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We numerically study an analogue black hole with two horizons with similarparameters to a recent experiment. We find that the Hawking radiation exists ona background which contains a density oscillation, a zero-frequency ripple. TheHawking radiation evolves from spontaneous to self-amplifying, while thebackground ripple grows steadily with no qualitative change. It is seen thatthe self-amplifying Hawking radiation has a non-zero frequency. The backgroundripple appears even before the inner horizon is created, in contrast topredictions. This work is in agreement with the recent observation ofself-amplifying Hawking radiation, and explains some of the features seen. Incontrast to recent works, our study differentiates between the Hawkingradiation observed, and the evolution of the background.

Self-amplifying Hawking radiation and its background: a numerical study