Research-Stack/6-Documentation/famm/TURBULENCE_MODEL_ATLAS_GATE.md

Turbulence Model Atlas Gate

Purpose

Add the classical and modern turbulence-model family tree as an explicit model atlas for the FAMM / NUVMAP / 16D witness stack.

This document imports turbulence models as closure/witness gates, not as solved proof objects. The goal is to let the Warden choose, compare, scar, or hybridize turbulence models by region rather than treating the turbulence-model hierarchy as a single fixed ladder.

flow region
→ model-family candidate
→ closure assumptions
→ physics retained
→ CPU / memory cost
→ unresolved residual
→ witness strength
→ FAMM scar or promotion

Warden boundary

Allowed claim:

The stack now has an explicit atlas of turbulence model families and can reason about their closure assumptions, cost/physics tradeoffs, residual risk, and 16D witness requirements.

Disallowed claim:

Adding the atlas proves a better turbulence closure, beats DNS/LES/RANS benchmarks, or solves Navier-Stokes regularity.

Hard rule:

A turbulence model is a witness projection, not the flow itself.

Core taxonomy

The old chart has a one-axis tradeoff:

more physics ↔ less CPU time

The project atlas expands it to:

physics retained
CPU / memory cost
closure assumption burden
wall treatment burden
unresolved residual
scar pressure
witness strength
region-of-validity guard

Global packet

\Gamma_{\mathrm{turbulenceModel}}
=
(
X_{\mathrm{flow}},
\pi_{\mathrm{model}},
W_{\mathrm{closure}},
R_{\mathrm{residual}},
I_{\mathrm{flow}},
G_{\mathrm{validity}},
K_{\mathrm{cost}},
\epsilon
)

Packet term	Meaning
X_flow	original turbulent flow region
pi_model	projection into DNS / LES / RANS / hybrid / algebraic model
W_closure	closure assumption or resolved-scale witness
R_residual	unresolved/subgrid/Reynolds-stress residual
I_flow	invariant/quantity to preserve: mass, momentum, energy, vorticity, wall shear, spectra, etc.
G_validity	assumptions: incompressible/compressible, wall-bounded/free shear, separated/attached, high/low Re, etc.
K_cost	CPU, memory, mesh, timestep, solver cost
epsilon	model error / closure gap / numerical residual

0. Exact / near-exact resolution family

DNS — Direct Numerical Simulation

DNS_EXACT_RESOLUTION_GATE

Purpose:

solve the Navier-Stokes equations while resolving all dynamically relevant scales down to dissipative scales

Project role:

highest-physics reference witness
brutal cost
benchmark / calibration source
not a practical everyday route for high-Re engineering flow

Warden checks:

mesh resolves Kolmogorov scale
proper timestep / CFL
numerical dissipation recorded
boundary conditions recorded
not called exact if discretization error is unbounded

Filtered DNS / under-resolved DNS

FILTERED_DNS_WITNESS_GATE

Purpose:

DNS-like equations on a grid that may not fully resolve every scale; useful as data/witness but not full DNS

Project role:

calibration source with explicit resolution scar

1. LES family — spatially filtered turbulence

LES — Large Eddy Simulation

LES_FILTERED_SUBGRID_GATE

Purpose:

resolve large eddies, model subgrid-scale stresses

Canonical filtered form:

\partial_t \bar u_i + \bar u_j\partial_j\bar u_i
=
-\frac{1}{\rho}\partial_i\bar p
+\nu\partial_{jj}\bar u_i
-\partial_j\tau_{ij}^{\mathrm{sgs}}

Subgrid stress:

\tau_{ij}^{\mathrm{sgs}}
=
\overline{u_i u_j}-\bar u_i\bar u_j

Project role:

resolved-scale witness + subgrid residual channel

Smagorinsky SGS model

SMAGORINSKY_SGS_GATE

\nu_t=(C_s\Delta)^2|\bar S|

Role:

baseline eddy-viscosity subgrid closure

Scar risks:

over-dissipation
near-wall damping needed
poor transitional/backscatter behavior

Dynamic Smagorinsky / Germano dynamic model

DYNAMIC_SMAGORINSKY_SGS_GATE

Role:

computes local coefficient from test filtering rather than fixed coefficient

Scar risks:

coefficient noise
averaging choices
negative eddy viscosity / stability handling

WALE — Wall-Adapting Local Eddy-viscosity

WALE_SGS_GATE

Role:

near-wall LES subgrid model using local velocity-gradient invariants

Good for:

wall-bounded LES without ad-hoc damping in many cases

Vreman SGS model

VREMAN_SGS_GATE

Role:

algebraic SGS closure designed to vanish in certain laminar/shear cases and behave robustly near walls

Sigma SGS model

SIGMA_SGS_GATE

Role:

SGS model based on singular values of velocity-gradient tensor

One-equation SGS kinetic-energy model

ONE_EQUATION_SGS_K_GATE

Role:

transport subgrid kinetic energy and derive eddy viscosity from it

Mixed / similarity / Bardina model

BARDINA_SIMILARITY_SGS_GATE
MIXED_SGS_GATE

Role:

use scale similarity and/or combine similarity with eddy viscosity

Scar risks:

stability
backscatter control
need explicit residual/witness monitoring

Clark gradient model

CLARK_GRADIENT_SGS_GATE

Role:

Taylor/gradient expansion of subgrid stress

Approximate deconvolution model

APPROXIMATE_DECONVOLUTION_SGS_GATE

Role:

approximate unfiltered field from filtered field, then model SGS contribution

Coherent Structure / Structure-function SGS models

COHERENT_STRUCTURE_SGS_GATE
STRUCTURE_FUNCTION_SGS_GATE

Role:

subgrid closure based on coherent vortical structures or local structure functions

ILES / MILES — implicit LES

IMPLICIT_LES_NUMERICAL_SGS_GATE
MILES_GATE

Role:

use numerical dissipation of the scheme as implicit SGS model

Warden check:

numerical viscosity is the model; it must be measured, not ignored

2. Hybrid RANS / LES and scale-resolving simulation

DES — Detached Eddy Simulation

DES_HYBRID_RANS_LES_GATE

Purpose:

RANS near attached boundary layers, LES in separated regions

Role:

region-router between modeled and resolved turbulence

Scar risks:

grid-induced separation
gray-area behavior
incorrect shielding of boundary layer

DDES — Delayed Detached Eddy Simulation

DDES_HYBRID_GATE

Role:

DES with shielding to delay LES activation in attached boundary layers

IDDES — Improved Delayed Detached Eddy Simulation

IDDES_HYBRID_GATE

Role:

improved near-wall / wall-modeled LES and RANS-LES blending behavior

ZDES — Zonal DES

ZONAL_DES_GATE

Role:

explicitly prescribe RANS/LES zones by region

SAS — Scale-Adaptive Simulation

SAS_SCALE_ADAPTIVE_GATE

Role:

allows resolved unsteadiness based on local flow scale, often from RANS base model

PANS — Partially Averaged Navier-Stokes

PANS_PARTIALLY_AVERAGED_GATE

Role:

continuous bridge between RANS and DNS/LES by choosing unresolved kinetic-energy fraction

PITM — Partially Integrated Transport Model

PITM_PARTIALLY_INTEGRATED_GATE

Role:

scale-resolving hybrid based on partial integration of turbulence spectrum/transport

VLES — Very Large Eddy Simulation

VLES_GATE

Role:

resolve very-large structures, model more of the spectrum than LES

XLES / X-RANS variants

XLES_GATE
X_RANS_GATE

Role:

hybrid scale-resolving variants between RANS and LES

WMLES — Wall-Modeled LES

WALL_MODELED_LES_GATE

Role:

LES in outer layer plus wall model to avoid resolving viscous sublayer

3. RANS family — Reynolds averaging closures

RANS decomposes velocity into mean plus fluctuation:

u_i = \overline{u_i}+u_i'

and produces Reynolds stress:

R_{ij}=\overline{u_i'u_j'}

Mean equation:

\partial_t\overline{u_i}
+
\overline{u_j}\partial_j\overline{u_i}
=
-\frac{1}{\rho}\partial_i\overline p
+\nu\partial_{jj}\overline{u_i}
-\partial_j R_{ij}

