Inverse cascade avalanche model with limit cycle exhibiting period doubling, intermittency, and self-similarity

A one-dimensional avalanche "sandpile" algorithm is presented for transport in a driven dissipative confinement system. Sand is added at the closed in flow boundary and redistributed when the local gradient exceeds a threshold . The redistribution rule is conservative, nonlocal, and linear and is chos en to mimic fluid Row. Potential energy is dissipated by avalanches that al so expel matter at the open outflow boundary. The system then evolves throu gh an inverse cascade. A ''fluidization'' parameter L-f specifies the lengt h scale over which the algorithm operates. The limiting case of L-f=1 cell and L-f=N, the system size, are analytically soluble. For other values of L -f the emergent, large-scale dynamics of the system shows a variety of beha vior including a limit cycle that has a period-doubling sequence, intermitt ency, and a random walk.