We study a complex plasma under microgravity conditions that is first stabilized with an oscillating electric field. Once the stabilization is stopped, the so-called heartbeat instability develops. We study how the kinetic energy spectrum changes during and after the onset of the instability and compare with the double cascade predicted by Kraichnan and Leith for two-dimensional turbulence. The onset of the instability manifests clearly in the ratio of the reduced rates of cascade of energy and enstrophy and in the power-law exponents of the energy spectra. In general, when energy is put into a two-dimensional turbulent system, the energy spectrum splits into the inverse energy and direct enstrophy ranges -the so-called double cascade develops [10,11]. Its presence has been supported by computer simulations, but not unambiguously [12,13]. Only a few numerical simulations [14][15][16] and experiments [12,17,18] were able to simultaneously observe both cascades, which is challenging due to the large range of scales necessary to cover both the inverse and direct cascade [19]. Recently, it was suggested that the inverse cascade might not be robust, but depend on friction [16,20]. The evolution of the spectrum during the onset of two-dimensional forced turbulence was investigated in [21]. A recent topic of interest is the transition of weak wave turbulence to wave turbulence with intermittent collapses [22] and intermittency, i.e. strong nonGaussian velocity fluctuations, in wave turbulence [23][24][25][26], and so-called Janus spectra which differ in streamwise and transverse direction [27].In this paper, we present the first study of developing turbulence in dusty/complex plasmas. Complex plasmas consist of microparticles embedded in a low-temperature plasma. The microparticles acquire high charges and interact with each other. They can be visualized individually and thus enable observations on the kinetic level of, for instance, vortices [28][29][30], tunneling [31], and channeling [32]. Gravity is a major force acting on the microparticles in ground-based experiments. Under its influence, the particles are located close to the sheath region of