Research Projects

Available Potential Energy Density
The Available Potential Energy (APE) framework introduced in Winters1995 has proved useful in understanding the energetics of a Boussinesq flow by elegantly separating between adiabatic and diabatic energy pathways and providing evolution equations for the volume averaged APE (Ea). In this paper we derive a positive definite expression for the spatial APE density (Ea_d) that directly integrates to Ea. Ea_d consists of two terms. The first term (I1) quantifies the release of APE in the relocation of individual fluid parcels to their equilibrium height. The second term (I2) describes the energetic consequence of the compensatory displacement necessary under the Boussinesq approximation to conserve vertical volume flux with each parcel relocation. On a pointwise basis, this term adds to the first in such a way that a positive definite (physically meaningful) contribution to Ea is guaranteed. Figure 1 shows a spatial map of Ea_d (top), I1 (middle) and I2 (bottom) illustrating the cancellation between the two terms which result in Ea_d. Because Ea_d directly integrates to Ea, such maps are explicitly connected to known, exact, temporal evolution equation for kinetic, available and background potential energies.

Rotating Horizontal Convection
The role of surface buoyancy forcing in driving ocean circulation and establishing deep stratification remains a topic of debate that dates back to Sandstrom's theorem. 'Horizontal Convection' (HC), the generic name for the flow resulting from a buoyancy variation applied at a horizontal boundary of a fluid, is a useful conceptual model to study these effects (HC). In this paper we investigate the effects of rotation on the basic HC model. Below are a few animations showing the statistically steady buoyancy field resulting from Direct Numerical Simulations (DNS) (using FlowSolve) of 'Rotating Horizontal Convection' (RHC) in a channel configuration (conceptually similar to the ACC).
The first movie shows the mesoscale eddies and eddy filaments that develop in RHC (red/blue colors represent the buoyancy associated with hot/cold temperatures). The second movie focuses on the plume region (associated with deep convection in the ocean) illustrating the interaction between the eddies and the plumes. The regions of enhanced mixing associated with the plume and the eddies (as quantified in Winters1995) is shown in the third movie.