Force Fields in a Coastal System

In this piece let us attempt to see in simple terms – the dynamics of coastal systems through a different scientific angle. This angle is the Force Field Theory (or ENERGY FIELD) first proposed by Michael Faraday (1791 – 1867) in 1845 (see The Quantum World; for a short introduction of the concept). A Coastal Engineer’s works, or widely the works of a Civil Engineer belong to the domain of Gravitational Force Field, GFF – formulated by Isaac Newton’s (1642 – 1727) Universal Law of Gravitation (ULG); and its dynamic characterization by Albert Einstein’s (1879 – 1955) General Theory of Relativity (see Einstein’s Unruly Hair). The GFF is a ubiquitous invisible field that affects everything on the Earth’s gravitation field. It defines all the downslope processes, and establishes the necessity of doing work to create upslope events (see Upslope Events and Downslope Processes). We vividly see the gravitational active force in fast flowing streams – and the gravitational restoration force in waves. In all of a Civil Engineer’s works – the universal gravitational acceleration ‘g’ is present (for all practical purposes, g = 9.81 m/s^2 on Earth’s surface). This value appears in almost every relation – with the mass or density (mass per unit volume) of a substance – together they define the weight of the gravitational force. To be in perspective, while GFF defines the Natural World; as a member of the Quantum Field (QF) family, the EMFF is ubiquitous and defines the world of electromagnetism.
Perhaps the dynamics of a coastal system – for that matter of any open system on Earth’s surface – can be viewed for convenience, in terms of external excitation or agitation forces on a system – and its internal balancing responses. Alternatively, this duo represents Action-Reaction Fields – in terms of Newton’s Equation of motion translated into Navier-Stokes Equation (see Seabed Roughness in Coastal Waters). I have presented an early version (shown in the image) of the force-response field concept quite a while ago while giving a seminar at UBC and later at the University of Central Florida – where force and response fields were shown separately defining the dynamics of a coastal system. For simplicity of discussions, I like to discuss the coastal dynamics in terms of five interactive Force Fields: (1) Metocean Force Field, MOFF; (2) Extraterrestrial Force Field, ETFF; (3) Land Drainage Force Field, LDFF; (4) Heat Exchange Force Field, HEFF; and (5) Frontal Wave Force Field, FWFF. The hydro-sediment-seabed dynamics responding to these imposed forces are discussed in these five force fields. I have also included a brief on the Structure Response Field (if structures are present).
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A different way of looking at the Force Field Systems is through the Hydrodynamic Entropy as proposed in Entropy and Everything Else. All the force fields impart energy into water – transforming its dynamic characteristics. One very obvious example is the effect of a Frontal Wave Force Field – in transforming the dynamic characteristics of the medium – e.g. an oscillatory wave transforming into a translatory wave – generating the cascade of dissipation processes.
Let me attempt to refresh our understanding of a coastal system – based on pieces posted earlier: Coastal Water and Civil Engineering on our Seashore. A coastal system where the above interactive force fields function – is defined by two vertical boundaries (or the continuity of such boundaries into one or more depending on the type of physical barriers) and two horizontal boundaries (see more in Water Modeling piece). The horizontals are the water surface through which it interacts with wind – and the seabed, where it interacts with bottom resistance or reactive force. The verticals are: the open water boundary through which it interacts with its neighbors – and the shoreline of the topographical resistance or reactive force. One can also define other systems for the convenience of analysis and purpose (see Entropy and Everything Else).
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Metocean Force Field

• The water surface, a contiguous portion of the water column, or the whole water depth is the playground of MOFF. Atmospheric boundary layer generated by the turbulence of wind pressure and shear-stress – causes the formation of a water boundary layer defined by logarithmic decay of the imparted energy from the water surface down into the water column. Different aspects of this force field are elaborated in the Encyclopedia Chapters, Beaufort Wind Scale; Wave Hindcasting; and in the WIDCANVAS pieces: Ocean Waves; Transformation of Waves; Linear Waves; Nonlinear Waves; Spectral Waves; Waves – Height, Period and Length; Characterizing Wave Asymmetry and Storm Surge. Referring to them may prove useful while trying to understand the actions of MOFF. Further, I have tried to present wave motion dynamics in poetic terms – in the Ocean Waves piece.
  
• The MOFF forces the water body to respond in two ways with the GFF acting as the restoring force. To explain the two – I would rely on the Storm Surge piece posted earlier. The two are – the short surface wave and the long storm wave – both are generated by the dynamic pressure or kinetic energy exerted by MOFF; and their magnitudes are proportional to the square of the wind speed (Daniel Bernoulli, 1700 – 1782). The short surface wave transports the gained energy in progressive wave motions. Like the turbulent wind, these waves are highly irregular and spectral. The storm surge – on the other hand results from the hydrodynamic balance between the wind-induced water motion and the resistance of that motion by the coast. The result is the piling up of water at the coast – a standing long wave type oscillation. Along many coasts and bays around the world – MOFF causes seiche or meteo-tide that accentuates the high astronomical tide (see more on Storm Surge and Flood Barrier Systems).
  
