Ocean Waves

Rules of Thumb
(Meteorological-N Hemisphere)

• Looking at the wind, the low is on your right (Buys Ballot’s Law).
• If the wind direction doesn’t change as the pressure drops, the storm is coming straight at you.
• If the wind veers (CW variation) the storm is passing west of you.
• If the wind backs (CCW variation) the storm is passing east of you.

    Facts about Water

• One cubic meter weighs one metric ton.
• Because of its low compressibility, water acts like a solid when it strikes a solid surface at high speed. 

Rules of Thumb(Ocean Waves)

The governing equation, the dispersion relation for gravity waves, is ω 2 = gκ tanhκD where ω = 2πf is the radian frequency, the period T (units of seconds) is 1/f, κ = 2π / L is the wavenumber, L is the wavelength (units of meters), and D is the water depth. For deep-water waves the tanh is 1, so ω 2 = gκ .

From this we derive C =ω /κ = g /ω where C is the wave phase speed or travel speed of the disturbance (the group speed – the speed the wave energy travels at – is C/2). So C = gT/2π and L = gT2/2π as below.For resonant wave growth, a storm carries along the waves it generates at their group speed. Waves with periods of about 10 seconds are common at sea; their wavelength is 156 m and they travel at 15.6 meters/sec (or 31 knots) with a group speed of 15.5 knots.

The longest wind waves we see in the North Atlantic have periods of about 20 sec, leading to wavelengths of 624 m and phase speeds of 32 m/sec.

• Wave speed (and speed of generating wind) in knots is about 3 (actually g/Pi) times their period (time between crests) in seconds.
• Wave length (crest to crest) in meters is about 1.6 (actually g/2Pi) times the square of their period in sec.
• Yes, every seventh wave is higher:- waves travel in groups. 

Facts (Ocean Waves)

• As a wave passes, the water moves in a vertical circle, with surface speeds of about a tenth of the travel speed.
• When a wave breaks, the water surface speed at its crest approaches its travel speed.
• Waves begin to “feel the bottom”, slow down and get higher and steeper when the depth is less than one-quarter of their length.
• As waves approach a beach, their period doesn’t change (height, speed and wavelength do). 

Facts (Winds and Waves)

• In storms, the air-sea boundary becomes indistinct: spray fills the air, bubbles fill the water.
• Wave steepness (height/wavelength) is limited by breaking, so the highest waves have the longest wavelengths (and periods) and the highest speeds.
• The fastest-moving and “tightest” lows produce the highest waves.
• E Coast storms generate the longest, highest waves in their SE quadrant – there, the waves move with the storm as they grow with the local winds. 

Facts (Ocean Waves)

• Waves of all wavelengths and traveling in all directions are generated by a storm. As they leave the storm area they disperse, the longest wavelengths traveling the fastest
• A “rogue wave” is an unexpected one – often the result of the superposition of two wave trains traveling in different directions
• All numerical models fail to predict the very highest waves in intense storms