Waves in Atmospheric and Oceanic Systems



The atmosphere and oceans are two earth systems that are intricately linked with each other and are responsible for the earth’s weather and climate. Together, the two host the earth’s hydrologic cycle since they are large reservoirs of water (according to a USGS estimate, the atmosphere holds 13 trillion tons of water).  The oceans help to regulate temperature in the lower part of the atmosphere, while the atmosphere in turn is largely responsible for the circulation of ocean water through waves and currents. The atmosphere and oceans are replete with wave-like motion. Although some of these (sound waves) are abundantly clear to our ears, other, more powerful ones propagating through the atmosphere and oceans are silent and invisible. These waves are big, having wavelengths ranging from meters and kilometers (gravity waves) to thousands of kilometers (planetary waves). Atmospheric and oceanic waves don’t transport air or water across long distances. Rather, they push air and water molecules together and then apart. This results in little net movement but a lot of transfer of energy. This energy transport plays an important role in global weather, because gravity waves and planetary waves are able to push energy to regions of the atmosphere that don't receive a lot of solar or thermal energy. Both gravity and planetary waves are critically important on Earth and other planets. Their effects on the climate system and energy budget of a planet are both tremendous and varied: Europe's temperate climate (compared to the USA’s East Coast), the replenishment of the ozone hole, and the hexagon at Saturn’s pole are all caused by atmospheric waves.

Waves in the Oceans

In this section we shall review the different kinds of waves in the oceans and how they influence transfer of energy and ocean circulation. Ocean surface waves are the most common oceanographic phenomena that are known to the casual observer. The complex, random wave field of a storm-lashed sea can be studied and modeled using well-developed theoretical concepts. Many of these concepts relate to nonlinear processes which are not yet well understood. These include dynamical coupling between the atmosphere and the ocean, wave–wave interactions, and wave breaking.

Wave Generation by Winds:

Wind waves, or wind-generated waves in the ocean are surface waves that occur on the free surfaces of oceans in response to wind. Such waves can travel thousands of miles before reaching a shore. Wind generated waves range in size from small ripples, to waves over 30 m high. When directly generated and affected by local winds, a wind wave system is called a wind sea. After the wind ceases to blow, wind waves are called swells. A swell consists of wind-generated waves that are not significantly affected by the local wind at that time. They may have been generated elsewhere or at an earlier time when strong winds prevailed. Wind waves are random in the sense that waves generated in succession may vary in height, duration, and shape with limited or no predictability.

Ocean surface waves play an important role in air-sea interaction. Waves generated over the ocean surface are dissipated either by viscosity or breaking, giving up their momentum to currents. Thus, momentum from the wind is transferred to both ocean surface waves as well as currents. Surface waves affect upper-ocean mixing through both wave breaking and their role in the generation of Langmuir circulations. This breaking and mixing also influences the temperature of the ocean surface and thus the thermodynamics of air-sea interaction. Surface waves impose significant structural loads on ships and other structures.

The main attributes through which wind waves are reckoned are their amplitude, wavelength, period and direction. Factors that influence the generation and propagation of wind generated waves on the ocean surface are:

  1. Wind speed or strength relative to wave velocity – the wind must be moving faster than the wave crest for energy transfer.

  2. Stretch of the unobstructed surface over which the wind blows without significant change in direction (called the fetch).

  3. Length of the wave front measured perpendicular to the direction of propagation.

  4. Duration of wind that generated the wave, and

  5. Time for which the winds sustain.

Fig 1: Wind generated ocean waves associated with a strong gale.


