The decay of Saffman and batchelor turbulence subject to rotation, stratification or an imposed magnetic field

We consider unforced, statistically-axisymmetric turbulence evolving in the presence of a background rotation, an imposed stratification, or a uniform magnetic field. We focus on two canonical cases: Saffman turbulence, in which E(κ → 0) ∼ κ 2, and Batchelor turbulence, in which E(κ → 0) ∼ κ 4. It has recently been shown that, provided the large scales evolve in a self-similar manner, then u ⊥ 2ℓ ⊥ 2ℓ // = constant in Saffman turbulence and u ⊥ 2ℓ ⊥ 4ℓ // = constant in Batchelor turbulence (Davidson, 2009, 2010). Here the subscripts ⊥ and // indicate directions perpendicular and parallel to the axis of symmetry, and ℓ ⊥, ℓ //, and u ⊥ are suitably defined integral scales. These constraints on the integral scales allow us to make simple, testable predictions for the temporal evolution of ℓ ⊥, ℓ //, and u ⊥ in rotating, stratified and MHD turbulence.

Lateral spreading-induced abutment rotation in the 2011 Christchurch earthquake: Observations and analysis

A series of strong earthquakes near Christchurch, New Zealand, occurred between September 2010 and December 2011, causing widespread liquefaction throughout the city's suburbs. Lateral spreading developed along the city's Avon River, damaging many of the bridges east of the city centre. The short-to medium-span bridges exhibited a similar pattern of deformation, involving back-rotation of their abutments and compression of their decks. By explicitly considering the rotational equilibrium of the abutments about their point of contact with the rigid bridge decks, it is shown that relatively small kinematic demands from the laterally spreading backfill soil are needed to initiate pile yielding, and that this mode of deformation should be taken into account in the design of the abutments and abutment piles.