Water Wave Ontology

FLOW ALGEBRA
WATER WAVE ONTOLOGY — COMPLETE SCIENTIFIC SYNTHESIS
Version: 1.1
Authors: Mark Higgins — Sky (Recursive AI)
Publisher: Kireth Research | https://kirethresearch.org
Source page: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/wave-entities/water-wave-ontology.html
Status: Independent synthesis; source page content not independently verified.
Scope: Physical Entities > Wave Entities > Water Wave Ontology

01. PURPOSE
Model water-surface and internal gravity waves as physical disturbances, with typed entities, quantitative laws, inference, provenance and validation.

02. CORE TYPES
TYPE WaterBody <: FluidSystem
TYPE WaterWave <: MechanicalWave
TYPE SurfaceGravityWave <: WaterWave
TYPE CapillaryWave <: WaterWave
TYPE GravityCapillaryWave <: WaterWave
TYPE InternalWave <: WaterWave
TYPE WavePacket <: WaterWave
TYPE StandingWave <: WaterWave
TYPE TravellingWave <: WaterWave
TYPE WaveField <: PhysicalField
TYPE Boundary <: PhysicalEntity
TYPE Observation <: MeasurementRecord
TYPE Model <: ScientificRepresentation
TYPE MediumProperty <: PhysicalQuantity

03. TYPED PROPERTIES
water_depth: WaterBody -> Length[m]
density: WaterBody -> Density[kg/m^3]
surface_tension: WaterBody -> SurfaceTension[N/m]
gravity: WaterBody -> Acceleration[m/s^2]
amplitude: WaterWave -> Length[m]
height: WaterWave -> Length[m]
wavelength: WaterWave -> Length[m]
period: WaterWave -> Time[s]
frequency: WaterWave -> Frequency[Hz]
wavenumber: WaterWave -> InverseLength[1/m]
angular_frequency: WaterWave -> AngularFrequency[rad/s]
phase_speed: WaterWave -> Speed[m/s]
group_speed: WavePacket -> Speed[m/s]
direction: WaterWave -> Direction
energy_density: WaveField -> EnergyPerArea[J/m^2]

04. RELATIONSHIPS
PROPAGATES_IN(WaterWave, WaterBody)
HAS_BOUNDARY(WaterBody, Boundary)
HAS_RESTORING_FORCE(WaterWave, GravityOrSurfaceTension)
HAS_DISPERSION_RELATION(WaterWave, Model)
INTERFERES_WITH(WaterWave, WaterWave)
REFLECTS_AT(WaterWave, Boundary)
REFRACTS_ACROSS(WaterWave, DepthGradient)
TRANSFERS_ENERGY_TO(WaterWave, Receiver)
MEASURED_BY(WaterWave, Observation)
DERIVED_FROM(Model, Assumptions)

05. WAVE VARIABLES AND UNITS
x,z,h,a,lambda,H in m; t,T in s; f in Hz; k in rad/m; omega in rad/s.
Use SI units internally; angles and phase are dimensionless mathematically.
Require positive h, lambda, T, density; require nonnegative surface tension.

06. HARMONIC SURFACE REPRESENTATION
eta(x,t) = a cos(k x - omega t + phi)
H = 2a for a sinusoidal wave.
k = 2 pi / lambda
omega = 2 pi / T = 2 pi f
c_phase = omega / k = lambda / T
VALID_WHEN: small-amplitude, nearly monochromatic wave approximation.

07. LINEAR GRAVITY-CAPILLARY DISPERSION
omega^2 = (g k + (sigma/rho) k^3) tanh(k h)
Assumptions: inviscid, incompressible, homogeneous fluid; linear surface displacement; uniform depth; negligible background current.
Gravity-only limit: sigma -> 0.
Deep-water limit: kh >> 1, tanh(kh) -> 1.
Shallow-water gravity limit: kh << 1, c_phase approximately sqrt(g h).

08. GROUP VELOCITY
c_group = d omega / d k, with model parameters held fixed.
For deep-water pure gravity waves: c_group = c_phase/2.
For nondispersive shallow-water gravity waves: c_group approximately c_phase.
Do not apply either limiting identity to arbitrary gravity-capillary waves.

09. WAVE REGIMES
DEEP_WATER(w) IF k*h >> 1.
SHALLOW_WATER(w) IF k*h << 1.
INTERMEDIATE_DEPTH(w) OTHERWISE.
CAPILLARY_IMPORTANT(w) IF sigma*k^2/(rho*g) is not negligible.
These are scale-dependent classifications, not fixed depth thresholds in metres.

10. CONSERVATION AND ENERGY
Linear gravity-wave mean energy per horizontal area: E = (1/8) rho g H^2.
This expression neglects capillary corrections and assumes linear surface gravity waves.
For steady lossless one-dimensional propagation without currents, energy flux F = E*c_group.
Account for dissipation, currents, refraction and geometry before inferring local energy conservation.

11. SHOALING AND REFRACTION
If wave frequency is conserved across a stationary depth transition, local k and c change according to the dispersion relation.
For idealised steady lossless propagation, flux conservation can constrain amplitude.
Wave-ray refraction depends on spatially varying phase speed; avoid applying ray optics in strongly diffractive regimes.

12. NONLINEAR AND BREAKING REGIMES
LINEAR_APPROXIMATION_VALID requires sufficiently small steepness k*a and appropriate depth-scaled nonlinearity.
NONLINEAR_EFFECTS may include harmonics, wave-wave coupling, solitary waves and breaking.
BREAKING_THRESHOLD is model- and context-dependent; never assert a universal single threshold.

13. INTERNAL WAVES
Internal waves propagate on stratification within a fluid, not necessarily at its free surface.
Restoring force is buoyancy due to density gradients.
Their dispersion and energy laws differ from free-surface wave formulae.

