Wave turbulence (WT) occurs in systems of strongly interacting nonlinear waves and can lead to energy flows across length and frequency scales much like those that are well known in vortex turbulence. Typically, the energy passes although a nondissipative inertial range until it reaches a small enough scale that viscosity becomes important and terminates the cascade by dissipating the energy as heat. Wave turbulence in quantum fluids is of particular interest, partly because revealing experiments can be performed on a laboratory scale, and partly because WT among the Kelvin waves on quantized vortices is believed to play a crucial role in the final stages of the decay of (vortex) quantum turbulence. In this short review, we provide a perspective on recent work on WT in quantum fluids, setting it in context and discussing the outlook for the next few years. We outline the theory, review briefly the experiments carried out to date using liquid H 2 and liquid 4 He, and discuss some nonequilibrium excitonic superfluids in which WT has been predicted but not yet observed experimentally. By way of conclusion, we consider the medium-and longer-term outlook for the field.W ave turbulence (WT) (1, 2) is probably less familiar than ordinary (vortex) turbulence to most scientists, but the two sets of phenomena are actually very similar. Unlike electromagnetic waves in the vacuum, which are linear, and can therefore pass through each other unaltered, waves in a nonlinear medium interact with each other, sometimes strongly. WT manifests itself in systems of strongly interacting nonlinear waves. They form a disordered system in which there can be nondissipative flows of energy across the frequency and length scales, much as occur in vortex turbulence. WT arises in a wide variety of classical contexts, including, for example, surface waves on water (both gravity and capillary) (3-5), nonlinear optical systems (6, 7), sound waves in oceanic waveguides (8), shock waves in the solar atmosphere and their coupling to the Earth's magnetosphere (9), and magnetic turbulence in interstellar gases (10). There is a large and rapidly expanding literature, to which many relevant references up to mid-2010 are listed in ref. 2. As we discuss in more detail below, WT can also occur in quantum fluids, where it exhibits some distinctive features. Experimental studies have included surface waves on liquid H 2 (11) and liquid helium (12) and second sound in superfluid 4 He (13). Very recently, WT has been demonstrated and studied numerically in the nonequilibrium excitonic superfluids (14) that occur in semiconductors (15), including graphene (16).In section 1 we review briefly the theory of WT, concentrating on the aspects relevant to quantum fluids. Section 2 describes the relevant experiments reported to date, and also describes a numerical experiment showing that WT can also occur in semiconductor Bose-Einstein condensates (BECs). Finally, in section 4, we conclude and consider the future for research in the area.
Theory of Wave Turbulence in...