Propagation of North Atlantic Deep Water anomalies

Abstract

We present a simplified theory using reduced-gravity equations for North Atlantic Deep Water (NADW) and its variation driven by high-latitude deep-water formation. The theory approximates layer thickness on the eastern boundary with domain-averaged layer thickness and, in tandem with a mass conservation argument, retains fundamental physics for cross-equatorial flows on interannual and longer forcing time scales. Layer thickness anomalies are driven by a time-dependent northern boundary condition that imposes a southward volume flux representative of a variable source of NADW and damped by diapycnal mixing throughout the basin. Moreover, an outflowing southern boundary condition imposes a southward volume flux that generally differs from the volume flux at the northern boundary, giving rise to temporal storage of NADW within the Atlantic basin. Closed form analytic solutions for the amplitude and phase are provided when the variable source of NADW is sinusoidal. We provide a nondimensional analysis that demonstrates that solution behavior is primarily controlled by two parameters that characterize the meridional extent of the southern basin and the width of the basin relative to the equatorial deformation radius. Similar scaling applied to the time-lagged equations of Johnson and Marshall provides a clear connection to their results. Numerical simulations of reduced-gravity equations agree with analytic predictions in linear, turbulent, and diabatic regimes. The theory introduces a simple analytic framework for studying idealized buoyancy- and wind-driven cross-equatorial flows on interannual and longer time scales.