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This is a review of the theory of the modulational instability in idealisedfluid models of strongly magnetised plasmas and reduced models of geophysicalfluid dynamics, particularly the role it plays in the formation of zonal flows.The discussion focusses on the Charney-Hasegawa-Mima and Hasegawa-Wakatanimodels. Particular attention is paid to the wave turbulence - zonal flowfeedback loop whereby large scale zonal flows which are initially generated bymodulational instability of small-scale drift/Rossby waves tend to subsequentlysuppress these small scale waves by their shearing action. This negativefeedback can result in a dynamic equilibrium in which large scale zonal flowsgrow by drawing energy from small scale turbulence but suppress the small scaleturbulence in the process until a balance is reached. In this regime, the levelof small scale turbulence is greatly reduced compared to the level one wouldobserve in the absence of the zonal flows.

Modulational Instability in Basic Plasma and Geophysical Models