• Following the wave pieces posted earlier, a clarification of short (or short legged) and long (or long legged) waves are necessary. To do that, let us revisit the 3 fundamental parameters: wave height H (simply the height from trough to crest), local wave length L or wave period T (measured simply from crest to crest, L in space and T in time), and the local still water depth d. A wave is a true short wave – when d/L > 0.5. A wave is a true long wave when d/L < 0.05. In between, a wave transitions from short to the long.
  
• Another important effect of MOFF is coastal upwelling and downwelling (see my 2017 Encyclopedia Chapter). These vertical water motions develop from a balance of wind-induced water motion, coastal resistance and the Coriolis Effect (see Characterizing Wave Asymmetry). Costal upwelling has a huge implication on modulating the weather pattern, and in fisheries population and abundance.
  

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Extraterrestrial Force Field

• The ETFF is caused by the Earth’s only satellite – the Moon, and the source of all our energy – the massive Sun (0.333 million times the mass of the Earth). The GFF of these three celestial masses defines the Earth-Moon-Sun System. An interaction takes place between the spinning Earth’s centrifugal outward force and the inward gravitational force of the system. All masses on Earth respond to the imposed forces – but the massive ocean water responds most (tidal effect on land masses is not effective, because land mass is heavy and rigid to distort; and atmospheric tide is hardly measurable because air density is too light). The result is the swelling of ocean water where outward force is the strongest and depletion where the outward force is the weakest. The generated wave is very large – 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 a very small amplitude but a long period roughly equal to half day (see more on Ocean Waves). The strongest tide results when Moon-Sun acts in unison – resulting in fortnightly spring tide (during the Full and New Moons); and the weakest – the fortnightly neap tide occurs when Moon-Sun forces are out of phase (during the 1st and 3rd Quarters).
  
• The generated ocean tide – small in amplitude – propagating into the shallow coastal shelf, gets amplified into higher amplitudes (see more on Transformation of Waves). 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. Further, as pointed in earlier pieces, the transformation of a long wave (tide, tsunami and storm surge) – is modulated by the processes of funneling, resonance and shoaling. One spectacular example of such transformation is the vigorous tidal actions – with tides coming from two ends of the Discovery Passage in British Columbia (I had the opportunity to model this tidal phenomena using Mike21 hydrodynamic modeling suite).
  
• As outlined before in the Ocean Waves piece, 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). Their works led us to see tide as a composite mosaic of many tides – which can be decomposed into harmonic components of different periods, amplitudes and phases (that can be attributed to different generating forces). In very shallow water, some shallow-water harmonic components are highly amplified – giving birth to overtides and compound tides of different periods – different than the parent tide (e.g. my 1991 COPEDEC-PIANC paper). The rise and fall in water level is associated with oscillating horizontal movement of water causing tidal currents.
  

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Land Drainage Force Field

• In elaborating LDFF, I will rely mostly on WIDECANVAS pieces: Coastal River Delta and Managing Coastal Inlets; on the 2002 ASCE article  Alluvial Deltas; on my Ph.D. Dissertation; on the 1990 IEB journal paper; on the 1995 JCR paper; and on the 1994 and 1990 Elsevier papers. The LDFF – mainly active in river mouths, estuaries and contiguous coastal ocean – comes with three distinct forcing characteristics: (1) the discharge of lighter density fresh/brackish water on to the ambient ocean salt water; (2) the volume and seasonality of this fresh water discharge; and (3) the volume, seasonality of the sediment discharge and sediment granular size distribution. Let us attempt to elaborate these three aspects of LDFF briefly.
  
• Density Driven Circulation. In absence of other force fields – riverine/estuarine fresh water flow rides on top of the heavy saline water – creating a stratified water column – with the top fresh water flowing outward into the sea – and bottom saline water moving in to balance the loss of fresh water. This process often with distinct halocline – termed as Estuarine Circulation – is ideal when the receiving coastal ocean is deep. When both MOFF and ETFF are active, the vertical stratification is destroyed by the MOFF induced mixing and circulation – and by tidal pumping of the ETFF. The effects often create horizontal stratification in shallow coastal oceans - with predominance of saline tide on one side, and fresh/brackish water on the other. As revealed in my 1990 works, a spectacular example of the horizontal stratification exists in the low-aspect-ratio (depth/width) coastal ocean at the Ganges-Brahmaputra-Meghna river mouth.
  