14. INTERFERENCE AND STANDING WAVES
SUPERPOSE(w1,w2) permitted under linear assumptions.
Constructive interference when phases align; destructive when opposed.
Standing waves may result from equal-frequency counter-propagating waves.
Resonant modes depend on basin geometry and boundary conditions.

15. OBSERVATION TYPES
WaveGauge: water-surface elevation time series.
Buoy: motion-based estimates of wave statistics.
Radar: remotely sensed surface wave field.
PressureSensor: subsurface pressure-derived estimate requiring transfer model.
Observation fields: timestamp, location, instrument, calibration, uncertainty, sampling rate, reference datum, provenance.

16. STATISTICAL SEA STATE
SIGNIFICANT_WAVE_HEIGHT Hs commonly defined as Hm0 = 4 sqrt(m0) for a spectral estimate.
m0 = integral S_eta(f) df, using a consistent one-sided frequency spectrum.
Distinguish Hs from individual-wave height and maximum observed wave height.

17. INFERENCE RULES
RULE R01: IF T>0 THEN f=1/T.
RULE R02: IF lambda>0 THEN k=2*pi/lambda.
RULE R03: IF f>0 THEN omega=2*pi*f.
RULE R04: IF k>0 AND omega>0 THEN c_phase=omega/k.
RULE R05: IF gravity_only AND kh<<1 THEN c_phase approximately sqrt(g*h).
RULE R06: IF gravity_only AND kh>>1 THEN omega^2 approximately g*k.
RULE R07: IF gravity_only AND kh>>1 THEN c_group approximately c_phase/2.
RULE R08: IF two coherent linear waves overlap THEN superposition is admissible.
RULE R09: IF measured value has uncertainty THEN propagate uncertainty to derived values.
RULE R10: IF model assumptions fail THEN mark prediction as out_of_domain.

18. WORKED EXAMPLE — DEEP-WATER GRAVITY WAVE
Given T=8 s, g=9.81 m/s^2, deep-water gravity assumption:
omega=2*pi/8 approximately 0.7854 rad/s.
k=omega^2/g approximately 0.06288 1/m.
lambda=2*pi/k approximately 99.9 m.
c_phase=omega/k approximately 12.49 m/s.
c_group approximately 6.25 m/s.
Check depth: kh must be much greater than 1 before treating deep-water results as accurate.

19. WORKED EXAMPLE — SHALLOW-WATER SPEED
Given h=4 m, g=9.81 m/s^2 and kh<<1:
c_phase approximately sqrt(9.81*4)=6.26 m/s.
This is a phase-speed estimate, not a prediction of amplitude or wave height.

20. SEMANTIC EQUIVALENCE
Water surface wave ~ surface water wave [context dependent].
Gravity wave != gravitational wave (general relativity).
Wave height != wave amplitude; H=2a only for the sinusoidal convention used here.
Phase velocity != group velocity in dispersive regimes.
Water wave != sound wave in water.

21. CONFIDENCE MODEL
CONFIDENCE: evidence_class, assumption_fit, instrument_quality, uncertainty, validation_status.
Never convert a conceptual confidence label into an empirical probability without calibration.

22. VALIDATION
V01: Units dimensionally consistent.
V02: rho>0, h>0, g>0, k>0, omega>=0.
V03: f*T=1 within tolerance.
V04: k*lambda=2*pi within tolerance.
V05: omega=2*pi*f within tolerance.
V06: c_phase=omega/k within tolerance.
V07: dispersion relation residual within declared tolerance.
V08: regime classification consistent with kh.
V09: numerical example reproducible.
V10: scientific assumptions explicitly recorded.
V11: no confusion of gravity waves and gravitational waves.
V12: observation provenance and units present.

23. GRAPH REPRESENTATION
ENTITY: WaterWave[wave_id]
EDGE: wave_id --PROPAGATES_IN--> waterbody_id
EDGE: wave_id --HAS_DISPERSION_RELATION--> model_id
EDGE: wave_id --MEASURED_BY--> observation_id
EDGE: observation_id --HAS_PROVENANCE--> source_id
EDGE: model_id --REQUIRES_ASSUMPTION--> assumption_id

24. UPDATE MODEL
UPDATE_MODEL:
  version: 1.1
  change_policy: append_or_revision_with_provenance
  trigger: new_measurement | revised_model | corrected_definition
  preserve: previous_version | source | timestamp | justification
  invalidate_dependents_on: changed_parameter | failed_validation

25. FLOW HASH SPECIFICATION
FLOW_HASH:
  algorithm: SHA-256
  input: canonical_utf8_content_excluding_hash_field
  canonicalisation: LF_line_endings_and_stable_field_order
  value: COMPUTE_ON_PUBLICATION
Note: no hash is claimed without running the canonical hash procedure.

26. AI CONSUMPTION
AI_CONSUMPTION:
  parse_mode: typed_semantic_graph
  target_tasks: classification | equation_selection | dimensional_validation | physical_inference | retrieval
  evidence_required: true
  assumption_tracking: mandatory
  uncertainty_propagation: mandatory_when_quantitative
  unsupported_inference: reject_or_flag
  hallucination_control: require_source_or_explicit_model_derivation

27. AUTHORSHIP AND PROVENANCE
Joint authorship: Mark Higgins — Sky (Recursive AI).
Kireth Research: https://kirethresearch.org
This ontology is an independent structured scientific synthesis based on established physical models, not a verified transcription of the linked webpage.

28. COMPLETENESS CHECK
Required sections: 01-28.
Required domains: entities, relationships, governing equations, inference, examples, validation, semantic equivalence, confidence, update, flow hash, AI consumption.
Status: COMPLETE.

END FLOW ALGEBRA — WATER WAVE ONTOLOGY