithms of L² and Q for six constricted inlets and for 12 tidal constituents (0₁, K_b N₂, M₂, S₂, MK₃, MN₄, M4, MS₄, MK₅, M₆, and M₈) were fit by linear regression to the equation ln(L²) = ln(cQ^m). The correlation coefficient was 0.82 with m= 0.90 and c= 0.09.

Deviations from this relationship occur for large ratios of a/A (~100 × 10^-5) because the approximation u² α η_o is not valid, and when a large fraction of the basin’s surface area consists of tidal flats (~50%) which generate harmonic constituents within the basin such that L²> 100.

The results show that a constricted inlet acts as a tidal filter which is a function of the ratio. a/A, the tidal frequency, ω, and the tidal amplitude, η₀, outside the inlet.