Oceanic Rossby Waves:

Rossby waves are waves that naturally occur in rotating liquids. Within the oceans, these form as a result of the rotation of the earth. They are fundamentally different from the surface waves, in that they are slow moving, huge, undulating movements of the ocean that stretch horizontally across the planet for hundreds of kilometers in a westward direction. Rossby waves are also known as planetary waves. The motion of these waves is complex. The horizontal speed of a Rossby wave is dependent upon the latitude of the wave. In the Pacific for instance, waves at lower latitudes (closer to the equator) may take months to a year to cross the ocean. Waves at mid-latitudes may take 10-20 years to make the journey. The vertical motion of Rossby waves is small at the ocean’s surface and large along the deeper thermocline (the transition area between the ocean’s warm upper layer and colder depths). This variation in vertical motion of the water’s surface can be quite dramatic: the typical vertical movement of the water’s surface is generally four inches or less, while the vertical movement of the thermocline for the same wave is approximately 1000 times greater. In other words, for a four inch or less surface displacement along the ocean surface, there may be more than 300 feet of corresponding vertical movement in the thermocline far below the surface.

Due to the small vertical movement along the surface, oceanic Rossby waves are undetectable by the human eye. Scientists typically rely on satellite radar altimetry to detect the massive waves. They are so large and massive that they can change earth’s climatic conditions. Along with rising sea-levels, King Tides, and the effects of El Nino, oceanic Rossby waves contribute to high tides and coastal flooding in some regions of the world. They play a significant role in shaping the weather and climate.

Other Waves in the Oceans:

Tsunami Waves: Tsunami, or seismic sea waves are a series of waves caused by the displacement of a large volume of sea water. Unlike normal ocean waves, which are generated by wind, tsunami waves are generated by the displacement of water. The sea water may be displaced due to underwater earthquakes, volcanic eruptions, slumping of sediments piled on the continental shelves down the continental slope, meteorite impacts, and other underwater explosions (including detonations of underwater nuclear devices). Tsunami waves generally consist of a series of waves, with periods ranging from minutes to hours, arriving in a so-called “internal wave train”. They do not resemble normal sea waves, because their wavelength is far longer. They initially resemble a rapidly rising tide, for which reason they are often (wrongly) referred to as tidal waves.

While ordinary wind waves have a wavelength of about 100 m and a height of roughly 2 m, a tsunami has a much larger wavelength of up to 200 km above the deeper parts of the ocean, where it travels at a velocity of well over 800 km/hr. Owing to the enormous wavelength the wave oscillation at any given point takes 20 to 30 minutes to complete a cycle and has an amplitude of only about 1 m. This makes tsunamis difficult to detect over deep water, where ships are unable to feel their passage underneath. But as the tsunami waves approach the coast and the waters through which they travel become shallow, wave shoaling compresses the waves and their speed decreases below 80 km/hr, the wavelengths diminish to less than 20 km and their amplitudes grow enormously. When the tsunami's wave peak reaches the shore, the resulting temporary rise in sea level is termed run up. Since the waves still have the same very long periods, they may take minutes to reach full height. Except for the very largest tsunamis, the approaching wave does not break, but rather appears like a fast-moving wall of water.

Tsunami wave heights of tens of meters can be generated by large seismic events. Although they affect the entire ocean, their destructive power in coastal areas is enormous. Tsunami waves resulting from the 1782 earthquake in the South China Sea killed an estimated 40,000 people. In 1883 some 36,500 people were killed by tsunami waves in the South Java Sea, following the explosion of Indonesia’s Krakatoa volcano. In northern Chile more than 25,000 people were killed by tsunami waves in 1868. In the north Atlantic, tsunami waves generated by the 1775 Lisbon earthquake (epicentre ~200 km SW of Lisbon), killed as many as 60,000 people in Portugal, Spain, and North Africa. Waves as high as 7 m were recorded in the Caribbean, across the Atlantic Ocean. According to the U.S. National Oceanic and Atmospheric Administration (NOAA), the Pacific is the most active tsunami zone, but tsunami waves can be generated in other bodies of water including the Caribbean and Mediterranean Seas, the Indian and Atlantic Oceans and in inland lakes. About 80% of tsunamis occur in the Pacific Ocean. The 2004 Indian Ocean tsunami – a series of devastating waves, with heights up to 30 m – was caused by a magnitude 9.3 undersea megathrust earthquake off the west coast of Sumatra. It is reckoned among the deadliest natural disasters in human history, inundating coastal communities in 14 countries bordering the Indian Ocean and killing 230,000 people.

