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Linear Wave Theory

Solves the linear wave dispersion relation using Newton-Raphson iteration to compute wavelength, phase celerity, and group velocity for monochromatic waves. Also derives wave steepness and relative depth (d/L) for water depth classification. Follows the USACE Coastal Engineering Manual Part II Chapter 1 formulation applicable across deep, intermediate, and shallow water regimes.

inputs

3 fields

context

5 archetypes

engine

both

outputs

5 scored fields

contract fields

Parameter Map

3 inputs to 5 scored outputs

  • wave_period_s

    floathidden in hard

    Wave period T

    3 to 18s

  • water_depth_m

    float

    Water depth d

    0.5 to 100m

  • wave_height_m

    floatfrom archetype

    Wave height H

    0.1 to 10m
wavelength_mtol 0.05

Wavelength L (m)

wave_celerity_m_per_stol 0.05

Wave phase celerity C = L / T (m/s)

group_velocity_m_per_stol 0.05

Group velocity C_g = n * C (m/s)

wave_steepnesstol 0.02

Wave steepness S = H / L (dimensionless)

relative_depthtol 0.02

Relative depth d/L (dimensionless); >0.5 deep, <0.05 shallow, else intermediate

visibility contract

Difficulty Ladder

all_giveneasy

Moderate period and depth — all parameters given, straightforward dispersion solve

all fields visible
all_givenmedium

Extreme depth ratio conditions — all parameters given, deep or very shallow regime

all fields visible
partialhard

Wave period hidden — agent must estimate from wave height via empirical wind-wave relationships (T approx 3.5-5.5 * sqrt(H))

wave_period_s

scenario bands

Archetype Atlas

deep_ocean_swell

3 contexts

Deep ocean swell with long period waves in open water

wave_period_s10 to 18
water_depth_m50 to 100
wave_height_m0.5 to 4

tasman-sea-offshore / great-australian-bight / coral-sea-deep

continental_shelf

3 contexts

Continental shelf with moderate depth and intermediate-period waves

wave_period_s6 to 12
water_depth_m10 to 40
wave_height_m0.5 to 5

gold-coast-shelf / sydney-offshore-buoy / perth-canyon-approach

nearshore_approach

3 contexts

Nearshore zone with waves approaching the coastline

wave_period_s5 to 12
water_depth_m2 to 10
wave_height_m0.3 to 3

bondi-beach-nearshore / manly-surf-zone / noosa-heads-approach

shallow_estuary

3 contexts

Shallow estuary or harbour entrance with short-period waves

wave_period_s3 to 7
water_depth_m0.5 to 4
wave_height_m0.1 to 1.5

moreton-bay-entrance / darwin-harbour-channel / port-phillip-heads

reef_platform

3 contexts

Shallow reef platform with long-period ocean swell

wave_period_s8 to 16
water_depth_m1 to 5
wave_height_m0.3 to 2.5

ningaloo-reef-flat / great-barrier-reef-lagoon / heron-island-platform

rendered task

Generation Preview

tasman-sea-offshore-deep-ocean-swell-preview

difficulty
hard
visibility
partial
archetype
deep_ocean_swell
site context
tasman-sea-offshore
instruction excerptlinear-wave-theory_calc.py

visible fields

  • water_depth_m50 to 100 m
  • wave_height_m0.5 to 4 m

withheld schema

wave_period_swavelength_mwave_celerity_m_per_sgroup_velocity_m_per_swave_steepnessrelative_depth
Deep ocean swell with long period waves in open water. tasman-sea-offshore. Required outputs: wavelength_m, wave_celerity_m_per_s, group_velocity_m_per_s, wave_steepness, relative_depth