A simple steady state theory of the geostrophic velocity field on the isopycnal surface predicts the existence of current spirals associated with the Jacobian of the potential vorticity (q) and the pressure (p) fields on that surface, J(q, p). The rotation of the horizontal velocity on the isopycnal surface with density is proportional to J(q, p). Thus, vertical velocity spiral exists when the Jacobian J(q, p) is non zero, that is, the q isoline intersects with the p isoline (isobaric line). The P-vector method has been developed to compute the absolute velocity (V) from observed density data alone. We use summer and winter T, S data from the joint US-Russian Arctic Ocean Atlas. The inverted Arctic Ocean circulation consists with the current observations. The dynamically consistent (T, S, V) fields can be used as initial conditions for Arctic Ocean modeling and prediction.