  In Ann. Math., 170 (2009), 1417-1436, C. De Lellis and L. Sz\'ekelyhidi Jr.
constructed wild solutions of the incompressible Euler equations using a
reformulation of the Euler equations as a differential inclusion together with
convex integration. In this article we adapt their construction to the system
consisting of adding the transport of a passive scalar to the two-dimensional
incompressible Euler equations.