Closure problem:

model R_ij

Linear eddy-viscosity / Boussinesq assumption

BOUSSINESQ_EDDY_VISCOSITY_GATE

-R_{ij}
=
2\nu_t\overline S_{ij}
-
\frac{2}{3}k\delta_{ij}

Role:

assume turbulent stresses align with mean strain

Scar risks:

anisotropy
curvature
rotation
separation
secondary flows
strong strain history

4. Zero-equation / algebraic closures

Prandtl mixing-length model

PRANDTL_MIXING_LENGTH_GATE

\nu_t=l_m^2\left|\frac{dU}{dy}\right|

Role:

simple wall/shear eddy-viscosity estimate

Cebeci-Smith algebraic model

CEBECI_SMITH_ALGEBRAIC_GATE

Role:

algebraic boundary-layer eddy-viscosity model with inner/outer formulation

Baldwin-Lomax algebraic model

BALDWIN_LOMAX_ALGEBRAIC_GATE

Role:

classic algebraic model for attached aerodynamic boundary layers

Van Driest damping / wall damping functions

VAN_DRIEST_DAMPING_GATE

Role:

near-wall damping correction for mixing-length/eddy-viscosity models

5. One-equation RANS closures

Spalart-Allmaras model

SPALART_ALLMARAS_ONE_EQUATION_GATE

Role:

transport a modified turbulent viscosity variable; common for external aerodynamic boundary layers

Project role:

cheap RANS closure with better physical content than algebraic models

Scar risks:

massive separation
complex recirculation
strong anisotropy
non-equilibrium turbulence

Baldwin-Barth one-equation model

BALDWIN_BARTH_ONE_EQUATION_GATE

Role:

older one-equation eddy-viscosity model for aerodynamic applications

6. Two-equation RANS closures

Standard k-epsilon

K_EPSILON_STANDARD_GATE

Variables:

k = turbulent kinetic energy
ε = dissipation rate

Eddy viscosity:

\nu_t=C_\mu\frac{k^2}{\epsilon}

Role:

robust industrial free-shear / many engineering flows

Scar risks:

near-wall treatment
adverse pressure gradient
strong separation
curvature/rotation

RNG k-epsilon

K_EPSILON_RNG_GATE

Role:

renormalization-group motivated k-epsilon variant with improved strain/curvature behavior in some regimes

Realizable k-epsilon

K_EPSILON_REALIZABLE_GATE

Role:

variant designed to satisfy certain mathematical realizability constraints on Reynolds stresses

Low-Re k-epsilon variants

LOW_RE_K_EPSILON_GATE

Role:

resolve near-wall region with damping functions / low-Re corrections

Standard k-omega / Wilcox k-omega

K_OMEGA_STANDARD_GATE

Variables:

k = turbulent kinetic energy
ω = specific dissipation rate

Eddy viscosity:

\nu_t=\frac{k}{\omega}

Role:

strong near-wall behavior; sensitive to free-stream ω

SST k-omega — Menter Shear-Stress Transport

K_OMEGA_SST_GATE

Role:

blends k-omega near wall with k-epsilon-like behavior away from wall; includes shear-stress limiter

Project role:

industrial default candidate for adverse-pressure-gradient and separated aerodynamic flows

Baseline k-omega / BSL

K_OMEGA_BSL_GATE

Role:

blended k-omega/k-epsilon baseline without full SST limiter behavior

k-kl-omega transition model

K_KL_OMEGA_TRANSITION_GATE

Role:

three-equation transition-sensitive model using laminar kinetic energy plus k/omega variables

k-tau / k-zeta / related two-equation variants

K_TAU_VARIANT_GATE
K_ZETA_VARIANT_GATE

Role:

alternative time-scale or variable transformations of two-equation turbulence closures

7. Three-/four-equation and transition closures

v2-f model

V2_F_GATE

Role:

near-wall turbulence anisotropy and wall-normal velocity scale model, often four-equation

