Two‐dimensional co‐oscillations in a rectangular bay: Possible application to water‐level problems

Abstract

The two‐dimensional response of a rectangular bay of uniform depth to a fluctuating water‐level disturbance imposed at its mouth is examined in the framework of linear shallow‐water equations on a nonrotating earth. The imposed forcing is periodic in time but spacially varying in the transverse direction along the mouth of the bay. The response is presented both in terms of the amplification factor, which is the ratio of the imposed amplitude at the mouth to that at the closed end of the bay, and the structure of the height field within the bay. The two‐dimensional character of the response becomes more pronounced as the wavelength of the disturbance at the mouth decreases and as the width of the bay increases. Positive and negative amphidromic systems can be generated in the bay for disturbances propagating along the mouth of the bay even though the earth's rotation is neglected. The origin of the water‐level fluctuations at the mouth of the bay could be due to tides, storm surges, or tsunamis. This study indicates the importance of measuring the spacial variations in the water‐level fluctuations along the mouth of the bay, instead of assuming them to be spacially uniform, when attempting to explain the water‐level response within the bay.

Keywords:

• co‐oscillations
• rectangular bay
• two‐dimensional problem
• no‐rotation case