Tutorial 5 — Current, waves, and convergence

Goal: add a current, a regular Airy wave, and an irregular JONSWAP sea to a dynamic mooring line; then show that the result is converged in time step and mesh.

Decks: examples/dynamic_chain_held.dat, dynamic_chain_current.dat, dynamic_chain_waves.dat · Route: EI = 0 cable dynamics · Run time: < 1 s each

The baseline

dynamic_chain_held.dat is a 410 m chain in 50 m of water with the fairlead held at the surface. It adds two options to a static deck:

0.05         dtM       - CableDyn internal time step (s)
10.0         TMax      - Standalone simulation duration (s)

New-Item -ItemType Directory -Force results | Out-Null   # already there after the quickstart
.\CableDyn_driver.exe .\examples\dynamic_chain_held.dat .\results\held

The held line starts in static equilibrium and nothing disturbs it, so every row of held.out repeats the static values (FairTen1 = 1005.63 kN). This is the first check of any dynamic model: a system started at equilibrium with no forcing must stay there. A drift here would point to an inconsistent initial condition.

Environment records

The current and wave decks differ from the baseline by one row each:

uniform 1.0 0.0 0.0  current   - Current model and X/Y/Z velocity (m/s) {none; uniform; profile}

airy 2.0 8.0 0.0     waves     - Wave model, height, period, and direction (m, s, deg) {none; airy; jonswap}

  • current accepts none, uniform vx vy vz, or a two-level profile z1 vx1 vy1 vz1 z2 vx2 vy2 vz2; use a WaterKin current table for more levels. The static initial condition includes the current’s steady drag, so the line starts the march at rest in the current.

  • waves accepts, for example, none, airy H T direction (regular linear wave), or jonswap Hs Tp gamma direction (irregular sea); stream, pm/issc, torsethaugen, and ochihubble rows and multi-train wavetrain rows are shown below and listed in OPTIONS reference and defaults. Waves need WtrDpth for dispersion.

  • WaveSeed (default 1) selects the random JONSWAP realisation: the same seed always reproduces the same sea, and extreme-value statistics need several seeds.

  • rampTime (default 0, off) fades the waves in from still water with a half-cosine over the given time. The static initial condition has no waves, so switching the full sea on at t = 0 gives a start-up transient; a ramp of one to two peak periods, e.g. 16.0 rampTime, removes it. Discard at least the ramp window from the statistics.

  • The fluid loads are Morison drag and added mass on the relative velocity, plus Froude–Krylov and buoyancy from the wave field. Directions are in degrees from +X toward +Y.

Full syntax and restrictions are in OPTIONS reference and defaults. In a coupled run of OpenFAST (maintained by NLR, the National Laboratory of the Rockies, formerly NREL) the host’s SeaState supplies these fields instead (Tutorial 9 — A floating wind turbine in OpenFAST).

Run the three cases for 60 s

Copy the three decks, set TMax to 60.0 in each, and add a JONSWAP copy of the wave deck with jonswap 2.0 8.0 3.3 0.0 waves. Then:

.\CableDyn_driver.exe .\current60.dat .\results\current60
.\CableDyn_driver.exe .\airy60.dat    .\results\airy60
.\CableDyn_driver.exe .\jonswap60.dat .\results\jonswap60

FairTen1 statistics over the settled window 20–60 s:

Case

Mean (kN)

Std (kN)

Min (kN)

Max (kN)

held, still water

1005.63

0

1005.6

1005.6

uniform current 1.0 m/s

1020.34

0

1020.3

1020.3

Airy, H = 2 m, T = 8 s

1005.95

1.28

1003.0

1008.0

JONSWAP, Hs = 2 m, Tp = 8 s, γ = 3.3

1005.81

0.72

1003.7

1008.2

Interpretation: the current adds a steady drag that raises the mean tension by 15 kN; the waves leave the mean unchanged and add a small oscillation, because with the fairlead held the waves can only act on the line itself. In a real floating system the dominant dynamic tension comes from the platform motion, which you add with a motion file (Tutorial 4 — Prescribed fairlead motion) or by coupling to OpenFAST (Tutorial 9 — A floating wind turbine in OpenFAST). The JONSWAP record is irregular: judge it by statistics and spectra over a long window (Tutorial 8 — Python studies and post-processing), never by one peak.

Time-step convergence

Repeat the Airy case at dtM = 0.1, 0.05, and 0.025:

dtM (s)

Mean (kN)

Std (kN)

Min (kN)

Max (kN)

0.1

1005.95

1.24

1003.1

1008.0

0.05

1005.95

1.28

1003.0

1008.0

0.025

1005.95

1.30

1002.9

1008.2

The mean is converged at every step and the standard deviation changes by less than 2 % between 0.05 and 0.025 s — adequate for this quantity. Compare means, standard deviations, ranges, and, for fatigue, damage-equivalent loads; one final value proves nothing.

