Key Formulas & Equations
Simplified: ρ ≈ 1025 kg/m³ (average surface)
Salinity: S = 1.80655 × Cl (chlorinity in ‰)
Pressure at Depth: P = Patm + ρgh
Speed of Sound: c = 1449.2 + 4.6T - 0.055T² + 0.00029T³ + (1.34 - 0.01T)(S - 35) + 0.016z
Snell's Law: sin(θ₁)/c₁ = sin(θ₂)/c₂
SOFAR Channel: Sound channel at ~1000 m depth
Ekman Transport: VE = τ/(ρf)
Ekman Layer Depth: DE = π√(2Km/f)
Geostrophic Current: v = (1/ρf) × (∂P/∂x)
Equilibrium Tide: h = (3/2) × (M/m) × (R⁴/d³) × (cos²θ - 1/3)
Wave Speed (Deep Water): c = √(gλ/2π)
Wave Speed (Shallow Water): c = √(gh)
Alkalinity: ALK = [HCO₃⁻] + 2[CO₃²⁻] + [B(OH)₄⁻] + [OH⁻] - [H⁺]
pH: pH = -log[H⁺] (surface ocean: ~8.1)
Omega (Ω): Ω = [Ca²⁺][CO₃²⁻]/Ksp
Core Concepts
Ocean Currents
Large-scale movements of ocean water. Surface currents driven by wind; deep currents by density differences (thermohaline circulation).
Plate Tectonics
Theory explaining the movement of Earth's lithospheric plates. Creates mid-ocean ridges, trenches, and drives the rock cycle.
Marine Ecosystems
Diverse habitats from coral reefs to deep-sea vents. Include intertidal zones, pelagic zone, and benthic zone.
Coastal Processes
Wave action, tides, and currents shaping coastlines. Includes erosion, sediment transport, and beach formation.
El Niño and La Niña
Climate patterns in the Pacific Ocean affecting global weather. El Niño: warm phase; La Niña: cool phase.
Ocean Acidification
Decrease in ocean pH due to CO₂ absorption. Affects marine organisms with calcium carbonate shells and skeletons.
Deep-Sea Exploration
Study of the ocean floor and deep-water ecosystems. Uses submersibles, ROVs, and sonar mapping.
Tsunamis
Large ocean waves caused by underwater earthquakes, volcanic eruptions, or landslides. Travel at high speed in deep water.
Worked Examples
Example 1: Pressure at Depth
Problem: Calculate pressure at 1000 m depth (ρ = 1025 kg/m³, Patm = 101,325 Pa).
Solution:
P = 101,325 + 1025 × 9.81 × 1000 = 101,325 + 10,055,250 = 10,156,575 Pa ≈ 100 atm
Example 2: Wave Speed
Problem: Calculate deep-water wave speed for wavelength 100 m.
Solution:
c = √(gλ/2π) = √(9.81 × 100/6.28) = √156.2 = 12.5 m/s
Example 3: Shallow Water Wave Speed
Problem: Calculate wave speed in 5 m deep water.
Solution:
c = √(gh) = √(9.81 × 5) = 7.0 m/s
Practice Problems
Problem 1
Calculate pressure at 500 m depth.
Answer: P = 101,325 + 1025 × 9.81 × 500 = 5,127,575 Pa ≈ 50 atm
Problem 2
Calculate wave speed for wavelength 50 m in deep water.
Answer: c = √(9.81 × 50/6.28) = 8.8 m/s
Problem 3
Calculate Coriolis parameter at 30°N.
Answer: f = 2 × 7.292×10⁻⁵ × sin(30°) = 7.29×10⁻⁵ s⁻¹
Problem 4
Identify the pH of surface ocean water.
Answer: ~8.1
Problem 5
Calculate shallow water wave speed in 10 m depth.
Answer: c = √(9.81 × 10) = 9.9 m/s
Problem 6
Calculate Ekman transport if wind stress = 0.1 N/m² and f = 10⁻⁴ s⁻¹.
Answer: VE = 0.1/(1025 × 10⁻⁴) = 0.976 m²/s
Problem 7
Identify the depth of the SOFAR channel.
Answer: ~1000 m