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We present a theoretical investigation into the dynamics of a viscous gravity current subjected to spatially-finite lubrication (i.e., a `slippery patch'). The work is motivated by grounded ice sheets flowing across patches of basal meltwater which reduce the ice-bed frictional coupling, causing perturbations enhancing ice motion, with implications for increased ice flux into the ocean and sea level rise. The flow is characterized by transitions between shear- and extension-dominated dynamics, which necessitates boundary-layer solutions at the transition points. We develop a depth-integrated analytical model of Newtonian flow which concisely reveals fundamental relationships between ice sheet geometry (thickness, surface slope, and slippery patch length) and the magnitude and spatial extent of resulting horizontal deviatoric stresses. This reduced-order analytical model shows good quantitative agreement with numerical simulations using 2-D Newtonian Stokes equations, which are further extended to the case of a non-Newtonian flow. From the reduced-order model, we rationalize that the slippery patch-induced stress perturbations are exponentially-decaying functions of distance upstream away from the patch onset. We also show that the amplitude of the perturbation scales linearly with the surface slope and patch length while the decay lengthscale scales linearly with ice thickness. These fundamental relationships have implications for the response of the Greenland Ice Sheet to the inland expansion of basal meltwater presence over the coming warming decades.

We present multi-band Hubble Space Telescope imaging that spans rest-frame near-ultraviolet through near-infrared wavelengths (0.3-1.1 $\mu$m) for 12 compact starburst galaxies at z=0.4-0.8. These massive galaxies (M_stellar ~ 10^11 M_Sun) are driving very fast outflows ($v_{max}$=1000-3000 km/s), and their light profiles are dominated by an extremely compact starburst component (half-light radius ~ 100 pc). Our goal is to constrain the physical mechanisms responsible for launching these fast outflows by measuring the physical conditions within the central kiloparsec. Based on our stellar population analysis, the central component typically contributes $\approx$25% of the total stellar mass and the central escape velocities $v_{esc,central}\approx900$ km/s are a factor of two smaller than the observed outflow velocities. This requires physical mechanisms that can accelerate gas to speeds significantly beyond the central escape velocities, and it makes clear that these fast outflows are capable of traveling into the circumgalactic medium, and potentially beyond. We find central stellar densities comparable to theoretical estimates of the Eddington limit, and we estimate $\Sigma_1$ surface densities within the central kpc comparable to those of compact massive galaxies at $0.5