codiff.f

This file computes the diffusion coefficients for rotational mixing: one for angular-momentum transport (COD) and one for composition transport (COD2), from the characteristic velocities of the rotational instabilities, at each interface between shells.

• Inputs: the arguments HRU (the radius of each shell's midpoint, not logged) and M; the velocities VES (meridional circulation), VGSF (Goldreich–Schubert–Fricke instability) and VSS (secular shear) in TEMP2_MOD, computed by VCIRC; the variable $f_c$, the argument VFC (SECULR's array, filled by GETFC); in NMLPAR_MOD, the multipliers FW, FC, FESC, FGSFC, FSSC, the switch LVFC, the constant background coefficient CODM, LCODM, and LNOJ. All options are set in PARMIN.
• Who calls it: SECULR.
• Outputs: COD, COD2 and RMID (arguments), from element 2 on: no routine sets COD(1) or COD2(1), and their readers, ROTGRID and MIXGRID, start at element IBEG+1 ≥ 2 (rotgrid.f, lines 189–197↗, rotgrid.f, lines 205–210↗, mixgrid.f, lines 133–138↗; settled from the code, Nov 9, 2026). HLE in TEMP2_MOD, set to zero (lines 101–106↗; the line HLE(I)=RMID(I) is commented out): unused?, since its only reader is the column "LENGTH" of CHECKJ's detailed print, which is switched off (checkj.f, line 326↗, checkj.f, line 363↗); the header's "characteristic velocity length scales" (lines 70–71↗) are thus not computed.
• Unused?: the local arrays FADV, FADV0 (formerly /ADVEC/, declared only here, line 57↗).

Element $i$ refers to the interface between shells $i-1$ and $i$, at $r_{\mathrm{mid},i} = \tfrac12(r_i + r_{i-1})$. With $v = v_\mathrm{ES} + v_\mathrm{GSF} + v_\mathrm{SS}$: $$D_J = 4\pi f_w\, v\, r_\mathrm{mid}, \qquad D_X = 4\pi f_w f_c \left(f_{c,\mathrm{ES}}\,v_\mathrm{ES} + f_{c,\mathrm{GSF}}\,v_\mathrm{GSF} + f_{c,\mathrm{SS}}\,v_\mathrm{SS}\right) r_\mathrm{mid},$$ with $f_{c,\mathrm{ES}}$, $f_{c,\mathrm{GSF}}$, $f_{c,\mathrm{SS}}$ = FESC, FGSFC, FSSC, as on VCIRC's page; or, with a variable $f_c$ (LVFC), $D_X = D_J\,f_c(r)$. The two sets of factors differ: FES, FGSF, FSS scale the velocities in VCIRC; FESC, FGSFC, FSSC weight each mechanism's share of composition mixing only. With LCODM, a constant CODM is added to $D_J$ ($4\pi f_w\,\mathrm{CODM}$; "MHP 9/14," "MHP 8/13"). It is added to $D_J$ only, never to $D_X$, in both branches (lines 129–131↗, lines 135–138↗): the Physics namelist page describes CODM as a magnetic diffusion term for angular-momentum transport (below), and KNOWN_ISSUES.md issue 1 records the same (settled from YREC's documentation, Nov 9, 2026). With LNOJ, $D_J = 0$: composition is mixed but angular momentum is not transported (MHP 9/93). So the coefficient is a velocity times a length, the radius: $v\,r$ is in cm$^2$ s$^{-1}$, and the factor $4\pi$ belongs to the form in which the equation is solved: ROTGRID multiplies the coefficients by $\rho r^4\,d\chi/dr$ and $I/(mr^2)$ (its comment: "a factor of 4PI has already been included in CODIFF"), giving the $D$ of DCOEFT's equation. The $\mu$-gradient enters only through the velocities: with IMU = 3, VCIRC subtracts the $\mu$ currents (VMU, scaled by FMU) from VES and VGSF before they reach CODIFF (vcirc.f, lines 540–566↗), and CODIFF does not read VMU (settled from the code, Nov 9, 2026).

Physics Options (Angular momentum transport): LCODM adds a magnetic diffusion term CODM to angular-momentum transport (0 is pure hydrodynamics; 9e4 matches the constraints on the solar core's rotation; the code's default is 2.5e4); FW scales all angular-momentum diffusion coefficients, and FC the mixing coefficients relative to them, usually calibrated on lithium depletion (in clusters or the Sun). LVFC, experimental, is the variable-FC model of Zahn (1991).