OSX-2004 TR Revision Cards

Thomas Rippeth Lectures

  • Created by: Rachelezy
  • Created on: 19-12-21 16:56

Shelf Sea Basics

Shelf Sea Facts:

  • 7% of total SA of the ocean
  • Depth range of shore - 200m  (e.g. Depth of Irish Sea ~50m)
  • 15-30% total oceanic primary production
  • Currents dominated by tidal flow of 0.2 - 2ms-1
  • 20-50% of total CO2 open ocean storage
  • ~70% global dissipation of tidal energy

Lots of turbulence for mixing. Residual currents account for transport. Large inputs of nutrients via river run-off

Sea level 120m lower in the past (Irish Sea did not exist). First large scale synthesis of carbon budget in shallow seas of NW European Shelf. Carbon entering seas from atmosphere = ~40%

  • Low-cost dumping grounds
  • ~40% of global pop. live within 100km of sea = industrial activity
  • Sea hypoxia --> excess nutrients --> nuisance plankton blooms
  • Exploitation of fish stocks (e.g. 25% biomass removed by fishing each year from North Sea)
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Liverpool Bay as a Shelf Sea Resource


  • Fishing (not as popular as it used to be)
  • Oil and Gas Extraction (1.2 mil cubic feet of gas. 150mil barrels of oil. Future carbon storage and hydrogen
  • Gwynant y Mor Offshore windfarm (576MW)
  • Waste Disposal (Nutrients, heavy metals and organic pollutants)
  • Resources (Aggregates, fisheries)

Was identified as an area with potentially below good ecological status. UK government taken to court to provide evidence that it was at good ecological status.


  • Increased loading of nutrients into estuaries and coastal waters. Can lead to algal blooms - lower O2 levels - hypoxic waters
  • Can result in harm algal blooms, dead zones, and killing of fish and other marine organisms within that habitat
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Shelf Sea Regimes

1. Region of Freshwater Influence (ROFI) - Transition between freshwater inflow from estuaries and sea

2. Homogenous regions - Water column well mixed by turbulence generated by tidal stresses on seabed

3. Tidal mixing front

4. Seasonal Stratified Zone - Water too deep, currents too weak, fro complete mixing. Thermally stratified during the summer period

5. Internal Tides - Generated at shelf break - travel onshore and mix water column

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Principle of Continuity

Key Points:

  • Mass must be conserved (As SW is almost incompressible)
  • Continuity of mass = Continuity of Volume
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Conservation of Volume

Key Points:

  • Water input into a 'full' container must be flowing out elsewhere at the same rate
  • Sea level assumed to remain constant
  • Full containers include fjords, bays and partially-enclosed seas

Qin + R + P = Qout + E       SO      Qout - Qin = (R+P) - E = X (Freshwater Content) (No impact on salt in the basin)

X > 0   Qout - Qin > 0 = Net outflow from basin   X < 0 Qout - Qin < 0 = Net inflow from basin

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Conservation of Salt

Key Points:

  • Total amount of salt in the ocean is constant
  • Socean.Qin = Sbasin.Qout

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Estimating Inflow and Outflow

Qin = X.Sbasin / (Socean - Sbasin)

Qout = X.Socean / (Socean - Sbasin)

(Known as Knudsen Relations)

When you know outflow you can calculate Flushing Time (Time taken to replace ALL the water in a basin/sea/bay etc.T ~ V/Q, where V = Volume of basin etc. and Q = Outflow rate

Equations are used to estimate inflow and outflow based on:

* Salinity of water

* Freshwater Fraction (X)

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Conservation of Volume & Salt in the Mediterranean

Key Points:

  • Semi-enclosed sea
  • Freshwater dominated (by evaporation)
  • Net flux of water into Med to balance water lost by evaporation

Conservation of Volume: Salt left behind when evaporation occurs (increase in salinity). Salinity of water leaving Med is HIGHER than salinity of water entering (Two-layer flow - Less salty Atlantic Water enters over top of exiting Med. water)

Conservation of Volume = Qin = Qout + E

Conservation of Salt = QinSAtlantic - QoutSMed

(How to derive an equation for Q on flashcard)

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Conservation of Volume & Salt in the Irish Sea

Key Points:

  • Partially enclosed
  • Shelf Sea
  • Temperate
  • Residual flow of Irish Sea = S to N (Water enters through St George's Channel in the S and exits through the North Channel in the N)
  • Freshwater mainly from river inflow (Can make assumption that X = R)

Conservation of Volume = Qn = Qs + R

Conservation of Salt = QsSs = QnSn

Defining flow rate, where Q = Flow rate into the Irish Sea:

Q = Qs, so Qn = Q + R

(How to rewrite equation in terms of Q is on flashcard)

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The Aral Sea (When water is not conserved)

Key Points:

  • Major irrigation scheme (Removed most of river inflow before it got to the Aral Sea)
  • River flow greatly decreased
  • Evaporation stayed the same

As sea level declined, it became two basins

Volume of water decreased due to imbalance of inflowing rivers and evaporation. The mass of salt remained the same, so salinity increased of the remaining water

Driven by short-term economic gain, leading to long-term economic disaster for communities that lived by the Aral Sea

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Calculating Velocities

Q = u.A

u = Q/A

A = cross-section area (m^2)

(Remember to always check your units!)

