In the Ocean Waves blog on this page, I have briefly talked about the composition of a visible Natural wave with many invisible component waves – in other words with the Multiplicity of diverse waves. Ocean waves, for that matter all Natural wave phenomena are spectromatic and asymmetric with the visible Duality of highs and lows. As one practical example, I have also mentioned in that page how some tidal waves are defined by the superimposition of many high harmonic shallow-water tides. Let us try to explore more to see how the systems of Duality and Multiplicity work exactly.
The phenomenon of Duality is somewhat obvious – in the most visible manifestation of the top wave crest and the bottom wave trough. Duality does not mean that there are just the two of something – but that the two are the inseparable and complementary components of the unity - union of the two opposites combined together in the pursuits to reaching the symmetry of stability. Duality should be understood as the incremental motions of the opposites geared toward achieving agreement and dynamic equilibrium. It cannot be described by a divisive phrase like either/or, but rather by a unity phrase of Multiplicity like this, that, and the others.
Before going further, I am tempted to briefly explore some of the ancient Eastern thoughts on this topic. In one of the simplest ways of explaining the Buddha’s Perfection of Wisdom Discourse, Buddhist scholar Nagarjuna (150 – 250 CE) at an earlier informal establishment of the world’s second earliest University at Nalanda (427 – 1192CE) stated: That which is the element of light is seen to exist on account of darkness; that which is the element of good is seen to exist on account of bad; that which is the element of space is seen to exist on account of form. In a similar platform of thoughts, the Duality principle is expressed as the union of the opposites – Yin and Yang in the Daoist philosophy.
Coming back to the Natural waves, it is interesting to see how the crest and trough are related to each other within the framework of elastic resistance to deformation – the trough is forced by the flow of energy to work up to the phase of the crest, while the gravitational pull drags the crest to work down to the phase of the trough. The process is associated with a forward motion and a compensating reverse motion of the medium particles required to completing the loop. This balancing act between the excitation energy and gravity indicates that the crest and trough work together to attain stability and equilibrium.
As the Natural waves and these ancient thoughts tell us, the Duality of the opposites in a society should be interpreted as something convergent – not something divergent. Duality and Multiplicity are not chaos, but rather Nature’s way of responding to the excitation in order to propagate and dissipate the gained energy. Perhaps one relevant lesson from the Duality principle is that, a democratic rule can only prove meaningful and stable if the oppositions and others are truly accommodated in governance. We can talk about this more in the SOCIAL INTERACTIONS page at some other time.
Let us turn our attention to the Multiplicity in waves. To help us understand better, I have constructed a simple image showing four sinusoidal or symmetric waves of different amplitudes and frequencies. In the shown image, the horizontal x-axis is time normalized by the period of the first wave, and the vertical axis is water level in meter with reference to mean or still water level (SWL). These four monochromatic waves when superimposed, added to the asymmetric and spectromatic wave shown as the envelope. In addition to losing the symmetry, the envelope has amplified at some phases and reduced at others. While this fundamental principle holds in all cases, one needs to understand that a Natural wave in the open ocean is much more complex with the superimposition of many spectral waves coming from all different directions.
Perhaps one more example would clarify things. We all know about the illumination of light – that it is composed of a spectrum of seven distinct colors. Most Natural waves – be it light, sound, electromagnetism or any other mechanical waves such as those we have described – are characterized by the Duality envelope of the crest and trough, but within which exists the Multiplicity of component waves. This Multiplicity is the building block of the Duality.
The suggestion that Multiplicity is the building block of the Duality indicates that a monochromatic wave is not sustainable in Nature for long. Why is that? To find the answer we have to turn to Isaac Newton (1643 – 1727) again, to his famous Third Law of Motion – that every action has an equal and opposite reaction. As soon as a monochromatic wave is formed, it invokes reactive waves from the boundary. The resulting superimposition of the active and reactive waves turns an original monochromatic wave into a spectromatic one. In a near ideal case, when the reactive wave is reflected perfectly, the superimposition causes what is known as the standing wave – with the depressed high-current nodes and high-amplitude anti-nodes. A standing wave is the perfect example of a stalemate.
Why are all these discussions important? Perhaps seeing a wave and pondering about its components are very helpful in unraveling many of the Natural and social mysteries. It is because of the fact that excitation always distorts the medium to a wave form. It is how the medium attempts in time to return back to its non-excited tranquil stage by balancing itself through the processes of transmission, absorption and losses of energy. But to keep our understanding in true perspective, it is important to note however that for the electromagnetic waves and gravitational radiations traveling at the very high speed of light, no medium is necessary to transport energy.
Now I like to turn my attention to a different question. Is the Duality we have described same as Relativity? Although the two appear to indicate the same meaning, I would argue that while the Duality is real, the concept of Relativity is subjective, resulting from our differences in perceptions of things. However the Duality and Relativity could converge at some points or levels when our perception approaches the reality of Duality, or when the Duality can be stressed or extrapolated to explain something that could approach the level of Relativity. For example, light and darkness represent the reality of Duality, but the perception of the good relative to the bad could only mean Duality, if the definitions of and the difference between good and bad are well-established and accepted across the board. Nagarjuna’s explanation includes both the reality of Duality and the concept of Relativity.
Let us try to clarify the concept of Relativity further through the mind of a champion thinker. Albert Einstein (1879-1955) – the pioneer of the General Theory of Relativity – described it in an attractive but understandable way for non-scientists: When a man sits with a pretty girl for an hour, it seems like a minute. But let him sit on a hot stove for a minute and it's longer than any hour. That's relativity. Scientists often explain a simple phenomenon like lightning thunder; and how it is perceived differently. One standing at the platform will perceive the phenomenon differently than the one riding the speeding train. This different perception of the same event by different persons depending on their states of motion is Relativity.
Or we can think about our own change of perceptions – things were tall and long when we were little, but the same things appeared shorter and shorter as we grew up. All these arguments lead us to say that the truth of things is nothing but the subjective perception one experiences. In other words, in our perception or measurement, nothing is absolute – time is not absolute, space is not absolute, our social interactions are not absolute. This raises the issue that there are two basic types of truths – absolute and relative. Let us get back to this concept at some other time in the future.
Do the Duality and Multiplicity of the same phenomenon continue to remain the same as they evolve in space and time? In analogous with the transformation of propagating waves, the Duality and Multiplicity of the same phenomenon at one place and time are not the same in different places and times. This means that a downstream phenomenon can be traced to the upstream source, but they are not the same.
Here is an anecdote to ponder:
The disciple asked the master, “Sir, how come I continue not seeing things as described.”
The master took a pause and looked at the disciple and laughed, “Aha! Aha! That is because you are standing in the dark. Stand in the sunlight and watch how your shadow changes shape and size as the daylight passes.”
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- by Dr. Dilip K. Barua, 14 July 2016
In this blog 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 between 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 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.
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.
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 and wave length – 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 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.
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.
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.
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 land - 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. 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!
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.
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.
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