16 Consider the following balance in an ocean of depth h of flat bottom Sverdrup RelationConsider the following balance in an ocean of depth h of flat bottom(1)(2)Integrating vertically from –h to 0 for both (1) and (2), we have(neglecting bottom stress and surface height change)(3)(4)whereare total zonal and meridional transport of masssum of geostrophic and ageostropic transports
17 (3) and (4) can be written as DefineWe have(3) and (4) can be written as(6)(5)Differentiating, we have
18 We have Sverdrup equation Using continuity equationAnd defineWe have Sverdrup equationVertical component of the wind stress curlIfThe line provides a natural boundary that separate the circulation into “gyres”
19 is the total meridional mass transport Geostrophic transportEkman transportOrder of magnitude example:At 35oN, -4 s-1, 2 m-1 s-1, assume x10-1 Nm-2 y=0
20 Alternative derivation of Sverdrup Relation Construct vorticity equation from geostrophic balance(1)Assume =constant(2)Integrating over the whole ocean depth, we have
21 whereis the entrainment rate from the surface Ekman layerat 45oNThe Sverdrup transport is the total of geostrophic and Ekman transport.The indirectly driven Vg may be much larger than VE.