Ocean Waves

1. Intro
In this article I like to pay attention to one of my favorite professional interests – and it is the mystery and beauty of wave processes that continuously agitate the ocean and pound on shores.
Well, where to begin on this interesting topic? The coastal waterfront has been the gateway of contacts among countries from time immemorial – facilitating cultural exchanges, discoveries, trade and commerce. In modern times, interests and importance of coastal waters have only increased manifold. Harnessing of oceanic resources, waterfront living, recreation, and maritime ports are some of the major important social and economic activities that keep people relaxed and busy in coastal waters. Waves attract people by the sheer display of dynamics – soothing and constructive at some time, but destructive and intimidating at other. It seems humans have a natural affinity for the dynamics of vibrating energy as we see in ocean waves. Let us continue more along this line of thinking in the SCIENCE & TECHNOLOGY page in the future (links in Widecanvas Home Page).
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2. Wave Science - Medium of Propagation, Causes and Effects
For now, I am thinking of describing the beauty of ocean wave processes with a little poem. But before that a brief discussion of some basic wave processes may be of some help. Perhaps adding a few lines on the physics of wave-types will lay a firm foundation in understanding waves. One of the best ways is to discuss different wave types – distinguished in terms of: the causal factors of disturbing force; the restoring force; the particle oscillation relative to the propagation direction; and the position of the propagating wave within the medium.

• (1) Disturbance: Mechanical – e.g. seismic action on Earth; wind action on water, and Non-mechanical – e.g. an electromagnetic wave or radiation in vacuum.
  
• (2) Restoration: Gravity – e.g. ocean waves, and Elasticity – e.g. seismic waves.
  
• (3) Propagation: Transverse – medium particles oscillate perpendicular to the direction of energy propagation, like ocean waves and seismic S-waves and Longitudinal – medium particles oscillate parallel to the direction of energy propagation in pressure waves of compression-rarefaction, like sound waves and seismic P-waves.
  
• (4) Medium: Surface Waves – e.g. wind waves, Body Waves – e.g. seismic waves and Internal Waves – in stratified mediums.

