ALBERT

Description: The establishment of an upstream intrusion of a buoyant fluid discharged into an open-channel flow of uniform density and finite depth is studied numerically using the full Navier-Stokes and diffusion equations. The problem is posed as an initial-boundary-value problem for the laminar motions of a Boussinesq fluid. The equations are integrated numerically by finite-difference methods. The flow patterns produced are controlled by the influx of buoyancy; therefore they are characterized by an inflow densimetric Froude number. A comparison with available experimental data provides favourable support to the theoretical predictions. The critical value of densimetric Froude number of the source of a vertically downward inflow at the free surface of a channel is determined. For densimetric Froude number less than critical, an intrusion is established on the upstream side of the source. Because dissipative mechanisms associated with viscosity take a finite time to intervene, the intrusion starts as an inviscid gravity current with a propagation speed greater than the surface velocity of the stream. The front speed is proportional to the phase velocity of long internal waves. Subsequently, the front decelerates as the interfacial friction, and, if applicable, the boundary frictional forces increase simultaneously with mass entrainment across the interface. The current slows down towards a two-zone equilibrium: (1) the zone encompassing the current behind the frontal zone, where a steady state is approached with respect to the inertial frame of reference; (2) the frontal zone, where the upstream speed approaches a steady speed of frontal advance, albeit small. The upstream intrusion alters the flow pattern of the ambient stream dramatically. A significant feature of both the upstream and downstream currents is the presence of surface convergence with concomitant downwelling near the fronts. As the upstream front decelerates, wavelike disturbances are excited just behind the front at frequencies characteristic of internal waves. As the front approaches steady state, these disturbances appear to be damped. This problem has practical implications in the design of once-through cooling-water systems for power plants taking their cooling water from rivers. © 1984, Cambridge University Press. All rights reserved.