Tides, Waves & Currents Notes

Last reviewed 30 Sept 2026 · 7 min read

Tides

Tides are the periodic rise and fall of the sea level caused mainly by the gravitational attraction of the moon and the sun on the ocean water, together with the rotation of the earth.

The moon, being much closer, has about 2.2 times the tide-producing effect of the sun.
Spring tides occur at new moon and full moon, when the sun, moon and earth are in line and the two effects add: the highest high tides and lowest low tides (largest range).
Neap tides occur at the first and last quarters, when the sun and moon act at right angles: the smallest range.
The tidal period is about 12 hours 25 minutes for a semi-diurnal tide (a lunar day of 24 h 50 min).

Types of tide

Type	Description
Semi-diurnal	Two high and two low tides of nearly equal height each lunar day (typical of the Atlantic; also the east coast of India in part)
Diurnal	One high and one low tide a day (some places in the Gulf of Mexico, parts of the south-east Asia)
Mixed	Two high and two low tides of unequal height (the Pacific coasts; Mumbai)

Tidal levels and datum

Term	Meaning
HAT / LAT	Highest / lowest astronomical tide
MHWS / MLWS	Mean high / low water springs
MHWN / MLWN	Mean high / low water neaps
MSL	Mean sea level
Tidal range	Difference between successive high and low water; spring range = MHWS − MLWS
Chart datum (CD)	The reference level for soundings on nautical charts and for depths in ports, usually near the lowest astronomical tide (in India, the level of the lowest low water at spring tides)

Tidal predictions are published as tide tables (Indian Tide Tables); the depth of water at any moment = charted depth + height of tide.

Waves

Sea waves are generated mainly by the wind blowing over the water. Their size depends on wind speed, duration and fetch (the distance over which the wind blows). Terms:

Wave height ( $H$ ) — vertical distance from trough to crest; wave length ( $L$ ) — horizontal distance between successive crests; period ( $T$ ) — time between successive crests; frequency $f = 1/ T$ .
Amplitude $a = H /2$ ; celerity (speed) $C = L / T$ ; steepness $H / L$ ; wave number $k = 2 π / L$ .
Significant wave height ( $H_{s}$ ) — the average of the highest one-third of the waves in a record (about $H_{1/3}$ ); it is close to the height an observer would estimate visually. Related: $H_{ma x} \approx 1.8 H_{s}$ in a storm of a few hundred waves (design wave for structures is usually chosen for a return period, 50–100 years).

Linear (Airy) wave theory

For a wave in water of depth $d$ :

L = \frac{g T ^{2}}{2 π} tanh (\frac{2 π d}{L}), C = \frac{L}{T} = \frac{g T}{2 π} tanh (\frac{2 π d}{L})

Region	Depth ratio $d / L$	Approximate formulae
Deep water	$> 0.5$	$L_{0} = \frac{g T ^{2}}{2 π} = 1.56 T^{2}$ (m); $C_{0} = 1.56 T$ (m/s)
Transitional	0.05 to 0.5	Full formula (iterate)
Shallow water	$< 0.05$	$C = g d$

In deep water the wave is not affected by the sea bed; in shallow water the speed depends only on the depth.

Energy and power

The energy per unit crest width per unit surface area (per metre of crest length per unit area) is

E = \frac{1}{8} ρ g H^{2} (J/m^{2})

The wave power (energy flux) per metre of crest is $P = E C_{g}$ , where the group velocity $C_{g} = n C$ with $n = \frac{1}{2}$ in deep water and $n = 1$ in shallow water; in deep water $P \approx \frac{ρ g ^{2}}{32 π} H^{2} T$ .

Worked ExampleExample — deep-water wave

A wave of period $T$ = 8 s in deep water:

$L_{0} = 1.56 \times 8^{2} = 99.8 m$ ; $C_{0} = 1.56 \times 8 = 12.5 m/s$ (about 45 km/h).

For $H$ = 2 m and seawater $ρ$ = 1025 kg/m³: $E = \frac{1}{8} \times 1025 \times 9.81 \times 2^{2} = 5, 028 J/m^{2}$ ; $C_{g} = 6.24$ m/s; power per metre crest ≈ 31.4 kW/m.

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