Split energy cascade induced by spontaneous flow transition in two-dimensional thermal turbulence

Two-dimensional turbulence is characterized by an inverse energy cascade from small scales to large ones, in contrast to the direct downscale energy cascade in three dimensions. Here, we report a split energy cascade in purely 2D thermal turbulence, i.e. the coexistence of direct and inverse energy cascades separated at intermediate scales. This phenomenon is induced by a spontaneous transition in the flow topology, during which the domain-sized circulatory roll is squeezed and intense randommoving eddies that provide a channel for downscale energy flux emerge. The flow mode analysis and orientation order of velocity field reveal that this flow transition is a critical behavior with bi-stability.