ζ-f / zeta-f model

ZETA_F_GATE

Role:

elliptic relaxation / wall-blocking inspired variant using velocity-scale ratio

Intermittency / gamma-Re-theta transition model

GAMMA_RE_THETA_TRANSITION_GATE

Role:

transition model with intermittency and transition momentum-thickness Reynolds number variables

e^N / boundary-layer transition method

E_N_TRANSITION_GATE

Role:

linear stability / amplification-factor transition prediction, often coupled to boundary-layer/RANS methods

Langtry-Menter transition model

LANGTRY_MENTER_TRANSITION_GATE

Role:

correlation-based transition model often used with SST

8. Reynolds Stress Transport Models

RSM / RSTM — Reynolds Stress Model

REYNOLDS_STRESS_MODEL_GATE

Purpose:

solve transport equations for individual Reynolds stress tensor components plus scale equation

Role:

higher-physics RANS closure; avoids simple Boussinesq alignment assumption

Classic chart note:

roughly 7 additional PDEs in common formulations

Scar risks:

pressure-strain closure
wall reflection terms
numerical stiffness
boundary conditions
model constants

LRR Reynolds stress model

LRR_REYNOLDS_STRESS_GATE

Role:

Launder-Reece-Rodi style pressure-strain closure family

SSG Reynolds stress model

SSG_REYNOLDS_STRESS_GATE

Role:

Speziale-Sarkar-Gatski nonlinear pressure-strain closure family

Elliptic blending Reynolds stress models

ELLIPTIC_BLEND_RSM_GATE

Role:

near-wall anisotropy and wall-blocking behavior using elliptic blending/relaxation ideas

9. Nonlinear eddy-viscosity / algebraic stress models

Nonlinear Eddy Viscosity Models

NONLINEAR_EDDY_VISCOSITY_GATE

Role:

extend Boussinesq model with nonlinear strain/rotation tensor terms

Explicit Algebraic Reynolds Stress Models — EARSM

EARSM_GATE

Role:

approximate Reynolds stress anisotropy algebraically from strain/rotation invariants, often derived from RSM equilibrium assumptions

Quadratic / cubic constitutive relation models

QUADRATIC_CUBIC_STRESS_CLOSURE_GATE

Role:

higher-order tensor polynomial stress-strain closures

10. Compressible / high-speed turbulence additions

Compressibility corrections

COMPRESSIBILITY_CORRECTION_GATE

Role:

modify RANS/LES closures for dilatation, turbulent Mach number, shock interaction

Shock-unsteadiness / shock-capturing scar gate

SHOCK_TURBULENCE_INTERACTION_GATE

Role:

flag regions where shock/turbulence coupling makes closure assumptions fragile

Morkovin-hypothesis guard

MORKOVIN_GUARD_GATE

Role:

records whether compressible boundary layer assumptions are expected to be valid

11. Multiphase / reacting / MHD turbulence closures

These are not one universal closure; they are model families layered on top of turbulence closures.

Scalar flux / turbulent Prandtl-Schmidt closures

TURBULENT_PRANDTL_SCHMIDT_GATE

Role:

model turbulent transport of heat/species/scalars

Combustion turbulence closures

TURBULENCE_CHEMISTRY_INTERACTION_GATE
EDC_COMBUSTION_GATE
FLAMELET_TURBULENCE_GATE
PDF_COMBUSTION_TURBULENCE_GATE

Role:

model turbulence-chemistry interaction; separate Warden guard from pure flow closure

Multiphase turbulence closures

MULTIPHASE_TURBULENCE_GATE
TWO_FLUID_TURBULENCE_GATE
DISPERSED_PHASE_TURBULENCE_GATE

Role:

turbulence modulation by particles/bubbles/droplets and interphase coupling

MHD turbulence closures

MHD_TURBULENCE_GATE
ALFVENIC_TURBULENCE_WITNESS_GATE

Role:

magnetohydrodynamic turbulence; links to plasma chiral drag and Alfvén-wave witness channels

12. Reduced-order / data-driven turbulence models

These must be treated as model-augmentation gates, not automatic truth.

