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New quasi-Bayesian (hybrid) Crame´r-Rao bound (CRB) expressions are herein derived for far-field deep-sea direction-of-arrival (DOA) estimation with a nominally linear towed-array that 1) is deformed by spatio-temporally correlated oceanic currents, which have been previously overlooked in the towed-array shape-deformation statistical analysis literature, 2) is deformed by temporally correlated motion of the towing vessel, which is modeled only as temporally uncorrelated in prior literature, and 3) suffers gain-uncertainties and phase-uncertainties in its constituent hydrophones. This paper attempts to bridge an existing literature gap in deformed towed-array DOA-estimation performance analysis, by simultaneously a) incorporating several essential fluid-mechanics considerations to produce a shape-deformation statistical model physically more realistic than those previously used for DOA performance analysis and b) rigorously derive a mathematical analysis to characterize quantitatively and qualitatively the DOA estimation's statistical performance. The derived CRB expressions are parameterized in terms of the towed-array's physically measurable nonidealities for the single-source case. The new hybrid-CRB expressions herein derived are numerically more stable than those in the current literature.