# 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 M_{2} tide on the ocean side of the inlets varied from 18 cm to 98 cm with corresponding M_{4}/M_{2} ratios of 0.28 and 0.01. The response function L^{2} (the squared ratio of the basin tide amplitude, 03B7;_{b}, to the ocean tide amplitude, 03B7;_{o}), for the semidiurnal tides (N_{2}, M_{2}, and S_{2}) 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 L^{2} and Q for six constricted inlets and for 12 tidal constituents (0_{1}, K_{b} N_{2}, M_{2}, S_{2}, MK_{3}, MN_{4}, M4, MS_{4}, MK_{5}, M_{6}, and M_{8}) were fit by linear regression to the equation ln(L^{2}) = 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 u^{2} 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 L^{2}> 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, η_{0}, outside the inlet.

## Keywords

Tidal Flat Flood Tide Tidal Amplitude Tidal Constituent Tidal Inlet## Preview

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