Atmosphere Ocean Science Colloquium
Turbulence, Stressed Horizontal Convection and Oceans' Overturning Circulation
Speaker: Francesco Paparella, Università del Salento
Location: Warren Weaver Hall 1302
Date: Tuesday, April 14, 2015, 3:30 p.m.
Historically the word 'turbulence' has been used with many meanings. But in the sense of Kolmogorov, a turbulent flow is one that:
- has a cascade
- obeys the law of finite dissipation
Horizontal convection occurs when a fluid is only forced by buoyancy differences along a surface of constant potential energy, (e.g. water in a box with insulating boundaries, except at the top surface where a non-uniform temperature is prescribed). We prove that for horizontal convection the law of finite dissipation does not hold: if viscosity goes to zero at constant Prandtl number, then the kinetic energy dissipation per unit mass in the fluid also goes to zero, rather then to a finite, positive limit. However, the fluid is not necessarily still, nor steady. In fact, numerical solutions show that development of a cascade. We then extend the heuristic scaling law for the boundary layer thickness, due to T. Rossby, to the case in which a mechanical surface stress is applied at the surface in such a way as to oppose the buoyancy forcing. Finally we discuss the relevance of our findings as a building block of the current understanding of the oceans' meridional circulation.