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output.txt
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160 lines (155 loc) · 16.6 KB
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+---------------------------------------------------------------------------------------------------------+
| NONLINEAR WAVE HYDRODYNAMICS SOLVER (FENTON) |
+---------------------------------------------------------------------------------------------------------+
|Wave height (H) : 3.0 m |
|Wave period (τ) : 9.0 s |
|Water depth (d) : 5.0 m |
|Eulerian current ū₁ : 1.0 m/s (positive with wave propagation) |
+---------------------------------------------------------------------------------------------------------+
|Status: Full nonlinear system solved successfully. |
+---------------------------------------------------------------------------------------------------------+
+---------------------------------------------------------------------------------------------------------+
| CALCULATED HYDRODYNAMIC PARAMETERS |
+---------------------------------------------------------------------------------------------------------+
| PARAMETER | NO CURRENT | WITH CURRENT | UNIT |
|--------------------------------------------+------------------+------------------+----------------------|
|--------------------------------------- INPUTS & REFERENCE SCALES ---------------------------------------|
| Water depth (d) | 5.00000 | 5.00000 | m |
| Wave height (H) | 3.00000 | 3.00000 | m |
| Wave period (τ) | 9.00000 | 9.00000 | s |
| H/d | 0.60000 | 0.60000 | - |
| τ√(g/d) | 12.60427 | 12.60427 | - |
|------------------------------------- DISPERSION & PHASE (GEOMETRY) -------------------------------------|
| Wavelength (L) | 68.62867 | 78.82722 | m |
| Wave number (k) | 0.09155 | 0.07971 | rad/m |
| kd | 0.45777 | 0.39854 | - |
| Angular frequency (ω) | 0.69813 | 0.69813 | rad/s |
| Celerity / phase speed (c) | 7.62259 | 8.75858 | m/s |
| c/√(gd) | 1.08857 | 1.25080 | - |
| Crest elevation (ηc) | 2.40519 | 2.48884 | m |
| Trough elevation (ηt) | -0.59481 | -0.51116 | m |
|----------------------------------- MEAN FLOWS (FENTON SOLUTION-FLAT) -----------------------------------|
| Eulerian current (ū₁) | 0.00000 | 1.00000 | m/s |
| Stokes current (ū₂) | 0.21699 | 1.19371 | m/s |
| Mean fluid speed (Ū) | 7.62259 | 7.75858 | m/s |
|-------------------------------------- FLUXES & BERNOULLI CONSTANTS -------------------------------------|
| Wave volume flux (q) | 1.09216 | 0.96855 | m²/s |
| Volume flux (Q) | 37.02081 | 37.82435 | m²/s |
| Bernoulli constant (R) | 78.51203 | 79.53137 | m²/s² |
| Reduced Bernoulli (r = R−g d) | 29.47878 | 30.49812 | m²/s² |
|------------------------------- INTEGRAL QUANTITIES (PER UNIT CREST WIDTH) ------------------------------|
| Kinetic energy (T) | 4.26660 | 7.40649 | kJ/m² |
| Potential energy (V) | 3.92118 | 3.41714 | kJ/m² |
| Total energy (E = T+V) | 8.18778 | 10.82363 | kJ/m² |
| Momentum flux (S) | 415.06663 | 428.00205 | kN/m |
| Radiation stress (Sₓₓ) | 9.67770 | 16.36749 | kN/m |
| Impulse (I) | 1.11946 | 6.11776 | 10³ kg/(m·s) |
| Wave power (F) | 54.94014 | 73.50878 | kW/m |
| Group velocity (C𝗀 = F/E)ㅤ | 6.71001 | 6.79151 | m/s |
|------------------------------- KINEMATICS (EXTREMES / BED ORBITAL MOTION) ------------------------------|