• Seasonal Fresh Water Discharge. Seasonality of the freshwater outflow has a substantial influence on the river-mouth hydrodynamics – from pushing the freshwater front out into the sea during the high-flow period – to the modification of tidal wave – to letting salt-water to intrude into the lower river reaches during the lean-flow period. As I have shown in my 1995 IEB paper, the Seasonality Index (mean monthly/mean annual) of the Ganges River varies from 0.2 during the dry season to 3.5 during the monsoon. With such a high seasonal fluctuation – and together with actions of other rivers of the Ganges-Brahmaputra-Meghna system, the estuarine front is pushed out into the open ocean during the monsoon (1990 IEB journal paper).
  
• Seasonal Sediment Delivery. Sediment transport is a power function of discharge – therefore the same scenarios of seasonality play a role in LDFF. However, there is a certain amount incoherence or hysteresis between water and sediment discharge (the 1995 IEB paper). Additionally, the characteristics of sediment granular distribution are also seasonal – determining the nature of delta progradation.
  

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Heat Exchange Force Field

• Compared to others, HEFF has a rather subtle – even negligible effect on the coastal hydrodynamics. Therefore no term related to HEFF appears in the general description of the Navier-Stokes Hydrodynamic Equation (e.g. in 2D depth-averaged modeling; but must account for it in 3D modeling). For aquatic lives – however, HEFF is very important – some are dependent on and look for warm waters – while for others cold water is important. Therefore - HEFF appears as an important parameter in the Water Quality Modeling. The water body interacts with the air-temperature above its surface – in gains or losses of heat according to the 2nd Law of Thermodynamics (e.g. high to low, one-way process; see Entropy and Everything Else). This process occurs in the Thermodynamic Force Field or TDFF domain (see The Quantum World) - in molecular diffusion mode. When hydrodynamic actions are strong due to such factors as wind and current - an extra two-way mixing mechanism is added, thus augmenting the HEFF processes.
  
• The HEFF process primarily gives rise to sharp lines of temperature difference or thermocline in the capacity of micro-circulation. Hydrodynamic actions in turbulent eddies (see Turbulence) is responsible for mixing of thermally stratified water bodies - destroying the thermocline in the process. Also, fast flowing streams or high energy fluid motions do give birth to heat in frictional dissipation of energy at the bed.
  
• I only became aware of HEFF when I was working on a project tasked to assess hydrodynamic characteristics of Lynn Canal, Alaska. This deep U-shaped fjord is stratified with distinguishable thermocline. Analyses of long time-series data have revealed how the water column is thermally stratified with the nature of stratification changing shape and gradient responding to seasonal heat gain during Spring-Summer – and heat loss during Autumn-Winter. The investigated area of the Lynn Canal system is characterized by a stable thermal minimum zone at a depth of about 140 m – below which a rather stable layer of positive temperature-gradient (temperature increases with depth) resides – which remain rather irresponsive to the surface heat gain or loss at the surface. The top layer from surface to the thermal minimum, on the other hand is characterized by negative temperature gradient (temperature decreases with depth) – that changes in response to seasonal heat grain or loss. The implication of such a stratification is that dynamic mixing and circulation is confined within the top layer – with the rest of deep water column literally not knowing what happens at the top.
  

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Frontal Wave Force Field

• The FWFF is the most energetic and dramatic of all the coastal force fields. It generally pertains to the processes of Hydrodynamic Entropy – a term coined in Entropy and Everything Else. It is generated by the sudden release of built-up pressures or accumulated energy (the closest analogy of FWFF is the sonic boom in acoustics) by some triggers. Such accumulation of hydrodynamic energy could occur for many different reasons – impoundment and obstruction are two of them. But basically it happens when the rate of accumulation far exceeds the dissipation processes. The fundamentals of the FWFF are same as what are discussed in the Nature’s Action and Upslope Events and Downslope Processes. Let us attempt to understand the coastal FWFFs in simple terms. The four of them are: Tidal Bore, Tsunami, Flood Barrier Collapse and Storm Surge. Breaking of waves (see The Surf Zone) also creates FWFF – occurring rather regularly, the phenomenon defines beach evolution – in erosion, sedimentation and longshore sand transport. Many episodes of FWFF take people and authorities by surprise – as they are random in occurrence and remain beyond the purview of conventional forecasting.
  
