Mixing by a turbulent plume in a confined stratified region

Abstract

An experimental and theoretical study of the mixing produced by a plume rising in a confined stratified environment is presented. As a result of the pre-existing stable stratification, the plume penetrates only part way into the region; at an intermediate level it intrudes laterally forming a horizontal layer. As time evolves, this layer of mixed fluid is observed to increase in thickness. The bottom front advects downward in a way analogous to the first front in the filling box of Baines & Turner (1969), while the lateral spreading of the plume occurs at an ever-increasing level and an ascending top front results. We develop a model of this stratified filling box; the model predicts the rate at which the two fronts advance into the environment.It is found that stratification in the environment, when smooth, has no significant influence on the dynamics of the descending front. We show that the rate of rise of the ascending front is determined by the turbulent mixing occurring at the spreading level. Entrainment of environmental fluid from above into the overshooting plume is significant; as a result, a density interface develops at this level. Asymptotically, the system reaches a state in which a bottom convecting layer, with an almost homogeneous density, deepens in a stratified background. The model proposed for this large-time behaviour is based on the simple energetic formulation that a constant fraction of the kinetic energy supplied by the plume, for mixing across the interface, is converted into potential energy of the convective layer. Our experimental results suggest an efficiency of approximately 50 % for this conversion.We discuss our results in the light of previous studies on turbulent penetrative convection and conclude that the theory developed should be valid for an intermediate range of values of the Richardson number characterizing the dynamic conditions at the interface. The model is applied quantitatively to the process of cooling of a room wherein stratification is relevant. The geological problem of replenishment of a magma chamber by a light input of magma is also analysed.

Violent expiratory events: on coughing and sneezing

“…This turbulent plume theory has proven to be sufficient to capture key features of many geophysical and environmental flows, including the emission of industrial effluent, the emission of volcanic hydrothermal plumes or thermals and the ejections of bubble plumes in lakes (e.g. Scorer 1978;Cardoso & Woods 1993;Gonnermann & Manga 2007;Woods 2010). Here, we adapt such an approach in order to describe the dynamics of violent expiratory events.…”

Entrainment by turbulent fountains

“…Baines 1975;Kumagai 1984;Baines et al 1993;Cardoso & Woods 1993;Lin & Linden 2005). If one considers a jet projected upward toward a density interface from a source within a (dense) homogeneous lower layer then the links between entrainment by a fountain and entrainment across an interface become apparent.…”

“…Typically fluid from a localised source is ejected vertically upwards within a stratified (often two-layer) environment to form a fountainlike flow above the interface and the entrainment flux inferred by measuring the time derivative of the height of the interface (e.g. Baines 1975;Kumagai 1984;Cardoso & Woods 1993). Although these flows are indeed fountain-like their entrainment is influenced by the stratification which tends to flatten or 'pancake' the turbulent structures responsible for the entrainment.…”

Scaling Laws for the Heterogeneously Heated Free Convective Boundary Layer

“…This circulation tries to bring in all small plumes that originate at the surface into the adjacent large structure. In the region near the CBL top, lateral spread of a plume occurs very fast (Baines and Turner 1969;Cardoso and Woods 1993) such that the entire region in between the plumes is part of the downward flow from the beginning. As soon as the CBL has grown so large that the plumes merge into a single one, while the overturning circulation still exists, we enter the optimal state in which the KE peaks (Fig.…”