Study of internal wave generation by tide-topography interaction |
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| Authors: | Toshiyuki Hibiya |
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| Institution: | (1) Earthquake Research Institute, University of Tokyo, 1-1 Yayoi, Bunkyo-ku, 113 Tokyo, Japan;(2) Present address: Department of Oceanography, University of British Columbia, 6270 University Boulevard, V6T 1W5 Vancouver, British Columbia, Canada |
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| Abstract: | The generation mechanism of internal waves by a relatively strong tidal flow over a sill is clarified analytically. Special
attention is directed to the role of the tidal advection effect, which is examined by use of characteristics.
An internal wave which propagates upstream is gradually formed through interference of infinitesimal amplitude internal waves
(elementary waves) emanating from the sill at each instant of time. In the accelerating (or decelerating) stage of the tidal
flow, the effective amplification of the internal wave takes place as the internal Froude number exceeds (or falls below)
unity because during this period the internal wave slowly travels downstream (or upstream) while crossing over the sill where
elementary waves are efficiently superimposed. In fact, the variability in the internal wave field actually observed in a
realistic situation (Stellwagen Bank in Massachusetts Bay) is shown to be satisfactorily interpreted in terms of this mechanism.
Furthermore, by using this analytical model, the relation between the strength of the tidal advection effect and the resulting
internal waveform is clarified.
This theory is easily extended to include a vertically sheared steady flow. In this case, although the fundamental generation
mechanism is the same as above, the amplitude of the elementary wave varies with time depending on the relative direction
of the tidal flow and steady shear flow, so that the internal wave field over the sill differs markedly between the ebb and
flood tidal phases. As an example, the internal wave generation process over the sill in the Strait of Gibraltar is qualitatively
discussed on the basis of this analytical model.
The effect of vertical mixing caused by breaking of these large-amplitude internal waves on the coastal environment is also
pointed out. In particular, a brief discussion is made on the control of water exchange by the fortnightly modulation of tidal
mixing processes at the sills and constrictions in channels connecting freshwater sources with the ocean. |
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