A vortex flowmeter for measuring a flow rate of a process fluid, including a vortex generator arranged to generate vortices in a flow of the process fluid, a vortex sensor arranged to sense the vortices in the flow of the process fluid and responsively provide a sensor output related to the flow rate of the process fluid, measurement circuitry configured to receive the sensor output and provide a digital output, a memory configured to store measurements based upon the digital output; and diagnostic circuitry coupled to the memory arranged to detect instability in the flow of the process fluid based upon the measurements stored in the memory.