Scalar flux kinematics

The first portion of this paper contains an overview of recent progress in the development of dynamical-systems-based methods for the computation of Lagrangian transport processes in physical oceanography. We review the considerable progress made in the computation and interpretation of key material features such as eddy boundaries, and stable and unstable manifolds (or their finite-time approximations). Modern challenges to the Lagrangian approach include the need to deal with the complexity of the ocean submesoscale and the difficulty in computing fluxes of properties other than volume. We suggest a new approach that reduces complexity through time filtering and that directly addresses non-material, residual scalar fluxes. The approach is “semi-Lagrangian” insofar as it contemplates trajectories of a velocity field related to a residual scalar flux, usually not the fluid velocity. Two examples are explored, the first coming from a canonical example of viscous adjustment along a flat plate and the second from a numerical simulation of a turbulent Antarctic Circumpolar Current in an idealized geometry. Each example concentrates on the transport of dynamically relevant scalars, and the second illustrates how substantial material exchange across a baroclinically unstable jet coexists with zero residual buoyancy flux.