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An Experimental and Numerical Study of the Internal Wave Generation by Tide—Topography Interaction

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  • 1 Faculty of Engineering, Ibaraki University. Hitachi, Japan
  • | 2 Earthquake Research Institute, University of Tokyo, Tokyo, Japan
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Abstract

A stratified fluid response to barotropic oscillatory now over a large-amplitude obstacle is examined on the basis of the results of laboratory and numerical experiments. It is demonstrated that, when the obstacle height is fixed relative to the water depth (δ), the type of fluid response is dependent on two dimensional parameters, that is, the maximum internal Froude number at the top of the obstacle (Frm) and the oscillatory period normalized to the time interval an internal wave travels over the horizontal length scale of an obstacle (T d).

For the parameter range 0.5 ≤ Frm ≤ 1.75 and 1.5 ≤ T d ≤ 2.5, a detailed comparison is made between the results of laboratory and numerical experiments and shown to be in very good agreement. First and second mode internal waves are specifically identified over the leeside slope of the obstacle. When the value of Frmis greater than one, in particular, internal waves of large amplitude occur because the elementary waves converge at the vicinity of the critical point (where Froude number ∼1), these waves propagate upstream when the flow decreases and eventually reverses. Depending on the value of T dthey interact with the waves being formed over the other side slope of the obstacle. These observed features are successfully interpreted in terms of the method of characteristics.

Although temporal and spatial scales are quite different between natural and laboratory situation the evolving internal wave field actually observed over Stellwagen Bank in Massachusetts Bay can be well simulated in the present laboratory and numerical experiments where Frm,T d and δ are nearly adjusted to correspond to the observed values. This shows that these parameters indeed play a crucial role for the classification of the stratified fluid responses over a large amplitude bottom topography.

Abstract

A stratified fluid response to barotropic oscillatory now over a large-amplitude obstacle is examined on the basis of the results of laboratory and numerical experiments. It is demonstrated that, when the obstacle height is fixed relative to the water depth (δ), the type of fluid response is dependent on two dimensional parameters, that is, the maximum internal Froude number at the top of the obstacle (Frm) and the oscillatory period normalized to the time interval an internal wave travels over the horizontal length scale of an obstacle (T d).

For the parameter range 0.5 ≤ Frm ≤ 1.75 and 1.5 ≤ T d ≤ 2.5, a detailed comparison is made between the results of laboratory and numerical experiments and shown to be in very good agreement. First and second mode internal waves are specifically identified over the leeside slope of the obstacle. When the value of Frmis greater than one, in particular, internal waves of large amplitude occur because the elementary waves converge at the vicinity of the critical point (where Froude number ∼1), these waves propagate upstream when the flow decreases and eventually reverses. Depending on the value of T dthey interact with the waves being formed over the other side slope of the obstacle. These observed features are successfully interpreted in terms of the method of characteristics.

Although temporal and spatial scales are quite different between natural and laboratory situation the evolving internal wave field actually observed over Stellwagen Bank in Massachusetts Bay can be well simulated in the present laboratory and numerical experiments where Frm,T d and δ are nearly adjusted to correspond to the observed values. This shows that these parameters indeed play a crucial role for the classification of the stratified fluid responses over a large amplitude bottom topography.

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