Vector Operations in Hoskins and Simmons Coordinates
In my post Hoskins and Simmons (1974) Coordinate System, I derived the following scaling quantities which will be used to derive the vector operations of Grad, Div and Curl in Hoskins Coordinate system.
The coordinates in Hoskins coordinate system are dimensionless . (see nondimentionalization of Navier Stokes).
The gradient is defined as (see lectures on coordinate transforms):
The divergence is defined as:
The curl is defined by:
(note, the direction of the longitudinal coordinate is defined to obey the right hand rule)
This gives for the components
Which Simplifies to:
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