feat(libmeanfield): variadic refactor

also added normaliztion operator

libmeanfield/interface/operators/prepared_hydrostatic_equilibrium_operator.cppm

@@ -35,6 +35,7 @@ export namespace mean_field::operators {
         std::uint64_t enthalpyApplications{0};
         std::uint64_t gravityPotentialApplications{0};
         std::uint64_t bernoulliConstantApplications{0};
+        std::uint64_t rotationAmplitudeApplications{0};
         std::uint64_t combinedApplications{0};
 
         constexpr auto operator<=>(const PreparedHydrostaticAlgebraicJacobianStatistics &) const = default;
@@ -118,6 +119,14 @@ export namespace mean_field::operators {
             mfem::Vector &action
         ) const;
 
+        // Differentiates a multiplicative change Omega -> (1 + alpha) Omega
+        // at the frozen rigid rotation. Since Psi_rotation is quadratic in
+        // Omega, this contributes -2 alpha Psi_rotation to the hydrostatic row.
+        void ApplyRotationAmplitudeJacobianAction(
+            double fractionalAngularVelocityVariation,
+            mfem::Vector &action
+        ) const;
+
         void ApplyAlgebraicJacobianAction(
             const mfem::Vector &enthalpyVariation,
             const mfem::Vector &gravityPotentialVariation,