Mesh convergence

Double the elements (NumSegs 41 → 82) at dtM = 0.05: the mean moves from 1005.95 to 1005.65 kN (−0.03 %) and the standard deviation from 1.28 to 1.27 kN. The fairlead channel reports the line-end force (Tutorial 1 — A grounded catenary chain), so the mesh barely moves it. Decide the mesh on the quantity you report.

A convergence protocol

  1. Start at a dtM that resolves the shortest wave or motion period with at least 40–100 steps.

  2. Halve dtM until the statistics you report change by less than your tolerance.

  3. Refine the mesh the same way.

  4. Record both in the analysis report.

Irregular and spread seas

chain_torsethaugen_spread.dat puts the held chain in a Torsethaugen sea:

torsethaugen 5.0 11.0 30.0 waves
4.0       WaveSpreading
9         WaveDirections
100       WaveComponents
1         WaveSeed
20.0      rampTime

The wind-sea and swell peaks of the spectrum follow from Hs and Tp. Each frequency is spread over ±90° about 30° with D(θ) ∝ cos⁸(θ − 30°) in nine direction bins, and the same seed always gives the same sea. Over 20–300 s the fairlead tension has a mean of 1.006 MN and a standard deviation of 4.0 kN; with 0.0 WaveSpreading (long-crested) the deviation is 5.0 kN.

chain_two_train_sea.dat replaces the waves row (kept as none) by two wavetrain rows, each with its own heading and spreading (train i uses the seed WaveSeed + 7919 (i − 1)):

jonswap 3.0 7.0 3.3 0.0 6.0 wavetrain
jonswap 2.0 14.0 5.0 60.0 0.0 wavetrain

The fairlead tension deviation is 1.95 kN, against 1.58 kN for the wind sea alone.

MoorDyn-C kinematics files

moordynC_wavekin/chain_wavekin7_currents1.dat reads MoorDyn-C’s fixed-name files from its own folder. 7 WaterKin (value 7, as in MoorDyn-C’s WaveKin 7) loads wave_frequencies.txt, omega Re Im beta rows with the first at ω = 0: here nine components of a 2.5 m, 9 s JONSWAP sea travelling along +X. 1 Currents loads current_profile.txt, a z ux uy uz table rising from 0.2 m/s at the seabed to 0.6 m/s at the surface. The waves and current rows stay none: a second source is rejected as double counting. CableDyn evaluates the components and the profile exactly at every node, so water_grid.txt is not needed. The current enters the static state (fairlead tension 1.0076 MN against 1.0056 MN in still water), and the waves add a 2.1 kN standard deviation over 120 s.

Nonlinear regular waves

In shallow water a steep wave is not sinusoidal. stream_wave_shallow_chain.dat puts the 30 m R4 chain under stream 8.0 10.0 0.0 waves (H/d = 0.27), a Dean stream-function wave with 20 StreamOrder Fourier terms; airy_wave_shallow_chain.dat is the same deck with airy. Over t = 30–60 s:

Wave

FairTen1 min / max / mean (kN)

AnchTen1 min / max / mean (kN)

stream

134.5 / 168.5 / 151.7

19.6 / 39.0 / 29.1

Airy

133.0 / 168.6 / 151.3

22.8 / 38.7 / 30.6

The fairlead range barely changes (34.0 against 35.6 kN), but the anchor tension range is 22 % larger under the stream wave (19.4 against 15.9 kN).

Anisotropic seabed friction

laid_cable_cross_current.dat lays half of a 230 m cable on the seabed in a 1.2 m/s cross current (+Y), with different friction along and across the cable:

0.3  frictionMuAxial
1.0  frictionMuLateral

The static solve finds where the laid run stops sliding, and the 10 s march keeps it there. The current loads the run across its axis, so the lateral coefficient decides:

Friction (axial / lateral)

FairTen1 (kN)

TDP1s (m)

Sway at s = 160 m (m)

0.3 / 1.0 (deck)

59.0

109.8

0.01

1.0 isotropic

59.0

109.8

0.01

0.3 isotropic

64.3

117.5

11.8

none

73.9

128.0

19.6

A single coefficient equal to the axial value lets the laid run slide up to 16 m sideways and raises the fairlead tension by 9 %.

Exercises

  1. Current profile. Replace the uniform current by profile -50.0 0.2 0.0 0.0 0.0 1.0 0.0 0.0 current (0.2 m/s at the seabed, 1.0 m/s at the surface). How much of the mean-tension increase remains? (About 6 kN of the 15 kN: drag scales with the square of the local velocity.)

  2. Wave direction. Run the Airy case with direction 90°. The tension reacts more, not less: its standard deviation over 20–60 s rises from 1.28 kN at 0° to 1.88 kN at 90° (range 1003.0–1009.0 kN), with the mean unchanged at 1005.9 kN. Waves crossing the line broadside load its whole length with normal drag and inertia out of its plane, whereas head-on waves act partly along the line, most of all on the grounded and near-horizontal part.

  3. Spectrum. Run the JONSWAP deck for 600 s and plot its tension spectrum as shown in Tutorial 8 — Python studies and post-processing; the peak sits at 1/Tp = 0.125 Hz.

Next: Tutorial 6 — Synthetic ropes.