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Surface Exchange

Radiative heat fluxes:

  • Qs (1 - α) = Direct solar radiation (α = albedo)
  • Qb = back radiation

Latent heat transfer (Qe = heat transfer by evaporation)

Surface Heat Exchange occurs due to diff. in temp between sea surface and the atmosphere. Diffusion of higher to lower conc. from a warm surface to a cold atmosphere (Qh = Turbulent flux driven by temperature gradient)

Heat Budget: Qs (1-α) + Qv - Qb - Qh - Qe = Qt (Qv - Advection, Qt - Heat surplus/deficit) (Heat in - Heat out = change in temperature

Air-Sea Interaction (Consists of gas exchange and particulate matter (e.g. pollutants)):

  • Heat - Thermal stratification, Horizontal density gradients
  • Momentum - Haline stratification, Horizontal density gradients
  • Freshwater - Turbulence, Currents, Waves
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Distribution of Heat Input

Radiation decays exponentially through the water column

  • Typical Shelf Waters: >90% heat input within top 5m
  • Clear Water: 55% heat input top 1m. 70% input into top 3m

Cycle of Stratification and Mixing:

Mixing raises centre of gravity of the water column

Strong mixing - stratification column doesn't form - mote heat input when mixed - lower temperature in mixed state

Amount of heat input taken up by water column dependent on state of mixing

Max SST changes due to the amount of mixing take place

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Celtic Sea (Shelf Sea) - Seasonal Cycle

Time Frame: April 2014 - April 2015 (Strong seasonal cycle of heating)

- Cold water heavier than warm water. Density completely controlled by temperature as salinity stays constant

  • Stratification forms in April
  • Max. sea surface termperature in July
  • Deep water slowly warms until stratification is mixed out
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Fjords (Processes)

Key Points:

  • Glaciated environments and ROFI
  • Density determined by both temp. and salinity
  • Separated from ocean by a shallow entrance sill that restricts exchange


Vertical mixing powered by internal tides generated at shallow entrance sill. Can only replace water in basin if water coming in from ocean is heavier than water already in the basin.

Difference between shelf seas and fjords is that salinity changes during stratification in fjords, but salinity stays constant during stratification within shelf seas.

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Fjords (Clyde Sea Part 1)


  • Large fjord on west coast of Scotland
  • Water depths reach 180m within basin region
  • Connection to North Channel of Irish Sea is over a sill of depth 40m

Has salinity stratification where seasonality is necessary to reproduce observed shape of seasonal cycles in temperature and salinity, and hence density:

Summer: Cross-sill exchange confined to surface layers. Bottom water cut off from renewal and only modified by diffusion of warmer, freshwater water downwards driven by deep-water mixing

Winter: Cross-sill exchange and inflow ventilates whole column. Deep water replaved average twice by inflowing water during each winter

Brief period of mixing after temp. becomes unstable. Stratification virtually all-year round due to surface water being less saline than deeper water. But. in summer, surface water warmer

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Fjords (Clyde Sea Part 2)

Two Phases:

  • Deep water isolatedOR Deep water renewal

(water coming in from ocean and sinking to bottom of basin, pushing water upwards in basin)

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Fjords (Clyde Sea Part 3)

Extra Information from Research Paper:

Switchover between regimes become susceptible to episodes of complete vertical mixing

Water temperature low due to inversion in temperature structure

If system fails to mix completely in turnover, high cross-sill rates (inflow) results in :

  • reduction of temperature stratification
  • increase in water column stability

(Persistence of fully mixed state is a result of convection caused by intense cooling at the surface, sustained by a large, pre-existing heat reservoir in the deep water)

Deep water mixing energy supplied via internal oscillations

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Fjords (Estuaries - A physical introduction)

Keith R. Dyers

  • Presence of sills can restrict free exchange of water with the sea
  • Rocky floors or thin veneers of sediment. Only found in high latitudes of mountainous areas
  • River discharge small compared with total fjord volume. However, river flow often large with respect to the tidal prism, due to many fjords having restricted tidal ranges within their mouths

Deep Water Renewal (Four main processes involved):

  • 1. Tides - Spring tidal mixing at mouth can produce inward transfer of deeper, more dense water on each flood tide. Fortnightly renewal or monthly time-scale
  • 2. Meteorological forces - Down-estuary winds enhance entrainment bewteen brackish and mid-layers causing increased inflow at sill. Renewal intermittent
  • 3. River discharge - Increased discharge in surface layer creates enhanced mixing, Can lead to seasonal renewal
  • 4. Shelf processes - Annual cycle of water density off mouth will vary according to solar heating and variation in coastal current patterns. Renewal in late summer/ autumn.


