In this paper we develop a new cross-layer framework for adaptive spectrum management in practical mobile ad hoc networks. We first propose a two-step spectrum sensing algorithm with reduced hardware complexity which improves energy efficiency without requiring knowledge of the spectrum sparsity. We then incorporate our spectrum sensing algorithm into our proposed distributed spectrum access protocol, based on local orthogonality and well suited for clustered ad hoc networks. We show via simulations that our proposed cross-layer scheme achieves near-optimal spectrum utilization under various operating scenarios, and we provide design guidelines for all system parameters. Simulations also verify the robustness of our scheme, showing that its performance is only marginally affected by errors in the spectrum sensing phase.