Optimal Perturbation Growth in Axisymmetric Intrusions

B.R. Sutherland and C.P. Caulfield

J. Fluid Mech., in press

The cylindrical lock-release laboratory experiments of Sutherland & Nault (2007) showed that a radially advancing symmetric intrusive gravity current spreads not as an expanding annulus (as is the case of bottom propagating gravity currents), but rather predominantly along azimuthally periodic radial `spokes'. Here we investigate whether the spokes are associated with azimuthal perturbations which undergo `optimal' growth. We use a nonlinear axisymmetric numerical simulation initialized with the experimental parameters to compute the time-evolving axisymmetric base state of the collapsing lock-fluid. Using fields from this rapidly evolving base state together with the linearized perturbation equations and their adjoint, the `direct-adjoint looping' method is employed to identify, as a function of azimuthal wavenumber m, the vertical-radial structure of the set of initial perturbations which exhibit the largest total perturbation energy gain over a target time T. Of this set of perturbations, that which extracts energy fastest, and so is is expected to be observed first to emerge from the base flow, has azimuthal wavenumber comparable to the number of spokes observed in the experiment.