# Prescribed in-line oscillation: Dütsch Re 100 / KC 5 — PROTOCOL (review draft)

Production under test: `claude/moving-bodies-s3a` at `653fd997` (unchanged).
Primary source: Dütsch, Durst, Becker & Lienhart, J. Fluid Mech. 360, 249–271
(1998), doi:10.1017/S002211209800860X. Source facts below were verified from
the paper (Slack C0C78UFKGRM/1793335557.460509, TRON 1793356317–1793356724,
page numbers given). Everything marked ENGINEERING is our a-priori choice,
fixed before any benchmark result; it is not a paper uncertainty.

## 0. Source facts (with provenance)

- Motion (p.251): `x_c = -A sin(2 pi f t)`; paper phase phi = 0 is the mean
  position moving left at `-U_max`. KC = 5 gives `A/D = 5/(2 pi) = .7957747`.
- Start (p.254): the computation starts a quarter cycle before phi = 0, at
  `x = +A` with zero velocity (phi = -90°).
- Experiment (pp.252, 254–256): D = 10 mm, L = .65 m, tank 1.2 × .7 × .7 m,
  rho = 998.2 kg/m³, mu = 1.00818 mPa·s, Re = 100, KC = 5; LDA with 1° phase
  bins and 200 samples per node and degree; no quantified experimental error
  recovered.
- Profiles (Fig. 8, p.260): LAB-FIXED stations x1 = -6, 0, 6, 12 mm, i.e.
  x/D = -.6, 0, .6, 1.2, at phi = 180°, 210°, 330°; u1 and u2 versus x2.
- Original numerics (§2): cylinder-fixed accelerated frame (`x_i = x~_i +
  x_i,s`, outer velocity `-u_c`, inertial source `-rho du_c/dt`), O-grid outer
  diameter 120 D, illustrated 192 circumferential nodes, 720 steps/cycle; tank
  influence neglected.
- Force fit (verified): force ON THE BODY per unit span
  `F1 = -0.5 rho D c_d xdot|xdot| - (pi/4) rho D² c_i xddot` with `x = -A sin phi`;
  normalized by `0.5 rho D U_max²`: `c_d cos phi |cos phi| - (pi² c_i / KC) sin phi`.
  `c_i` is the ADDED-MASS coefficient; total inertia `c_m = c_i + 1` is a
  different convention and is not used.
- Table 1 computed Morison coefficients (c_d, c_i) for 96 / 192 / 384 perimeter
  nodes at dt/T = 1/720: (2.15, 1.42), (2.10, 1.45), (2.09, 1.45). These are
  fitted computed coefficients, not a measured force and not an error bar. The
  paper states the coarse direct force is closer to the finest direct force
  than the Morison fit, but gives no waveform-error norm.

## 1. Kinematics, time levels and phase bookkeeping

- Our run is in the LAB frame: the circle moves, the fluid is initially at rest
  (rho = 1, u = 0); no fictitious inertial source is added. Lab-fixed profile
  stations are compared directly (no frame transform needed).
- Geometry reference: the circle's base centre is the INITIAL position, the
  right turning point `x_mean + A`; the declared offset box is x in [-2A, 0],
  y = 0. The body is never teleported: offset 0 at s = 0.
- Elapsed time s = n dt from the start. Analytic position relative to the mean
  `x(s) = A cos(2 pi s / T)`, velocity `u(s) = -U_max sin(2 pi s / T)`; paper
  phase `phi = (360 s / T - 90) mod 360`.
- Step n moves from s_n to s_{n+1}: target offset `x(s_{n+1}) - A`; wall
  velocity = the single-step interval average `(x(s_{n+1}) - x(s_n)) / dt`
  (analytic, supplied, not differenced from stored offsets). The per-step
  force of `run(1)` / `read_force(normalize=True)` is attributed to that same
  interval.
- Paper cycle k = 1, 2, ... spans `s in [T/4 + (k-1) T, T/4 + k T)`; the
  initial quarter cycle (s < T/4) is cycle 0 and never scored. Every logged
  sample carries (k, phi). Example: phi = 330° of cycle 1 is at s = 7T/6.
- T is chosen as a multiple of 360 native steps, so phi = 180°, 210°, 330° fall
  exactly on step boundaries and 1° bins hold whole steps.

## 2. Resolution ladder (uniform grid, fixed Mach), ENGINEERING

| D (cells) | T (steps) | U_max = 5 D / T | nu_lat = U_max D / 100 | tau (3 nu + .5) |
|---|---|---|---|---|
| 20 | 2,520 | .039683 | .0079365 | .5238 |
| 40 | 5,040 | .039683 | .015873 | .5476 |
| 80 | 10,080 | .039683 | .031746 | .5952 |

- MRT collision. Mach fixed (Ma ≈ .0687); a separate Mach check at D = 40
  with T = 10,080 (U_max halved, tau .5238) is labelled MACH and not part of the
  ladder.
- Per-step displacement ≤ U_max ≈ .04 cells (bound .5).

## 3. Domain and boundaries (finite-domain reproduction), ENGINEERING

The paper's 120 D O-grid is not reproduced; our rectangular box is a
reproduction choice. The native dense channel (zero-velocity inlet,
pressure-NEQ outlet, bounce-back y walls) is a finite-domain approximation,
not infinite still fluid. The G4 x-periodic / y-slip override is a separately
labelled sensitivity family and never mixed into the primary ladder. The
runner owner confirms the zero-velocity inlet is supported as configured
before any run.

