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The linear stability of two well‐known energy‐ and enstrophy‐conserving schemes for the vector‐invariant hydrostatic primitive equations is examined. The problem is analyzed for a stably stratified Boussinesq fluid on an f‐plane with a constant velocity field, in height and isopycnal coordinates, by separation of variables into vertical normal modes and a linearized form of the shallow‐water equations...
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