We describe a family of generalized almost structures associated with a Monge-Ampère equation for a stream function of a 2D incompressible fluid flow. Using an indefinite metric field constructed from a pair of 2-forms related to the Monge-Ampère equation, we show the existence of generalized metric compatible structures in our family of generalized structures. Integrability of isotropic structures on the level of Dirac structures and differential forms is discussed.