This paper theoretically and experimentally investigates the exchange flow due to temperature differences between open water and a canopy of aquatic plants. A numerical model is used to study the interfacial shape, frontal velocity and total volumetric exchange, and their dependence on a dimensionless vegetation drag parameter. The numerical predictions are consistent with the laboratory measurements. There is a short initial period in which the force balance is between buoyancy and inertia, followed by drag-dominated flow for which there is a balance between buoyancy and drag forces. After the initial stage, the gravity current propagating into the canopy takes a triangular shape whereas the current propagating into the open water has almost the classic unobstructed horizontal profile, but with a slowly decreasing depth. Near the edge of the canopy, but in the open region, the flow is found to be critical with a unit internal Froude number. The exchange flow rate and the front speed in the canopy decrease slowly with time whereas the gravity current in the open water has a constant speed. The magnitude of the exchange flow decreases as the canopy drag increases. Empirical equations for the flow properties are presented. A movie is available with the online version of the paper.
The three-dimensional interaction of a surface wave with two oblique interfacial waves in a horizontally infinite two-layer fluid is analyzed asymptotically. The nondimensional density difference is taken as a perturbation parameter and simple expressions for the growth rates and kinematic properties of the waves are obtained. The results show that the interfacial wavelengths are an order smaller than the surface wavelength. Also, to the leading-order approximation, the interfacial waves have a frequency half that of the surface wave, and their directions differ by 180° in the horizontal plane. The interaction coefficients are found to be equal at the leading order. The asymptotic solution is compared with the exact solution, and an excellent agreement is obtained for the range of applicability of the asymptotic theory. The analysis is extended to interactions in a medium with sidewalls. A previous laboratory flume study is addressed, and the asymptotic theory is used to explain the experimental observations.
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