POD / Galerkin reduced-order models

POD_GALERKIN_ROM_GATE

Role:

low-dimensional basis for flow reconstruction/control

DMD / Koopman models

DMD_KOOPMAN_TURBULENCE_GATE

Role:

modal time-evolution and recurrence witness

Neural turbulence closures

NEURAL_TURBULENCE_CLOSURE_GATE

Role:

learn subgrid, RANS closure, correction, or wall model from data

Warden checks:

training distribution
generalization regime
physical constraints
invariance
stability
uncertainty
out-of-distribution flags

Symbolic-regression closures

SYMBOLIC_REGRESSION_CLOSURE_GATE

Role:

learn explicit algebraic/tensor closure forms that can be inspected and receipted

Bayesian / UQ turbulence model calibration

BAYESIAN_TURBULENCE_CALIBRATION_GATE
UQ_TURBULENCE_MODEL_GATE

Role:

parameter uncertainty, model-form uncertainty, posterior closure calibration

13. Wall-treatment atlas

Wall models are often as important as the turbulence model itself.

WALL_FUNCTION_GATE
ENHANCED_WALL_TREATMENT_GATE
LOW_RE_WALL_RESOLVED_GATE
TWO_LAYER_WALL_MODEL_GATE
EQUILIBRIUM_WALL_MODEL_GATE
NON_EQUILIBRIUM_WALL_MODEL_GATE
SLIP_WALL_MODEL_GATE

Warden checks:

y+ range
wall shear target
separation / pressure gradient
roughness
heat transfer
wall curvature
mesh resolution

14. Project-specific witness closures

These are the project's additions on top of classical models.

16D FAMM witness closure

FAMM_16D_WITNESS_CLOSURE_GATE

Purpose:

augment classical turbulence model with 16D audit packet: geometry, torsion, chirality, semantic/witness mass, recurrence, delta memory, scars, residuals, invariant overlap, route cost, receipt strength

Role:

not a replacement closure by itself; an audit/control layer for where a closure is safe or blind

Shadow Control Gap Map

SHADOW_CONTROL_GAP_TURBULENCE_GATE

Purpose:

explicitly record where the witness packet does not control the dangerous term

3D danger term:

(\omega\cdot\nabla)u

Gap shape:

\mathcal S_{\mathrm{gap}}
=
\left[
\| (\omega\cdot\nabla)u\|_{\mathrm{unwitnessed}}
-
C\,\mathcal W_{16D}
\right]_+

Photonic / Burgers residual witness

PHOTONIC_BURGERS_RESIDUAL_WITNESS_GATE

Purpose:

use fixed-point Burgers/triad solver plus external/stochastic witness channel as unresolved-mode indicator

Plasma chiral drag / Alfvénic witness

PLASMA_CHIRAL_DRAG_TURBULENCE_WITNESS_GATE

Purpose:

use chiral/Alfvénic wave rotation as signed torsion/witness receipt in MHD-like regions

OR-Tools regional model scheduler

OR_TOOLS_TURBULENCE_REGION_SCHEDULER_GATE

Purpose:

choose which turbulence model applies to which mesh region under budget and risk constraints

Decision variables:

x_region_model = 1 if model m is selected for region r

Objective:

minimize CPU cost + residual risk + scar pressure
maximize witness strength + invariant coverage

Constraints:

budget ≤ B
wall regions must satisfy wall-treatment guard
high-gap regions cannot use algebraic-only closure
scarred closures blocked unless explicitly reopened
DNS/LES only where mesh/time budget supports them

FAMM residual score for any turbulence model

R_{\mathrm{model}}
=
\lambda_1 R_{\mathrm{closure}}
+
\lambda_2 R_{\mathrm{wall}}
+
\lambda_3 R_{\mathrm{grid}}
+
\lambda_4 R_{\mathrm{time}}
+
\lambda_5 R_{\mathrm{invariant}}
+
\lambda_6 \Omega_{\mathrm{scar}}

Promotion condition:

R_{\mathrm{model}}\le\Theta_{\mathrm{region}}

Suggested region routing

Region / flow situation	Candidate model family	Warden caution
low-Re benchmark / small domain	DNS	cost explosion at high Re
separated unsteady flow	LES / DES / IDDES / SAS	grid and gray-area scars
attached aerodynamic boundary layer	SA / SST / algebraic if simple	adverse pressure gradient scars
industrial steady approximation	k-epsilon / SST / RSM	closure validity by regime
strong anisotropy / swirl / curvature	RSM / EARSM / nonlinear EVM	pressure-strain/model constants
near-wall heat transfer	low-Re / wall-resolved / enhanced wall	y+ and thermal wall functions
transition-sensitive flow	gamma-Re-theta / e^N / k-kl-omega	transition correlation domain
compressible/shock flow	compressible corrections + shock gate	shock/turbulence interaction scars
MHD/plasma-like flow	MHD turbulence + Alfvén witness	coupling assumptions
constrained compute browser/demo	algebraic / SA / reduced-order	never call it full physics

Stack placement

TURBULENCE_MODEL_ATLAS_GATE
→ DNS / LES / RANS / hybrid / algebraic model candidates
→ 16D Shell Atlas / PathEpigenetic gate / Chaos Game shrinker
→ FAMM shadow-gap audit
→ OR-Tools regional scheduler
→ Anti-FAMM closure-blindness attack
→ NUVMAP route memory
→ Warden promote / scar / reopen

Anti-FAMM checks

For every turbulence model, Anti-FAMM asks:

What term did the closure hide?
Where does the model look stable while the dangerous physics escapes?
Which wall/mesh/time guard failed?
Is the model outside its calibration regime?
Did numerical dissipation masquerade as physics?
Did the residual move into an unobserved shadow channel?

Best project sentence

The turbulence model atlas converts DNS, LES, DES, RANS, Reynolds-stress, k-epsilon, k-omega, Spalart-Allmaras, algebraic, transition, wall, compressible, multiphase, MHD, and data-driven closures into explicit witness gates. The Warden no longer asks only which model has more physics or less CPU cost; it asks which regional closure preserves the necessary invariants, exposes its unresolved residual, satisfies its wall/grid/validity guards, and carries enough 16D/FAMM witness strength to be promoted.

References

@book{pope2000turbulent,
  title     = {Turbulent Flows},
  author    = {Pope, Stephen B.},
  publisher = {Cambridge University Press},
  year      = {2000}
}

@book{wilcox2006turbulence,
  title     = {Turbulence Modeling for CFD},
  author    = {Wilcox, David C.},
  publisher = {DCW Industries},
  year      = {2006}
}

@article{spalart1992one,
  title   = {A one-equation turbulence model for aerodynamic flows},
  author  = {Spalart, P. R. and Allmaras, S. R.},
  journal = {AIAA Paper 92-0439},
  year    = {1992}
}

@article{menter1994two,
  title   = {Two-equation eddy-viscosity turbulence models for engineering applications},
  author  = {Menter, F. R.},
  journal = {AIAA Journal},
  volume  = {32},
  number  = {8},
  pages   = {1598--1605},
  year    = {1994}
}

@article{smagorinsky1963general,
  title   = {General circulation experiments with the primitive equations},
  author  = {Smagorinsky, Joseph},
  journal = {Monthly Weather Review},
  volume  = {91},
  number  = {3},
  pages   = {99--164},
  year    = {1963}
}

@article{germano1991dynamic,
  title   = {A dynamic subgrid-scale eddy viscosity model},
  author  = {Germano, M. and Piomelli, U. and Moin, P. and Cabot, W. H.},
  journal = {Physics of Fluids A},
  volume  = {3},
  number  = {7},
  pages   = {1760--1765},
  year    = {1991}
}

@article{spalart1997comments,
  title   = {Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach},
  author  = {Spalart, P. R. and Jou, W.-H. and Strelets, M. and Allmaras, S. R.},
  journal = {Advances in DNS/LES},
  year    = {1997}
}

@article{launder1975progress,
  title   = {Progress in the development of a Reynolds-stress turbulence closure},
  author  = {Launder, B. E. and Reece, G. J. and Rodi, W.},
  journal = {Journal of Fluid Mechanics},
  volume  = {68},
  number  = {3},
  pages   = {537--566},
  year    = {1975}
}