Kaveri is a 1st generation HSA-compliant APU. As a 1st generation, it is still missing some features of the HSA specification. One of those features is Mid-wave preemption, which means the ability to preempt a graphic/compute work in the middle, context-switch to a different wave (work) and then resume the original wave.
Without this feature, Kaveri needs to finish the wave and only then can it move to a different wave.
Having said that, there is already an infrastructure for running HSA applications on Kaveri in Linux (Ubuntu 13/14). See https://github.com/HSAFoundation/Linux-HSA-Drivers-And-Images-AMD for kernel bits and https://github.com/HSAFoundation/Okra-Interface-to-HSA-Device for userspace bits.
This infrastructure also supports the Aparapi and Sumatra projects on Kaveri - running Java code on the GPU.
Hope this helps.