Order (closed):
1. Smoke + ledger at D = 40, native BC, 40 D × 40 D (finite box).
2. Domain sensitivity before any literature statement: same BC, D = 40,
   L ∈ {20 D, 40 D, 60 D}; record the change in Fx waveform, c_d, c_i and the
   scored profiles.
3. Optional labelled BC sensitivity: one x-periodic / y-slip case at D = 40,
   40 D; reported as a delta against native only.
4. Only after step 2 passes: the D = 20 / 40 / 80 ladder on the chosen BC and
   domain (default 40 D if, against 60 D, `RMS(dFx)/F_ref` and |dc_d|, |dc_i|
   stay inside the section 6 bands).
- Memory/runtime: measured by a smoke run before each new size; measurements
  inform scheduling only, never tolerances.

## 4. Observables (raw, per step, preserved)

- `obs` Fx, Fy (CME) and all `MovingTables.DIAG` columns per step: CME,
  CME + Wen and CME + cover − uncover reported separately; crossings, eq_only,
  no_donor (no_donor must stay 0).
- Velocity u1, u2 on lab-fixed lines x/D = -.6, 0, .6, 1.2 (relative to the
  mean cylinder position) versus x2, at the scored phases. Lab frame
  throughout; if any body-frame intermediate is used, position and velocity
  are both transformed.
- Interpolation: bilinear on cell centres using only cells that are fluid at
  that step (flags read back via `get_flags()`); weights renormalized over the
  fluid corners; a sample with no fluid corner, or inside the circle at that
  step, is MISSING and logged, never set to zero. One-degree bins keep valid
  fluid weights. The numerical average need not mimic the 200 LDA samples.

## 5. Periodic-regime gate (every case, before any statistic), ENGINEERING

Ledger rows, same schema for every case: dx, dt (in D and T units); U_max, nu,
Re, KC (lattice and nondimensional); T (native steps, nondimensional);
duration (native steps, s/T, paper cycles); discard; accepted window; cycle
ledger; verdict PASS or FAIL-CLOSED.

Scales: `F_ref = 0.5 rho U_max² D`, `U_ref = U_max`; never a near-zero mean
force as denominator.

- Settling metrics, cycle k−1 → k, phase-aligned by step within the cycle:
  - waveform `RMS(dFx) / F_ref ≤ .02`;
  - `|d mean|`, `|d RMS|`, `|d peak|` of Fx, each `/ F_ref ≤ .01`;
  - scored profiles (fluid-only) `|du| / U_max`, `|dv| / U_max ≤ .03` at the
    three phases × four stations;
  - Morison `|dc_d| ≤ .02`, `|dc_i| ≤ .02`.
- Rule: all metrics for N = 3 consecutive whole paper cycles → settled.
- Discard: the initial quarter cycle plus the first 2 full paper cycles
  (s/T < 2.25). Settling is searched from cycle 3; cap 12 periods from s = 0;
  unsettled → FAIL-CLOSED (no literature, cross-resolution or VIV statistic).
- Common window: K = the largest first-settled cycle index over all compared
  cases; every case is scored on the same 3 cycles K .. K + 2 and must reach
  them within the cap (proportionally more native steps on finer grids), or
  the comparison is FAIL-CLOSED.
- The earlier G4 timing check (100 coarse vs 400 diffusive-fine steps) was a
  matched short transient, not periodic evidence.

## 6. Metrics and per-observable criteria (ENGINEERING, not paper uncertainty)

Three criteria stay separate; the G4 same-grid 2% target is not reused.

- Morison fit: least squares of the normalized per-step force over the
  accepted window against the two basis functions, each averaged over its
  single step interval, fixed paper phase, no free phase shift; c_d and
  added-mass c_i per force candidate.
- Cross-resolution: every scored observable's error against its reference must
  decrease monotonically D20 → D40 → D80 (necessary, not sufficient).
- Against Table 1 (computed fit, not measured force): at D ≥ 40,
  `|c_d - 2.09| ≤ .15` and `|c_i - 1.45| ≤ .15`, and monotone.
- Force waveform against its own Morison reconstruction: residual reported
  only, no pass/fail (the paper reports fit error above its coarse numerical
  error and gives no percentage).
- Fig. 8 LDA profiles: QUALITATIVE ONLY. The original figure could not be
  accessed or rendered; no digitized ordinates and no measurement uncertainty
  exist. After a digitization with figure number, tool and uncertainty note:
  `RMS(|du|, |dv|) / U_max ≤ .15` at D ≥ 40 and monotone; LDA error stays
  UNQUANTIFIED and is stated with every comparison.
- Fy sanity (not literature): `|mean Fy| / F_ref ≤ .05` in the accepted window.
- No force candidate is selected for an RHS by these results; each is
  reported.

Superseded (earlier drafts): the velocity-jump start, guessed stations and
phases, "C_M" for c_i, and the uncertainty wording; cycles 4–6, the 30-cycle
cap and the earlier tolerance numbers.

## 7. Order and scope

Protocol review → one-shot Dütsch driver (analytic `set_body` + `run(1)`,
cycle ledger, lab-fixed fluid-only station sampler, two-basis Morison fit; no
reusable runner until the first smoke shows shared helpers pay off; no
production change) → smoke (memory/runtime) → domain sensitivity →
ladder → physical-validation verdict → only then single-cylinder VIV. No AMR,
no pinball, no manuscript work.