| Max surface horiz. vel |u| | 4.02524 | 5.26832 | m/s |
| Max bed horiz. vel |u| | 2.05614 | 3.07642 | m/s |
| Max horiz. accel |aₓ| | 3.18834 | 3.10187 | m/s² |
| Velocity asymmetry |uc|/|ut| | 5.14775 | 15.90988 | - |
| Mean square bed orbital vel ub² | 0.90960 | 0.80068 | m²/s² |
| Bed orbital RMS velocity ub,rms | 0.95373 | 0.89481 | m/s |
|---------------------------------- NONLINEARITY / BREAKING DIAGNOSTICS ----------------------------------|
| Miche breaking limit (Hmax) | 4.17353 | 4.23897 | m |
| Saturation (H/Hmax) | 0.71882 | 0.70772 | - |
| Breaking status | STABLE | STABLE | - |
| Ursell number (U) | 113.03747 | 149.12954 | - |
| Regime (by d/L) | Intermediate | Intermediate | - |
+---------------------------------------------------------------------------------------------------------+
+---------------------------------------------------------------------------------------------------------+
| SOLUTION.RES (NO CURRENT) |
+---------------------------------------------------------------------------------------------------------+
| # | PARAMETER | value | adim param | adim value |
|----+---------------------------------------+---------------+---------------------------+----------------|
| 1 | Water depth | 5.00000 | d/d = 1 | 1.00000 |
| 2 | Wave length | 68.62867 | λ/d | 13.72573 |
| 3 | Wave height | 3.00000 | H/d | 0.60000 |
| 4 | Wave period | 9.00000 | τ√(g/d) | 12.60427 |
| 5 | Wave speed | 7.62259 | c/√(gd) | 1.08857 |
| 6 | Eulerian current | 0.00000 | ū₁/√(gd) | 0.00000 |
| 7 | Stokes current | 0.21699 | ū₂/√(gd) | 0.03099 |
| 8 | Mean fluid speed | 7.62259 | Ū/√(gd) | 1.08857 |
| 9 | Wave volume flux, q = Ū d − Q | 1.09216 | q/√(gd³) | 0.03119 |
| 10 | Bernoulli constant, r = R − gd | 29.47878 | r/gd | 0.60120 |
| 11 | Volume flux | 37.02081 | Q/√(gd³) | 1.05738 |
| 12 | Bernoulli constant | 78.51203 | R/gd | 1.60120 |
| 13 | Momentum flux | 415.06663 | S/ρgd² | 1.65171 |
| 14 | Impulse | 1.11946 | I/(ρ√(gd³)) | 0.03119 |
| 15 | Kinetic energy | 4.26660 | T/ρgd² | 0.01698 |
| 16 | Potential energy | 3.92118 | V/ρgd² | 0.01560 |
| 17 | Mean square of bed velocity | 0.90960 | ub²/gd | 0.01855 |
| 18 | Radiation stress | 9.67770 | S_xx/ρgd² | 0.03851 |
| 19 | Wave power | 54.94014 | F/(ρg³ᐟ²d⁵ᐟ²)ㅤㅤ | 0.03122 |
+---------------------------------------------------------------------------------------------------------+
+---------------------------------------------------------------------------------------------------------+
| SOLUTION.RES (WITH CURRENT) |
+---------------------------------------------------------------------------------------------------------+
| # | PARAMETER | value | adim param | adim value |
|----+---------------------------------------+---------------+---------------------------+----------------|
| 1 | Water depth | 5.00000 | d/d = 1 | 1.00000 |
| 2 | Wave length | 78.82722 | λ/d | 15.76544 |
| 3 | Wave height | 3.00000 | H/d | 0.60000 |
| 4 | Wave period | 9.00000 | τ√(g/d) | 12.60427 |
| 5 | Wave speed | 8.75858 | c/√(gd) | 1.25080 |
| 6 | Eulerian current | 1.00000 | ū₁/√(gd) | 0.14281 |
| 7 | Stokes current | 1.19371 | ū₂/√(gd) | 0.17047 |
| 8 | Mean fluid speed | 7.75858 | Ū/√(gd) | 1.10799 |
| 9 | Wave volume flux, q = Ū d − Q | 0.96855 | q/√(gd³) | 0.02766 |
