Abstract: Deep-sea long-range underwater acoustic channels typically exhibit cluster-sparse structures. Although various algorithms exploit such structural information to enhance channel estimation accuracy, these algorithms generally require prior knowledge of cluster parameters. This paper proposes an adaptive cluster-sparse Bayesian learning (ACSBL) channel estimation algorithm that constructs a hierarchical Bayesian model to jointly leverage sparsity and cluster structures, with variational Bayesian inference derived for adaptive parameter updating. The proposed algorithm enhances channel estimation accuracy by jointly exploiting sparsity and cluster structure, without requiring prior channel information such as cluster size, number of clusters, or cluster locations. To improve distortions caused by time-varying underwater acoustic channel, a turbo equalizer based on cross-domain processing is proposed, incorporating the adaptive cluster-sparse Bayesian learning channel estimation algorithm. The turbo equalizer consists of an equalizer operating in the delay-Doppler domain, a channel estimator, and a soft decoder operating in the time domain. The time-frequency domain channel is transformed into a quasi-static channel through delay-Doppler domain transformation, thereby mitigating the impact of channel variations on communication reliability. The proposed turbo equalizer enables cross-domain soft information exchange between the delay-Doppler domain and time domain through unitary transformation, effectively reducing error propagation probability and enhancing iterative equalization gain. Simulation results demonstrate the feasibility and robustness of the proposed method in deep-sea long-range underwater acoustic communications. Deep-sea long-range experimental results indicate that the proposed method achieves error-free transmission over communication distances of 324.9 km and 595.1 km, demonstrating its effectiveness in deep-sea long-range underwater acoustic communications.