An ocean wave is mechanical-gravity-transverse type. When regular wave propagation is forced to stop, or when an abrupt and sudden impact is forced on a medium – an intense pressure front builds up – giving birth to an Upslope Event. When the front is unleashed suddenly by some triggers – it results in the Downslope Processes of a frontal wave or shock wave – that does not have a recognizable trough, and propagates in the very high speed domain of supercritical flow. Tidal Bore, Tsunami and Wave-breaking (depth-limited plunging) are some of the examples of the frontal waves in a coastal system. Unlike regular waves, the high-pressure frontal waves dissipate relatively quickly due to high reactive frictional resistance, expansion (if any) and heat generation. See further in Upslope Events and Downslope Processes.
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3. Waves in Everyday Experience
All of us have seen the effects of disturbances in water – whether during playing in a bathtub or seeing ducks swimming in a pond, or on a large scale watching sailing ships. In each case water responds in a wave form to transport the gained energy imparted by the external pressure. Distortion of water into wave form lets the gained energy propagate by transmitting the dynamic pressure on to the adjacent water mass. The speed of this propagating wave energy – known as celerity, depends primarily on its period, and depth of the water body. A wave may occupy the whole water column or may just propagate near to the surface – the larger the wave the higher the influence of it in the water column.
The wave that we see, describable in terms of height – from the crest at the top to the trough at the bottom, period, wave length and phase – from crest to crest or from trough to trough, actually represents an envelope. Depending on the type, the envelope contains multitudes of superimposed waves of different heights and periods. These multitudes are caused by different forces and the corresponding water responses. Only the resultant addition of all – is visible in the envelope form. We will follow this discussion more closely in the next blog.
What are the propagation characteristics of an ocean wave? In analogous with optics, a wave is subjected to transformation as it propagates – its speed slows down in shoaling water resulting in amplification of the wave height – breaking in extreme cases when the wave form becomes unsustainable. If there are variable water depths within the wavelength, the wave refracts by traveling faster in deep water and slower in shallow water. It also diffracts to propagate into the shadow of a large obstacle. Both of these processes cause the wave to lose some of its energy.
The ocean is ubiquitous with wind waves (image credit: anon) – the irregular ones are locally generated by wind storms while the regular ones have propagated from a far distance. A wind-generated wave is highly irregular – and as it starts to disperse, the longer components of the wave-composite begin to separate propagating faster than the rest. One sees these waves called swells appear in places where there are no local winds. Also waves tend to rearrange themselves in groups of large and small ones – this process in essence results from the superimposition of many shorter waves of different amplitudes, frequencies and phases. 
How about other natural waves in the ocean – tide, tsunami, and storm surge? The first is a regular astronomical phenomenon that we see everyday along our coast. The tsunamis and storm surges, on the other hand, are episodic and impulsive. The powers of these two types of natural disasters bring in personal tragedies and serious damages and hardships accompanied by losses of lives, homes, properties and businesses.
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4. Long Waves
Let me try to go through these wave processes one by one. But before doing so, I like to give a brief on another wave characteristic to help us understand better. A wave is classified as long or long legged and short or short legged for convenience. A long wave has length larger than 20 times the local water depth. In contrast to short wind-waves, tide, tsunami and storm surge belong to long wave category, especially in coastal waters.
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4.1 Tide
The daily rise and fall of ocean water level attracted human imagination from ancient times, in particular because of its correlation with the phase of Moon. The workable explanations and predictions of the phenomenon, however came much later, and were worked out by many investigators. The notables among them were Galileo Galilei (1564 – 1642), Isaac Newton (1643 – 1727), Pierre-Simon Laplace (1749 – 1827) and Arthur Thomas Doodson (1890 – 1968).
The tide is the greatest manifestation of the gravitational attractions of astronomical bodies notably the Sun and Moon on ocean water. The forces act on everything though – from the atmospheric air to small water bodies, even on fluids of our body. We do not see tidal effect on land because land mass is too rigid to distort, also tide is hardly measurable in atmospheric air because air density is too low. In terms of human body, traditional Eastern therapeutic practices recognize this force with the suggestions that some symptoms of illness elevate in intensity during the lunar phases of full and new Moons when lunar attractions on Earth are the greatest.
An interaction takes place between the spinning Earth centrifugal outward force and the inward gravitational force of the Earth-Moon-Sun system. The resultant effects of these forces cause the water to swell where outward force is the strongest, and to deplete where the outward force is the weakest. The result is a very large wave – a periodic rise and fall of the ocean water that has crests on the opposite sides and troughs in between. As the phase of the Earth-Moon-Sun system changes – the generated astronomical tidal wave propagates throughout the ocean. This ocean tide has very small amplitude but a long period roughly equal to half a day.
Here comes the interesting part. As the small ocean tide propagates into the shallow coastal shelf, it gets amplified into higher amplitudes. Further into the coastal basins of different configurations and sizes at different latitudinal distances from the Equator, different components of the tidal wave responds differently to the natural periods of the basins. The result is that each tidal basin shows its unique response to the forced tide – some are high or low, some are semi-diurnal or diurnal in period, yet others are mixed in character. The rise and fall in water level is associated with oscillating horizontal movement of water causing tidal currents.
To give an idea of the tidal response, I like to briefly highlight the case of the mouth of the Ganges-Brahmaputra-Meghna River system where some shallow-water harmonic components are highly amplified. These tidal components - overtides and compound tides have periods less than half a day. Such a response is better shown by Fourier Analysis of the measured water levels. I had the opportunity to work on that, and the results were published in the 1991 Conference Proceedings of the Third International Conference on Coastal and Port Engineering in Developing Countries (PIANC-COPEDEC) held in Mombasa, Kenya.
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4.2 Tsunami and Storm Surge
Now let us turn our attention on the episodic wave phenomena – tsunami and storm surge. The seismic sea wave, known according to the Japanese term tsunami, is a series of impulsive water waves generated by sudden rupture of underwater earth’s crust, or by rapid slides of large landmass into water, or by sudden change in local atmospheric pressure. Following the alignment of disturbance, tsunamis radiate out directionally traveling long distances to reach coastal lands - far and near. Like all waves, a small tsunami in deep water shoals to monstrous waves as it propagates into the shallow water. Such large waves flood coastal lands with enormous inbound and outbound speeds causing havoc and destruction. A tsunami also changes its characteristics in response to the configurations of an enclosed basin or harbor. See more on this phenomenon in my Tsunami Modeling paper. Our memory is still fresh with the awful devastation and tragedy of Indonesian Banda Aceh tsunami of 2004 and the Tohoku Japanese tsunami of 2011. It seems no measure is adequate to control or prevent the devastating effects of a powerful tsunami.
Unlike other waves, storm surge generated by Hurricane winds most often does not have a definite wave form – its crest is more pronounced than the trough. It develops, as a Hurricane low pressure system moves along or across on to a shore. The low pressure at the eye of the Hurricane causes reciprocal rise in water level, and together with wind-shear the system causes huge water mass to pile up along the coast – at the right side of the propagating storm in the northern hemisphere. The storm surge superimposed on astronomical tide generates what is known storm tide.
The peak storm tide – a superimposition of high tide and peak storm surge – combined with high waves most often causes large coastal flooding, erosion and damages. Some of the most devastating recent Hurricane storm surges that still haunt people’s memories are the August 23, 2005 Hurricane Katrina on the Louisiana coast at New Orleans, and the October 22, 2012 Hurricane Sandy on the New York and New Jersey coasts. During a project work mission, I got trapped in the middle of a huge cyclonic storm surge that wiped out an entire Bangladeshi coastal village named Urir Char in 1985.  
Well, enough for now on some of the ocean wave basics. Time for a little poem!
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5. Ocean Waves in a Poem
Waves Continue to Pound on Our Shores
Whipping wind lashes on ocean’s back mercilessly
The ocean fumes in anger snatching some of the energy
The inflicted scars are long and short, deep and shallow
The born waves are noisy and undisciplined like the wind.
But the biggest scar is caused by Hurricane storms
Churning the ocean
Piling up huge mass of water on way to the land.
Then there is the Earth at the ocean floor
Suddenly waking up scratching itself
Ocean soothes the scratch in response
Giving birth to tsunami, long but shy in height.
If these Earthly processes are not enough to make ocean restless,
Here comes the Moon and Sun pulling the water mass 
Ocean responses by giving birth to tide – gentle and very shy in height,
But the lengthy and skinny wave covers long distances
Causing rise and fall of coastal waters on each day.
 