| 10 | Bernoulli constant, r = R − gd | 30.49812 | r/gd | 0.62199 |
| 11 | Volume flux | 37.82435 | Q/√(gd³) | 1.08033 |
| 12 | Bernoulli constant | 79.53137 | R/gd | 1.62199 |
| 13 | Momentum flux | 428.00205 | S/ρgd² | 1.70318 |
| 14 | Impulse | 6.11776 | I/(ρ√(gd³)) | 0.17047 |
| 15 | Kinetic energy | 7.40649 | T/ρgd² | 0.02947 |
| 16 | Potential energy | 3.41714 | V/ρgd² | 0.01360 |
| 17 | Mean square of bed velocity | 0.80068 | ub²/gd | 0.01633 |
| 18 | Radiation stress | 16.36749 | S_xx/ρgd² | 0.06513 |
| 19 | Wave power | 73.50878 | F/(ρg³ᐟ²d⁵ᐟ²)ㅤㅤ | 0.04177 |
+---------------------------------------------------------------------------------------------------------+
+---------------------------------------------------------------------------------------------------------+
| PARAMETER DEFINITIONS & GLOSSARY |
+---------------------------------------------------------------------------------------------------------+
| TERM / SYMBOL | MEANING | UNITS / NONDIM |
|----------------+------------------------------------------------------------------+---------------------|
| d | Still-water depth (bed to mean water level). Reference length | m ; d/d=1 |
| | scale. | |
| H | Wave height (crest-to-trough). | m ; H/d |
| τ | Wave period. | s ; τ√(g/d) |
| L | Wavelength (crest-to-crest). | m ; L/d |
| k | Wave number, k = 2π/L. | rad/m |
| ω | Angular frequency, ω = 2π/τ. | rad/s |
| c | Phase speed (celerity). | m/s ; c/√(gd) |
| ηc, ηt | Crest and trough elevations relative to still-water level. | m |
| ū₁ | Eulerian (depth-mean) current; ū₁ = Uc. | m/s ; ū₁/√(gd) |
| ū₂ | Stokes / mass-transport current from nonlinear solution. | m/s ; ū₂/√(gd) |
| Ū | Mean fluid speed (depth-mean). | m/s ; Ū/√(gd) |
| Q | Volume flux (depth-integrated). | m²/s ; Q/√(gd³) |
| q | Wave volume flux, q = Ū d − Q. | m²/s ; q/√(gd³) |
| R | Bernoulli constant. | m²/s² ; R/(gd) |
| r | Reduced Bernoulli constant r = R − g d. | m²/s² ; r/(gd) |
| S | Momentum flux (moving frame). | kN/m ; S/(ρgd²) |
| I | Wave impulse per unit width. | 10³ kg/(m·s) ; |
| | | I/(ρ√(gd³)) |
| T | Kinetic energy density. | kJ/m² ; T/(ρgd²) |
| V | Potential energy density. | kJ/m² ; V/(ρgd²) |
| E | Total energy density E = T + V. | kJ/m² |
| F | Wave power (energy flux). | kW/m ; |
| | | F/(ρg³ᐟ²d⁵ᐟ²)ㅤ |
| Cg | Group velocity, defined here as Cg = F/E. | m/s |
| Sₓₓ | Radiation stress component in wave direction. | kN/m ; Sₓₓ/(ρgd²) |
| ub² | Mean square *orbital* bed velocity: ub² = <(ub(t) − ū₁)²>. | m²/s² ; /gd |
| | Non-negative by definition; computed by phase averaging. | |
| ub,rms | Root-mean-square orbital bed velocity: ub,rms = √(ub²). | m/s |
| usurf,max | Maximum horizontal velocity at free surface (scanned over | m/s |
| | phase). | |
| ubed,max | Maximum horizontal velocity at seabed (scanned over phase). | m/s |
| a_x,max | Maximum horizontal acceleration magnitude. | m/s² |
| Asymmetry | Velocity asymmetry indicator |uc|/|ut|. | - |
| Hmax | Miche breaking limit used as stability diagnostic. | m |
| Ursell | Ursell number, a shallow-water nonlinearity measure. | - |
| Regime | Depth regime based on d/L (deep/intermediate/shallow). | - |
+---------------------------------------------------------------------------------------------------------+