The flow of deep-sea turbidity currents in meandering channels has been of considerable recent interest. Here we focus on the secondary flow associated with a subaqueous bottom current in a meandering channel. For simplicity, a saline bottom current can be used as a surrogate for a turbidity current driven by a dilute suspension of fine-grained sediment that does not easily settle out. In the case of open-channel flow, i.e., rivers, the classical Rozovskiian paradigm is often invoked to explain secondary flow in meandering channels. This paradigm indicates that the near-bottom secondary flow in a bend is directed inward, i.e., toward the inner bank. It has recently been suggested based on experimental and theoretical considerations, however, that this pattern is reversed in the case of subaqueous bottom flows in meandering channels, so that the near-bottom secondary flow is directed outward (reversed secondary flow), towards the outer bank. Experimental results presented here, on the other hand, indicate near-bottom secondary flows that have the same direction as observed in a river (normal secondary flow). The implication is an apparent contradiction between experimental results. We use theory, experiments, and reconstructions of case studies from field-scale flows to resolve this apparent contradiction based on the densimetric Froude number of the flow. We find three ranges of densimetric Froude number, such that a) in an upper regime, secondary flow is reversed, b) in a middle regime, it is normal, and c) in a lower regime, it is reversed. We apply our results at field scale to previous studies on channel-forming turbidity currents in the Amazon submarine canyon fan system (Amazon Channel) and the Monterey Canyon and a saline underflow in the Black Sea flowing from the Bosphorus. Our analysis indicates that secondary flow should be normal throughout most of the Amazon submarine fan reach, lower-regime reversed in the case of the Black Sea underflow, and upper-regime reversed in the case of the Monterey canyon. The theoretical analysis predicts both normal and reversed regimes in the Amazon submarine canyon reach.