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.

Choosing to make an effort: the role of striatum in signaling physical effort of a chosen action.

The possibility that we will have to invest effort influences our future choice behavior. Indeed deciding whether an action is actually worth taking is a key element in the expression of human apathy or inertia. There is a well developed literature on brain activity related to the anticipation of effort, but how effort affects actual choice is less well understood. Furthermore, prior work is largely restricted to mental as opposed to physical effort or has confounded temporal with effortful costs. Here we investigated choice behavior and brain activity, using functional magnetic resonance imaging, in a study where healthy participants are required to make decisions between effortful gripping, where the factors of force (high and low) and reward (high and low) were varied, and a choice of merely holding a grip device for minimal monetary reward. Behaviorally, we show that force level influences the likelihood of choosing an effortful grip. We observed greater activity in the putamen when participants opt to grip an option with low effort compared with when they opt to grip an option with high effort. The results suggest that, over and above a nonspecific role in movement anticipation and salience, the putamen plays a crucial role in computations for choice that involves effort costs.