Laboratory and numerical simulations of gravity-driven coastal currents: Departures from geostrophic theory

Abstract

Laboratory realizations and numerical simulations of buoyant, gravity-driven coastal plumes are summarized and compared to the inviscid geostrophic theory of Thomas and Linden (2007). The lengths, widths and velocities of the buoyant currents, as well as their internal structure and dynamics, are studied. Agreement between the laboratory and numerical experiments and the geostrophic theory is found to depend on two non-dimensional parameters which characterize, respectively, the steepness of the plumes isopycnal interface ( I) and the strength of horizontal viscous forces ( Ek H , the horizontal Ekman number). In general, the numerical and laboratory experiments are in good agreement when conducted at comparable values of I and Ek H . The best agreement between experiments (both laboratory and numerical) and the geostrophic theory are found for the least viscous flows, though important departures from the theoretical predictions are nonetheless found, particularly in the early development of the plume system. At elevated values of the horizontal Ekman number, laboratory and numerical experiments depart more significantly from theory, e.g., in the rate of plume movement along the coast. A simple extension to the geostrophic theory suggests that the discrepancy between the theoretical and experimental propagation speed should be proportional to the square root of the horizontal Ekman number. The numerical simulations confirm this relationship. For some combinations of the non-dimensional parameters, instabilities develop in the seaward edge of the buoyant plumes. The laboratory and numerical experiments are used together to infer the region within parameter space within which the instabilities occur. Mixing of ambient and buoyant fluids by the plume-edge instabilities is explored using the numerical results.