The born waves must travel transporting the gained energy
They disperse with letting the long-legged ones at the fore-front
And do not like when depths shoal up
Their speeds slow down and they protest the encounter by becoming taller
They find deeper water and bend to propagate faster through the deeps
But they must continue their journey on to the land
To pound on shores to dissipate energy.
Some are small capable of moving and shuffling sand only
Storm waves flood land eating away part of it.
The shy deep-water tsunami becomes monstrous protesting the shoaling depth
Its power sweeps many – big or small on its way.
 
See waves in all – in cycles of differences, highs and lows, ups and downs
In day and night and day again
In winter, spring, summer, fall and winter again
In jitters and ripples of society and economy
In birth, growth, decay, death and birth again
Of all living things, of all emotions
Of all powers great and small
Of all fame and disgrace
Of all wealth and poverty
Of all civilizations remarkable and mundane.
The cycle continues – the most visible sign that Nature and life are fluid
That it is the flow of energy that generates waves in all, 
To roll the Wheel of all existence on to the future.
That the rise and fall, ups and downs, are part of the same coin – the duality.
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Let us finish with a note on the sweet side of Isaac Newton. He took the vastness of ocean as a metaphor to appear very modest to reflect on his achievements: I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the seashores, and diverting myself in now and then finding a smoother pebble or prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.
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Here is an anecdote to ponder:
The disciple commented, “Sir, I am wondering about the waves in oceans – wind-waves and tide, and the episodes of Hurricanes and tsunamis, and thinking what do they tell us.”
The master smiled, “Good point! As happens in an ocean, a person is continuously bombarded with waves of information of different magnitudes and frequencies coming from all different directions. The situation has only been getting worse from the dawn of the internet age. Sadly people with malicious motives are using this great innovation to hack and target youths and vulnerable sections of the populace – seems like with virtual impunity.”
“Indeed that is very sad, Sir. But also so much information can be highly stressful, intimidating and confusing.”
 “And distracting too. A person’s actions and reactions are defined how he or she receives the information, filters and processes them. Most people filter and process the information rather intuitively – therefore one can only glean the bests when he or she possesses high mental and moral strengths reinforced by clear understandings of things.”  

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- by Dr. Dilip K. Barua, 7 July 2016

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