@@ -1031,11 +1031,10 @@ Date: 18/06/2026.
10311031
10321032Presenter: Angus Gibson (@angus-g ).
10331033
1034- With ** generalised vertical coordinates** , we know that vertical velocities permit
1034+ With ** generalised vertical coordinates (GVC) ** , we know that vertical velocities permit
10351035a range of grid evolution from fully Lagrangian (zero dia-surface transport) to fully
1036- Eulerian (zero grid velocity). For the * vertical Lagrangian-remap* method, we tend
1037- toward the fully Lagrangian side: the GVC $s$ follows fluid elements so that the
1038- dia-surface volume flux $w^{(\dot{s})} = 0$.
1036+ Eulerian (zero grid velocity). In MOM6, the dynamics are written in the fully Lagrangian sense:
1037+ the GVC $s$ follows fluid elements so that the dia-surface volume flux $w^{(\dot{s})} = 0$.
10391038
10401039If the model is using a purely Lagrangian coordinate, how do we have any control
10411040over it? In general, these coordinates drift to a less useful representation of the
@@ -1045,7 +1044,9 @@ processes. Even more simply, there is indeed irreversible mixing across surfaces
10451044that must be captured somehow.
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10471046The method has three steps:
1048- 1 . the Vertical Lagrangian step: evolve the model as above;
1047+
1048+ 1 . the Vertical Lagrangian step: evolve the model with a purely Lagrangian
1049+ generalised coordinate;
104910502 . the Vertical Regrid step: explicitly set the generalised coordinate;
105010513 . the Vertical Remap step: ensure consistency between the ocean state
10511052 and the new coordinate.
@@ -1071,6 +1072,7 @@ quantities are conserved.
10711072![ Vertical Lagrangian remapping] ( ../assets/vertical-lagrange-remap.png )
10721073
10731074There are two big advantages to using this method:
1075+
107410761 . There is no vertical CFL limit! As long as the remapping can handle
10751077 interpolation over more than a single cell, the target grid can be
10761078 arbitrary.
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