Tidal Waves: A tidal wave is a recurring shallow water wave caused by effects of the gravitational interactions between the oceans, and the Sun and Moon. The term “tidal wave” as often used to refer to tsunamis is incorrect as tsunamis have nothing to do with tides or tidal waves. Tides produce strong currents in many parts of the oceans, and may have speeds of up to 5 m/s in coastal waters. These impede navigation and cause mixing of coastal waters. Breaking internal waves and tidal currents are a major force driving oceanic mixing. Tidal mixing helps drive the deep circulation, and it influences both short- and long-term climate change. Tidal currents generate internal waves over seamounts, continental slopes, and mid-ocean ridges. Tidal currents can suspend bottom sediments, even in the deep ocean. Tides can also influence the orbits of satellites. Accurate knowledge of tides is needed for computing the orbit of altimetric satellites and for correcting altimeter measurements of oceanic topography. Apart from basic curiosity, the rise and fall of tides play an important role in the natural world, having a marked effect on maritime activities. Interest in tides is driven by the seafarer’s need for safe and effective navigation, and by the safety concerns of all those who work along the shore.

A tidal bore is a surge – a sudden increase in water depth – occurring on several rivers emptying into the ocean when tides get really big as they enter the river mouths. The surge of the incoming tide is so strong it temporarily reverses the flow of these rivers and appears as a crest of water traveling upriver. It is a rare natural phenomenon – not all coasts feature tidal bores. Conditions that appear to be necessary for the occurrence of tidal bores include a fairly shallow river channel, a narrow outlet to sea, a wide and flat estuary (place where the river meets the sea), and a large tidal range (area between the high and low tide), ~ 6 m. Tidal bores can be up to 7 m high and can travel more than 100 km inland. In the Garden Reach Dockyard at Kolkata, which is about 85 km from the mouth of the Hoogly River, the tidal bore rises by ~ 2 m.

Rogue Waves: Rogue waves, (also known as freak waves, monster waves, episodic waves, killer waves, extreme waves, and abnormal waves) are large, unexpected and suddenly appearing surface waves that can be extremely dangerous, even to large ships such as ocean liners. They have been part of marine folklore for centuries, but have only been accepted as a real phenomenon by scientists over the past few decades. They are greater than twice the size of surrounding waves, are very unpredictable, and unlike ordinary wind waves, often come unexpectedly from directions other than prevailing winds. Most reports of extreme storm waves say they look like “walls of water”. They are often steep-sided with unusually deep troughs. Since these waves are uncommon, measurements and analysis of this phenomenon is extremely rare.

Exactly how and when rogue waves form is still under investigation, but there are several known causes. Rogue waves may be created by constructive interference when swells, while traveling across the ocean, do so at different speeds and/or directions. As these swells pass through one another, their crests, troughs, and lengths may sometimes coincide and reinforce each other. This process can form unusually large, towering waves that quickly disappear. If the swells are travelling in the same direction, these mountainous waves may last for several minutes before subsiding. Rogue waves may also form due to focusing of wave energy. When waves formed by a storm develop in a water current against the normal wave direction, an interaction can take place which results in a shortening of the wave frequency. This can cause the waves to dynamically join together, forming very big ‘rogue’ waves. The currents where these are sometimes seen are the Gulf Stream and Agulhas current. Extreme waves developed in this fashion tend to be longer lived.


Waves in the Atmosphere

Atmospheric waves are periodic disturbances in the fields of atmospheric variables like surface pressure or geopotential height, temperature, or wind velocity, which may either propagate (traveling wave) or be static (standing wave). Atmospheric waves range in spatial and temporal scale from large-scale planetary waves (Rossby waves) to minute sound waves.

