Charlie Hogg

Correlating Lagrangian structures with forcing in two-dimensional flow

Lagrangian coherent structures (LCSs) are the dominant transport barriers in unsteady, aperiodic flows, and their role in organizing mixing and transport has been well documented. However, nearly all that is known about LCSs has been gleaned from passive observations: they are computed in a post-processing step after a flow has been observed and used to understand why the mixing and transport proceeded as it did. In many applications, the ability instead to control the presence or location of LCSs via imposed forcing would be valuable. With this goal in mind, we study the relationship between LCSs and external forcing in an experimental quasi-two-dimensional weakly turbulent flow. We find that the likelihood of finding a repelling LCS at a given location is positively correlated with the mean strain rate injected at that point and negatively correlated with the mean speed, and that it is not correlated with the vorticity. We also find that mean time between successive LCSs appearing at a fixed location is...

Inclined gravity currents filling basins: The influence of Reynolds number on entrainment into gravity currents

In many important natural and industrial systems, gravity currents of dense fluid feed basins. Examples include lakes fed by dense rivers and auditoria supplied with cooled air by ventilation systems. As we will show, the entrainment into such buoyancy driven currents can be influenced by viscous forces. Little work, however, has examined this viscous influence and how entrainment varies with the Reynolds number, Re. Using the idea of an entrainment coefficient, E, we derive a mathematical expression for the rise of the front at the top of the dense fluid ponding in a basin, where the horizontal cross-sectional area of the basin varies linearly with depth. We compare this expression to experiments on gravity currents with source Reynolds numbers, Res , covering the broad range 100 < Res < 1500. The form of the observed frontal rises was well approximated by our theory. By fitting the observed frontal rises to the theoretical form with E as the free parameter, we find a linear trend for E(Res ) over the range 350 < Res < 1100, which is in the transition to turbulent flow. In the experiments, the entrainment coefficient, E, varied from 4 × 10−5 to 7 × 10−2. These observations show that viscous damping can be a dominant influence on gravity current entrainment in the laboratory and in geophysical flows in this transitional regime.

Shoaling internal waves may reduce gravity current transport

Gravity currents descending along slopes have typically been studied in quiescent environments, despite the fact that in many geophysical settings there is significant externally driven motion. Here we investigate how the head of a gravity current is influenced by interfacial internal waves at the pycnocline of a two-layer ambient water column. Our experimental measurements show that larger amplitude internal waves, interacting with the gravity current, reduce both the mass transport by the gravity current and its thickness. These results suggest that the ambient internal wave field should be considered when estimating transport by gravity currents in geophysical settings with strong internal waves, such as lakes and the coastal ocean.