docs: VIV predeclare — source-verified box/position, seed, response-cycle window, instability definition

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Claude
2026-10-30 14:57:50 +00:00
co-authored by Claude Opus 5.5
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## Primary case (one case)
- Reference: Kolahdouz et al., arXiv:2003.12046, §4.1.1 (setup) and Qin et
al., arXiv:2003.12186, §4.5 (maximum amplitudes at U_red = 3…8: .075, .551,
.520, .459, .370, .084 D, as quoted by Grok/Astra from the text).
- Reference: Qin et al., arXiv:2003.12186, §4.5 (maximum amplitudes at
U_red = 3…8: .075, .551, .520, .459, .370, .084 D in the text, as quoted by
Grok/Astra) for the target; setup from Kolahdouz et al., arXiv:2003.12046,
§4.1.1 (read 2026-10-30 via ar5iv): U* sweep 3–8 with amplitudes only in
Fig. 3(b) (no text values), domain [−30, 45] D × [−30, 30] D with the
cylinder "initially at rest and centered at the origin", uniform inflow on
the left, zero normal traction and tangential velocity at the outlet, zero
normal velocity and tangential traction on y = ±30 D; no initial
perturbation and no total simulated time stated.
- Re = 150, U* = U/(f_n D) = 5, m/(rho D²) = 2 (m* = rho_s/rho_f = 8/pi),
zeta = 0, f_n = sqrt(K/M)/(2 pi) in vacuum. Transverse DOF only.
- Target: A_max = .520 D (peak amplitude, Qin §4.5). Multi-code reference
@@ -21,8 +27,8 @@ this page is jointly agreed.
- D = 40, MRT, dense double buffer; U_lat = .04, nu = U D / 150 = .010667,
tau = .532.
- Box 75 D × 60 D (3000 × 2400, Kolahdouz class); cylinder position as in
Kolahdouz (OPEN: confirm; default 20 D from the inlet, centred in y).
- Box 75 D × 60 D (3000 × 2400) with the cylinder 30 D from the inlet, 45 D
from the outlet, centred in y (Kolahdouz §4.1.1).
- Boundaries: uniform Zou–He inlet, NEQ outlet (rho = 1, backflow clamp),
free-slip y walls. Kolahdouz uses a traction outlet: declared mismatch.
- Qin's own VIV box (40 D × 20 D) is not used; a smaller box would be a
@@ -49,12 +55,25 @@ this page is jointly agreed.
## Window, failure semantics, acceptance (engineering, development stage)
- Settled when the per-cycle peak |y| changes ≤ 2 % between consecutive
10-cycle windows and the last 5 cycle peaks agree within 1 %; cap 150
oscillation cycles.
- Start: fluid at rest at U = 0 except the uniform inlet (impulsive start as
in the reference), body at rest. The reference states no perturbation; a
numerically symmetric start can delay or suppress lift, so one declared
seed is used: initial structural displacement y0 = +.05 D (2 cells) with
v0 = 0, released at t = 0. No other perturbation; not changed afterwards.
- Response cycles: delimited by consecutive upward zero crossings of y about
its running mean; per-cycle peak = max |y − mean| in that cycle.
- Settled when the per-cycle peak changes ≤ 2 % between consecutive 10-cycle
windows and the last 5 cycle peaks agree within 1 %. The 20 scoring cycles
follow settling and are included in the cap of 150 response cycles from
t = 0 (about 150 × 5,000 = 750,000 steps, t U/D ≈ 750); total steps and
t U/D are reported.
- Growth transient vs instability: amplitude growth from the seed that stays
below 1.0 D (about twice the largest reference peak, .551 D) is a physical
transient and is not a failure by itself. Instability = |y| > 1.0 D, a
non-finite value, or the offset box being reached.
- FAIL-CLOSED and reported (no sub-iteration, no RHS or parameter retune):
unsettled at the cap, |y| beyond the declared offset box, no_donor > 0, or a
growing/diverging amplitude (coupling instability at m* ≈ 2.55).
unsettled at the cap, instability as defined above (possible weak-coupling
instability at m* ≈ 2.55), or no_donor > 0.
- Score over the 20 cycles after settling: A_max/D (mean of cycle peaks) and
f/f_n (reported; no target).
- Acceptance: |A_max − .520 D| ≤ .052 D (±10 %), stated together with the