# ⚛  L1 Principle — RANS k-omega SST — Menter's two-eq turbulence model

**ID:** `L1-177` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Fluid Dynamics — *k-omega SST hybrid turbulence closure*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** reynolds stress SST
> **📡 Carrier:** mechanical · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553966

---

## 🧠 1. Introduction

**RANS k-omega SST — Menter's two-eq turbulence model** is a **nonlinear inverse problem** whose unknown lives in **reynolds stress SST** space, within the **k-omega SST hybrid turbulence closure** sub-domain of **Fluid Dynamics**.

Measurements consist of mechanical vibrations or strain signals via a **piv hot wire** sensing mechanism.

The forward operator applies, in order: L · mean flow ns operator; L · k eq operator; L · omega eq operator; L · blend fn operator; pixel-level spatial averaging on the detector.

Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds.

## ⚙ 2. Forward Model

Physical chain: **x** → L · mean flow ns → L · k eq → L · omega eq → L · blend fn → Spatial integration → **y** (detector).

```
y = ∫_A dA `L.blend_fn` `L.omega_eq` `L.k_eq` `L.mean_flow_ns` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.mean_flow_ns` | L · mean flow ns operator |
| `L.k_eq` | L · k eq operator |
| `L.omega_eq` | L · omega eq operator |
| `L.blend_fn` | L · blend fn operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Fluid Dynamics |
| Sub domain | k-omega SST hybrid turbulence closure |
| Carrier | mechanical |
| Problem class | nonlinear_inverse |
| Solution space | reynolds_stress_SST |
| Noise model | gaussian |
| Integration axis | spatial |
| Difficulty delta | 5 |
| L dag | 3.5 |

## 📡 4. Measurement Model

Conditional stability; mismatch parameters dominate at Omega bounds.

| Metric | Value |
|---|---|
| Metric | PSNR_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `rans_komega_sst` · **Forward operator:** `rans_komega_sst_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 256 |
| W | px | 256 |
| Z | — | 128 |
| Snr db | dB | 30 |
| C omega error | — | 0 |
| Wall fn error | — | 0 |
| Blend fn error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 32 – 2048 |
| W | px | 32 – 2048 |
| Z | — | 16 – 1024 |
| Snr db | dB | 0 – 40 |
| C omega error | — | 0.0 – 0.3 |
| Wall fn error | — | 0.0 – 0.3 |
| Blend fn error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 21.0

| Metric | Range |
|---|---|
| Psnr db | 10.0 – 45.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `500` and δ = `5`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0xf0f1522312f72f99dbf050bbee79a5329abfa17430091fa888b1c2db7a837e0c`
- **Chain tx hash:** `0xb4751b0207c073170d0e35585afecdf635810b2a2ca15e9964b65ccddc225b3d`
- **Chain block:** `41553966`

---

## File Mapping

This bundle consists of: `L1-177.md`, `L1-177.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-177.md` | Source of truth — edit this | Human or LLM |
| `L1-177.json` | Structured metadata for the registry | LLM regenerates from the sections above |

**Prompt for your LLM after editing this Markdown:**

> Read the attached Markdown. Regenerate the sibling `.json` so every field matches.
> Preserve the schema documented in the rows above.
> Output each file in its own fenced code block tagged with the filename.
> Output only the JSON object.

_This Markdown was auto-synthesized from the catalog row for `L1-177`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._