Gravity Waves in the Atmosphere:

When the interface between two fluids of different densities is disturbed, the force of gravity tries to restore the equilibrium. The interface returns to its original position, overshoots and oscillations then set in which propagate as waves.  This is something similar to the generation of ripples when a stone is dropped in a stagnant pool of water.  Since gravity (or buoyancy) is the restoring force hence the name - gravity waves. Such waves, also referred to as internal gravity waves or buoyancy waves, occur in abundance in the stable density layering of the upper atmosphere. Gravity waves are born when air masses are pushed up or down – perhaps by a thunderstorm, or when wind is forced up and over a mountain range. Jet stream shear and solar radiation are other triggers that may kick off gravity waves in the atmosphere. An initial small amplitude at the tropopause increases with height until the waves break in the mesosphere and lower thermosphere. Wavelengths of gravity waves in the atmosphere can range up to thousands of kilometres, while their periods may range from a few minutes to days. They may also be triggered when a parcel of air gets bumped against a region of different density. Their impact in the lower atmosphere usually remains regional, but by the time they reach the upper atmosphere, they build in amplitude and extent. In the upper atmosphere they can dominate atmospheric processes on a much larger scale, sometimes threatening the reliability of Earth-based communication systems. Most of the time, gravity waves in the atmosphere cannot be seen, but sometimes the compression of air results in cloud formation, because compressing air that is relatively humid results in condensation.  More often, especially in dry areas, the process of wave propagation is invisible. Clear-air turbulence, the bumps we feel on planes, is often the result of gravity waves breaking.

Their effects are visibly manifest in the curls of the stratosphere’s nacreous clouds (Fig 2), in the moving skein-like and billow patterns of the mesosphere’s noctilucent clouds (Fig 3) and in the slowly shifting bands of the thermosphere’s airglow (Fig 4). They do more than give clouds interesting shapes. They are vital in their role of transferring energy, momentum and chemical species between the different atmospheric layers and in the subsequent influence on upper atmosphere winds, turbulence, temperature and chemistry.

Fig 2: Nacreous clouds over Antarctica glow brightly with vivid iridescent colours.

Fig 3: Noctilucent clouds from Durham, England showing the characteristic pattern of streaks.

Fig 4: Banded airglow at a height of 90-100 km.

For details of these photographs visit: https://www.atoptics.co.uk/highsky/hgrav.htm

Atmospheric Rossby Waves:

Atmospheric Rossby waves, also called planetary waves are different from gravity waves. They occur largely due to the earth’s rotation. They are propagated by the rotational forces of the Earth, rather than gravity. Rossby waves are generated when a parcel of air gets bumped to a region with a different rotational speed and the Coriolis force pushes it back. Although gravity waves can propagate both vertically and horizontally, Rossby waves only propagate along meridians of longitude. Rossby waves greatly influence climate and weather on Earth. At mid-latitudes (between the subtropics and polar regions), a Rossby wave manifests itself as meanders in the jet stream, which then spin off to form the high and low pressure systems that we experience as weather. In the tropics, equatorial waves control precipitation by interacting with the convection cells over the oceans known as the Walker Circulation. This produces something known as the Madden Julien Oscillation, which can either bring bountiful rains or wreak havoc on East Africa and Indonesia. In either a cruel twist of fate or an argument for international agriculture markets, the result is reversed for each region so that bountiful conditions in East Africa mean ruinous conditions for Indonesia, and vice versa. According to the National Weather Service, atmospheric Rossby waves form primarily as a result of the Earth's geography. Rossby waves help transfer heat from the tropics toward the poles and cold air toward the tropics in an attempt to return atmosphere to balance. They also help locate the jet stream and mark out the track of surface low pressure systems. The slow motion of these waves often results in fairly long, persistent weather patterns.

Further Reading:

Ref: Elements of Physical Oceanography - JH Steele, SA Thorpe and KK Turekian

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