# Small-Scale Inlets as Tidal Filters

- David G. Aubrey and
- Lee Weishar

Published Online: 23 MAR 2013

DOI: 10.1029/LN029p0137

Copyright 1988 by the Springer-Verlag

Book Title

## Hydrodynamics and Sediment Dynamics of Tidal Inlets

Additional Information

#### How to Cite

Moody, J. A. (1988) Small-Scale Inlets as Tidal Filters, in Hydrodynamics and Sediment Dynamics of Tidal Inlets (eds D. G. Aubrey and L. Weishar), Springer-Verlag, New York. doi: 10.1029/LN029p0137

#### Publication History

- Published Online: 23 MAR 2013
- Published Print: 1 JAN 1988

#### Book Series:

#### ISBN Information

Print ISBN: 9783540968887

Online ISBN: 9781118669242

- Summary
- Chapter
- References

### Keywords:

- Bournes Pond Inlet;
- Herring River, Menemsha and Nauset;
- Inlet-basin characteristics;
- Ocean tide characteristics;
- Small-scale tidal inlets;
- Tidal measurements

### Summary

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, ηb, to the ocean tide amplitude, η0), 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 dimensionless number $${\rm Q} = {{\rm g} \over \eta }_o \left( {{{\rm a} \over {\omega {\rm A}}}} \right)ˆ2 $$ where g is the acceleration of gravity and co 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_{1}, N_{2}, M_{2}, S_{2}, MK_{3}, MN_{4}, M_{4}, 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 coefficientwas 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} ∝ η0 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 ofthe ratio. a/A, the tidal frequency, ω, and the tidal amplitude, ηo, outside the inlet.