Waves and Strong Tides (UMAP)

This module analyzes the motion of water underneath a surface wave in the ocean in order to determine formulas for the wave speed. Next, an idealized bay is considered and the same analysis is used to show that the length of the bay determines which waves can fit naturally in it. If any one of these waves has a period close to that of the tide, then this bay will resonate with the tide and experience a huge tidal range. Thus, changing the length of such a bay could cause daramatic changes in the tidal range. This result is used to illuminate the subject of harnessing the huge tides in the Bay of Fundy/Gulf of Maine system. An appendix on partial derivatives reviews the definition of a partial derivative and derives a particular equation, the continuity equation, that is used in the module.

Table of Contents:

INTRODUCTION

TIDES

SURFACE OCEAN WAVES

SURFACE WAVES FEEL THE OCEAN FLOOR

EQUATIONS FOR MOTION UNDERNEATH A SURFACE WAVE

PRESSURE UNDERNEATH A SURFACE WAVE

NATURAL FREQUENCIES OF A NARROW BAY

SOLUTIONS TO THE EXERCISES

APPENDIX ON PARTIAL DERIVATIVES

REFERENCES

ABOUT THE AUTHOR