A Time-Dependent Sverdrup Relation and Its Application to the Indian Ocean

Abstract

Abstract The Sverdrup relation is the backbone of wind-driven circulation theory; it is a simple relation between the meridional transport of the wind-driven circulation in the upper ocean and the wind stress curl. However, the relation is valid for steady circulation only. In this study, a time-dependent Sverdrup relation is postulated, in which the meridional transport in a time-dependent circulation is the sum of the local wind stress curl term and a time-delayed term representing the effect of the eastern boundary condition. As an example, this time-dependent Sverdrup relation is evaluated through its application to the equatorial circulation in the Indian Ocean, using reanalysis data and a reduced gravity model. Close examination reveals that the southward Somali Current occurring during boreal winter is due to the combination of the local wind stress curl in the Arabian Sea and delayed signals representing the time change of layer thickness at the eastern boundary. Significance Statement Sverdrup balance dictates the law of meridional transport of steady circulation in the upper ocean, and has been one of the foundations upon which our understanding of ocean circulation is built. However, for circulation forced by time-varying wind stress, with annual, interannual and decadal frequency, the governing law remains elusive. In this study, we introduce a time-dependent Sverdrup relation applicable to time-dependent wind-driven circulation. As an example, this relation is used to diagnose the monsoon-driven circulation in the Indian Ocean.