Terrain-Following

Complete 3D anelastic atmospheric dynamics system in terrain-following coordinates from Clark (1977), 'A Small-Scale Dynamic Model Using a Terrain-Following Coordinate Transformation', Journal of Computational Physics 24, 186-215. The full nonlinear Clark (1977) model assembled as a hierarchical composition of eight subsystems: the isentropic base state (Eqs. 2.6-2.9), Witch-of-Agnesi mountain topography (Eq. 7.1), the terrain-following coordinate transformation (Eqs. 2.20-2.27), the Smagorinsky turbulence closure (Eqs. 2.15-2.19), the anelastic momentum residuals (Eqs. 2.1-2.3), anelastic mass continuity (Eq. 2.4), anelastic thermodynamics with turbulent heat flux (Eq. 2.14) and the diagnostic pressure equation (Section 4). Migrated from AtmosphericDynamics.jl@816cc391 src/clark1977.jl:582 (`Clark1977AnelasticSystem` @component) — a pure subsystem composition (`System(Equation[], t; systems=[...])`, no coupling equations): the eight subsystems are inlined verbatim under `subsystems` (ESS spec §4.7) and remain dynamically independent. Purely algebraic — every subsystem is a diagnostic (observed-only) system with no time derivative. SI units throughout.

Diagnostic pressure equation for the anelastic atmosphere in terrain-following coordinates, from Clark (1977) "A Small-Scale Dynamic Model Using a Terrain-Following Coordinate Transformation", Section 4. Observed-only algebraic component: from the pressure-gradient-force divergences, the pressure-perturbation Laplacian terms, and a momentum-divergence source it computes the pressure-gradient-force divergence div_PF (with the terrain-following Jacobian factor G^(1/2) scaling the vertical term), the pressure Laplacian laplacian_p, and the diagnostic pressure equation residual pressure_residual (Eq. 4.2), which vanishes when the anelastic mass-continuity constraint is satisfied. Migrated from AtmosphericDynamics.jl@816cc391 src/clark1977.jl:499 (`DiagnosticPressure` @component); the upstream @constant g is declared as a fixed-default parameter.

Terrain-following coordinate transformation from Clark (1977) "A Small-Scale Dynamic Model Using a Terrain-Following Coordinate Transformation", Eqs. 2.20-2.23 and 2.27. Observed-only algebraic component: from the terrain surface height z_s, the domain height H, the transformed vertical coordinate z_bar, and the two terrain slopes dz_s_dx and dz_s_dy it computes the transformation Jacobian G^(1/2) = 1 - z_s/H (G_sqrt), the two metric coefficients G^(1/2)G^13 and G^(1/2)G^23 that carry the terrain slope into the transformed equations (G_sqrt_G13, G_sqrt_G23), the physical height z_phys recovered from z_bar (the inverse of the mapping z_bar = H(z - z_s)/(H - z_s)), and the diagnostic Jacobian factor ω_diag used to recover the contravariant vertical velocity ω (Eq. 2.27). The transformation maps the irregular lower boundary z = z_s(x,y) to the flat computational surface z_bar = 0 while preserving the rigid lid z = H at z_bar = H. Migrated from AtmosphericDynamics.jl@816cc391 src/clark1977.jl:157 (`TerrainFollowingTransform` @component).