  Two possible diagnostics of stretching and folding (S&F) in fluid flows are
discussed, based on the dynamics of the gradient of potential vorticity ($q =
\bom\cdot\nabla\theta$) associated with solutions of the three-dimensional
Euler and Navier-Stokes equations. The vector $\bdB = \nabla q \times
\nabla\theta$ satisfies the same type of stretching and folding equation as
that for the vorticity field $\bom $ in the incompressible Euler equations
(Gibbon & Holm, 2010). The quantity $\theta$ may be chosen as the potential
temperature for the stratified, rotating Euler/Navier-Stokes equations, or it
may play the role of a seeded passive scalar for the Euler equations alone. The
first discussion of these S&F-flow diagnostics concerns a numerical test for
Euler codes and also includes a connection with the two-dimensional surface
quasi-geostrophic equations. The second S&F-flow diagnostic concerns the
evolution of the Lamb vector $\bsD = \bom\times\bu$, which is the nonlinearity
for Euler's equations apart from the pressure. The curl of the Lamb vector
($\boldsymbol{\varpi} := \bsD$) turns out to possess similar stretching and
folding properties to that of the $\bdB$-vector.
