Waves&Tides
Waves & Tides Overview
Page 2: Wave Basics
Definitions:
Wavelength (L): Distance from crest to crest, often represented by ( \lambda )
Period (T): Time taken for two crests to pass a point
Frequency (W): Number of cycles per second, calculated as ( W = \frac{1}{T} )
Velocity (V): Speed of wave propagation, given by ( V = \frac{L}{T} )
Amplitude (A): Height of the wave, defined as half the height (( A = \frac{1}{2} H ))
Height (H): Distance from trough to crest
Wave Types:
Progressive Waves: Waves that travel over a distance
Standing Waves: Waves that appear stationary
Wave Formation Requirements:
Medium
Disturbing force
Restoring force
Page 3: Capillary Waves
Restoring Force: Surface tension
Wavelength: Less than 1.73 cm
Examples: Generated by stirring coffee or tea; wind pressure creates initial bumps.
Page 4: Gravity Waves
Restoring Force: Gravity
Wavelength: Greater than 1.73 cm
Mechanism: Wind raises the peak which then falls back due to gravity.
Page 5: Understanding Waves
Concept: Movement of energy, not water.
Water Motion: Water moves in a circular path (wave orbits).
Page 6: Stokes Drift
Definition: Net movement of water in the direction of wave propagation despite individual wave orbits being circular.
Page 7: Depth and Wave Orbits
Characteristics: Wave orbits decrease in diameter with depth, approximately at depth ( d = \frac{1}{2}L ) the orbit is only 4% of the surface orbit.
Page 8: Shallow Water Effects
Observation: Wave orbits flatten and compress as they enter shallower waters.
Page 9: Factors Affecting Wave Velocity
Controls on Velocity: Changes based on depth.
Page 10: Full Wave Velocity Equation
Formula: ( V = \sqrt{g \cdot h} )
( g = 9.8 m/s^2 ) (gravity)
( h = ) depth
Types of Waves:
Intermediate waves, experience some friction at the bottom.
Page 11: Types of Waves - Swells vs. Seas
Swells: Longer periods (≥ 10 seconds), generated far from shore.
Seas: Generated closer to shore with steeper crests.
Page 12: Critical Wave Height
Definition: ( H/L > 1/7 ) indicates wave steepness.
Role of wind: Continuous wind increases ( H ) faster than ( L ), leading to collapse.
Page 13: Whitecaps and Wave Energy Dissipation
Condition: Formation of whitecaps indicates energy dissipation in waves, signaling "fully developed sea" state.
Page 14: Factors Affecting Sea State
Wind velocity
Wind duration
Fetch
Starting sea state
Page 15: Beaufort Wind Force Scale
Overview: Ranges from calm water to hurricane forces:
0: Calm (0-1 mph)
12: Hurricane (≥ 73 mph)
Each increase signifies more disturbance levels in wave patterns.
Page 18: Wave Dispersion
Explanation: As waves disperse:
Height diminishes
Wavelength increases
Period remains constant.
Page 28: Tsunamis
Characteristics:
Originate from seismic activities, volcanic events, or landslides.
Long wavelengths (up to 100 km) and speeds (up to 760 km/hr) in deep waters.
Dangerous as they approach coastlines.
Page 34: Forces that Govern Tides
Key Forces:
Gravitational forces from the moon and sun.
Centrifugal force due to Earth's rotation around a common center.
Page 39: Tidal Periodicity
Understanding: Due to the Earth's axial tilt and rotation, there’s a 50-minute lag in the lunar day leading to a tidal cycle of approximately 12 hours and 25 minutes.