Identifying the location of a target in an unbounded underwater environment is a challenging task. Limited and intermittent communication only adds to the difficulty of the process. Many target search algorithms use communication as an essential structural component to coordinate Autonomous Underwater Vehicles' (AUV) motion and share sensory information. Multiple algorithms also depend mainly on a sensed gradient to find the target, which is not always available. Sweeping algorithms are generally time and resource consuming and usually cover directional subspaces. Random walk based search suffers from the dispersion problem and does not benefit from the distinguishing features of swarms. To address these concerns, we propose Constrained Spiral Flocking (CSF) search. It uses a self-terminating logarithmic spiral to expand from the drop-off location performing the search, then shrink back, bringing unsuccessful AUVs to the source location. No communication is involved except at the target to attract more AUVs. Flocking is also used to maintain swarming. The algorithm can find the target in any direction, and has a faster convergence for large swarm sizes compared to simple sweeping and random walk.