• The released FWFF pressure wave containing huge amounts of energy propagates at a celerity or speed of supercritical flow (c = square root of the product of ‘g’ and water depth; at 1-m water depth c = 3.1 m/s; compare that with the tranquil flow speed in the order of 0.5 m/s). The leading edge speed is even higher than supercritical flow ≈ some 1.4 to 2*c. A wave with such a high speed could propagate upstream, and cross and overtake obstacles and transports huge load of debris and sediments. The most spectacular examples of this incredible speed – are the recent 2004 Indonesia tsunami and the 2011 Japan tsunami (many of us witnessed the havoc of them in live coverage). Explained further and see more in Tsunami and Tsunami Forces.
  
• Tidal Bore. USGS Circular 1022 (1988) presented a catalogue of world-wide distribution of tidal bores. Tidal bores form during spring tides when the range is the highest. With the combined affects of shoaling and funneling – the propagating tide becomes highly asymmetric so much so that at a certain time maintaining the wave-form becomes unsustainable – the result is the breaking of the accumulated pressures – giving birth to tidal bores. As happens with other long wave transformations – the accumulation lets the integration of all different component tidal frequencies into one pressure wave. The propagating bore with its breaking sound is very spectacular – and the phenomenon has given birth to wave-surfing and tourist attractions – with people flocking together to witness this Nature’s action. While on an investigation vessel, I was once in the middle of tidal bores in a tidal channel in Bangladesh southeast coast. With bores coming from two different directions, very low water suddenly rose to a high level as the bore passed. If one plots the tidal height and current – the sudden rise of these two parameters becomes very vivid. While tidal bores are spectacular to watch, they also pose navigation hazards to small vessels. Tidal bores transports sediments and reshuffles alluvial sand to create islets and scour holes within a very short period of time.
  
• Tsunami. Let me highlight this FWFF based on the WIDECANVAS piece, Tsunami and Tsunami Forces and my 2006 Tsunami paper and 2008 ASCE article. Tsunami is a series of impulsive 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 (a phenomenon of MOFF). Following the alignment of disturbance, tsunamis radiate out directionally traveling long distances to reach coastal land – far and near. Tsunami characteristics change in response to the configurations of an enclosed basin or harbor. Like all waves, a small tsunami in deep water shoals to monstrous waves as it propagates into the shallow water. After breaking, Tsunami Run-ups flood coastal lands with enormous inbound and outbound speeds causing havoc and destruction. The arrival of Tsunami crest is preceded by the huge draw down or Sea Level Suck Out associated with the Tsunami trough. This phenomenon sucks out things from the shore out into the sea - exposing shoreline features - leaving many aquatic lives stranded in air. It catches offshore boats off-guard - and tragedies happen when people rush out to catch the stranded fishes.    
  
• Flood Barrier Collapse. In the Flood Barrier Systems, we have seen different aspects of water barriers. Such barriers are designed to hold the propagating storm surges and other flood waves – to protect areas behind them. The stoppage of propagating waves – lets accumulation and integration of pressures causing a very high turning moment on the barrier systems. The barriers while designed to protect townships and properties – are also like a human-made hazard – in a sense that they pose high risk. But the benefit of taking the risk is worth, because letting the frequent onslaught and inundation has the action of taking a bite on people’s livelihoods. The catastrophic failure of the flood barrier system protecting New Orleans – during Hurricane Katrina in 2005 – is one of the reminders of how vulnerable a flood barrier can be.  
  
• Storm Surge. Unlike other waves, storm surge (see more on 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 (note that a storm surge is not monochromatic, therefore some frequencies may resonate to the basin natural frequency) superimposed on astronomical tide generates the storm tide. The peak storm tide – a superimposition of high tide and peak storm surge – combined with high waves, causes large coastal flooding, erosion and damages.
  
• What we have discussed so far is positive storm surge that occurs on the right side of a land-falling Hurricane in the Northern Hemisphere. A negative storm surge, popularly known as the Sea Level Blow Out – also occurs simultaneously on the left side. Spectacular example of this phenomenon was emptying of Tampa Bay during the 2017 Hurricane Irma. 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. Among others, the 2011 WMO Guide to Storm Surge Forecasting (WMO No. 1076) is an excellent source on the science of storm surge.  
  

These force fields – apart from changing and affecting the Natural setting of Fluid, Solid and Life systems (see Warming Climate and Entropy), have forceful impacts on water-front and in-water civil engineering structures (see Civil Engineering on our Seashore). Aspects of them are discussed in several pieces posted earlier: Wave Forces on Slender Structures; Wave-Structure Interactions and Scour, Tsunami and Tsunami Forces; Flood Barrier Systems; Breakwater; and Uncertainty Propagation in Wave Loadings.
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Let me finish this piece with a Koan:
People are the most important institution. Irrespective of the governing system – if those in power fail to uphold the trust and confidence of this institution – of people’s aspiration and wellbeing – then the governance turns into tyranny.

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- by Dr. Dilip K. Barua, 25 August 2021

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