Multiple states in doubly driven flow

Abstract

It has been known since 1961 that if two components effect density, a convecting fluid may possess multiple stable states for the same boundary conditions. Until recently, analytical and numerical calculations have been conducted for application to climate models. Laboratory observations were absent. Experiments have now produced the anticipated multiple states and also give new insight into their physical nature. A new, wider range of applications to estuary and coastal water circulation is indicated. In the experiments a chamber of water was heated from below and exposed to a constant volume flux of salty water from above. This was connected to a large reservoir of fresh room temperature water through two horizontal tubes, one near the top and the other near the bottom. Parameters were such that the time constant for change of temperature was less than the time constant for change in salinity. The experiments confirmed the principal prediction of theory — that two states can exist for the same boundary conditions. The range of two stable states was mapped as a function of the temperature forcing for fixed salinity flux. For low thermal forcing, the salinity driven state was found. This had very slow exchange of warm and very salty water with the reservoir. Density due to salinity was greater than that from temperature. Above a critical forcing an additional state could exist. This possessed exchange with the reservoir in the opposite direction of warm and much lower salinity water above approximately 1.5 times the critical forcing, only the thermal state was found. A second example driven by stress and heat flux also exhibits multiple states. Two examples are analyzed.