LECTURE 13 LargeScale Ocean Circulation Gyre Circulation Sverdrup

LECTURE 13 Large-Scale Ocean Circulation: Gyre Circulation

Sverdrup Transport What about the western boundary? ? ? We are not conserving mass (note the behavior at the western boundary!)

Sverdrup Transport Problem is that we cannot satisfy two lateral boundary conditions with a solution to a first order equation

Breakdown of Sverdup Model The Sverdrup solution must break down near the western boundary Let us hypothesize the existence of a boundary layer of zonal width ‘e’ that provides the return flow of the interior Sverdrup transport

Breakdown of Sverdup Model The Sverdrup solution must break down near the western boundary Let us hypothesize the existence of a boundary layer of zonal width ‘e’ that provides the return flow of the interior Sverdrup transport

Stommel Gyre Model The Sverdrup solution must break down near the western boundary Let us hypothesize the existence of a boundary layer of zonal width ‘e’ that provides the return flow of the interior Sverdrup transport

Stommel Gyre Model The Sverdrup solution must break down near the western boundary My satisfies the requirement of no basin-integrated meridional transport at any latitude, as it must

Stommel Gyre Model The Sverdrup solution must break down near the western boundary My satisfies the requirement of no basin-integrated meridional transport at any latitude, as it must

Stommel Gyre Model What is the missing physics? In boundary layer, we can no longer ignore friction Stommel (1948) introduced a ‘bottom friction’ model Model frictional stresses by Raleigh Friction Terms Consider once again the fundamental equations, Differentiate with respect to y and x respectively, Subtract second from first,

Stommel Gyre Model What is the missing physics? In boundary layer, we can no longer ignore friction Stommel (1965) introduced a ‘bottom friction’ model Model frictional stresses by Raleigh Friction Terms As long as flow is non-divergent Divergence Equation

Stommel Gyre Model Relative Vorticity Absolute Vorticity Conservation But As long as flow is non-divergent

Stommel Gyre Model Relative Vorticity Absolute Vorticity Conservation But Within western boundary layer we have a balance between changes in planetary vorticity and frictional dissipation of relative vorticity

Stommel Gyre Model Relative Vorticity Absolute Vorticity Conservation But Within interior we have the Sverdrup relationship Which we can re-write or This represents a balance between changes in planetary vorticity and windstress input of relative vorticity Within western boundary layer we have a balance between changes in planetary vorticity and frictional dissipation of relative vorticity

Stommel Gyre Model Let us return to the western boundary layer, where we have the balance, Within western boundary layer we have a balance between changes in planetary vorticity and frictional dissipation of relative vorticity

Stommel Gyre Model Let us return to the western boundary layer, where we have the balance, But this is only the boundary layer solution! This must couple to the interior (Sverdrup) solution Within western boundary layer we have a balance between changes in planetary vorticity and frictional dissipation of relative vorticity

Stommel Gyre Model Let us return to the western boundary layer, where we have the balance, But this is only the boundary layer solution! This must couple to the interior (Sverdrup) solution The full solution is thus,

Stommel Gyre Model We require no net meridional transport!

Stommel Gyre Model We can use continuity of the horizontal flow field to derive an expression for the zonal velocity We can thus define a streamfunction:

Stommel Gyre Model b=0 We can thus define a streamfunction: b 0

Stommel Gyre Model Stommel Model Eddy-Resolving Ocean GCM In reality, Western Boundary Current Separates Stommel Model obviously an idealization, but it captures the essence of westward intensification of ocean currents

Consider an idealized global ocean Apply observed zonally-averaged windstress profile to each basin

Consider an idealized ocean basin Pacific Atlantic Southern Ocean Apply observed zonally-averaged windstress profile to each basin

Consider an idealized ocean basin