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Production vs Respiration

Phytoplankton Production:

  • Uptake = carbon, nutrients
  • Release = O2
  • Production proportional to light intensity

Phytoplankton Respiration:

  • Uptake = O2
  • Release = carbon, nutrients
  • Respiration constant with depth

Compensation Depth:

  • Condition for net phytoplankton growth (intermediate)
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Biological Consequences of Seasonal Variation in S

1) Formation of stratification retains phytoplankton in euphotic zone (promotes spring bloom)

2) Presence of stratification isolates surface layer

3) If respiration > production, oxygen can get used up. Anoxic conditions sometimes found in fjords and lakes

4) As heat gets mixed down, nutrients get mixed up

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Shelf Sea Stratification

Vertical Mixing - Drive net CO2 drawdown and occurs only in stratified water. Accounts for 20-50% of total open-ocean CO2 storage through the shelf sea pump

Fixation of CO2 - Occurs in short-lived phytoplankton blooms in surface layer. More sustained growth of subsurface chlorophyll maximum (SCM) - observed to persist through summer stratification period

Thermocline Shear - Internal Tides. When stratified tidal flows over sharp topography, energy transfer from barotropic tide to an internal wave that may radiate away from the generation zone. Effectiveness of driving thermocline dependent on how much energy is lost through friction at the seabed

Baroclinic near-inertial oscillations - Circular motions rotating clockwise in N.Hemisphere. Triggered by abrupt changes in forcing and usually to sudden changes in wind direction

(Internal tides more efficient at mixing as they generate turbulence where gradients are largest, in thermocline, whereas barotrophic tends to mix already homogenous water close to the seabed)

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Turbulent Flow:

  • Large internal friction - known as eddy viscosity
  • Transfer through turbulent eddies. Move 'packets' of fluid between different layer

Laminar Flow:

  • Small internal friciton - known as molecular viscosity
  • Transfer through molecules moving between adjacent layers

(Eddy viscoity ~2-4 orders of magnitude greater) (Is the transfer of heat, momentum, salt etc.)

(Across distances > few mm, eddies of turbulence mix water more effectively than molecular motion. Random movement of eddies is much larger than molecular. Eddy diffusion is also different in that it is the same for all properties - i.e. heat, salt, and nitrate will have the same eddy diffusion constant)

(Typical eddy diffusivity for horizontal diffusion in ocean is ~500 m2s-1, about 10^9 times the molecular diffusivity for heat)

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Boundary Layer Turbulence

Fricitonal drag at sea bed produces a velocity shear. Near bed flow is slowed down relative to that higher up

Turbulence produced by the flow over and around roughness elements of the bed.

Energy for turbulent mixing derived from kinetic energy dissipated by water flowing across a rigid rough boundary

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Surface Mixed Layer

Surface Mixed Layer:

  • Thin mixed layer at surface due to convection
  • Lose heat from surface of ocean cooling water will then sink
  • When addressing wind stress, a larger surface mixed layer is formed (pycnocline)
  • Rate of kinetic energy transfer to turbulent eddies (aW^3) (a = constant, W - Wind speed)
  • Increase in PE calculated by b.h.Q (b = constant, h = surface layer thickness, Q = heating rate)

Wind-induced shear -> Turbulence -> Mixing

Deep Ocean:

  • Turbulent mixed layer usually overlies the region the region of stable stratification (seasonal pycnocline) 
  • Where turbulence is infrequent due to shear instability and breaking internal waves
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Shelf Sea Tides

When moving tides from deep ocean to shelf sea, tidal currents speeds increase, as well as the tidal range. Result of energy propagating from ocean onto shelf, under influence of the Earth's rotation (Kelvin Waves) that are reflected by coastlines

Shelf width often comparable to tidal wavelenth, where resonance may occur. Large tides and strong tidal range

Long Wave Speed:

c = (gD)1/2  (D = water depth)

c = f x λ  ( λ = tidal wave length)

  • As tidal wave progresses to shallower water, the wave slows down
  • D is decreased
  • If f stays the same, and λ increases, wave amplitude is increased
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Tidal Friction in the Menai Strait

Tidal heights are differenty at each end of the Strait due to a surface slope

  • Forces along channel pressure gradient
  • Tidal friction influences position of moon in relation to the Earth

Flow opposed by friction:

  • Removal of energy (m.v^2) and momentum (m.v) from flow
  • Sometimes referred to as Reynold's Stress (τ
    (Equal to mean rate of transfer of momentum across a surface by turbulent motion)

Balance between flow and friction:

  • Tidal flow not constant with depth
  • Friction greatest near seabed (becomes lesser nearer to the surface)
  • Force driving flow is gravitational pull forcing water to flow down the Strait (Slope term growing faster than friction opposing the flow)
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Water Column Structure in Shelf Seas

Vertical structure controlled by interaction of buoyancy input with two 'stirring engines'

  • Stress on seabed determined by turbulence
  • Big tidal amplitudes determine nature of water column structure through a heating, stirring balance
  • Mixing occurs when turbulence wins out in the heating, stirring balance

Tidal Mixing and Plankton Production:

If tidal currents are strong enough to mix the water colum all year, there is a continuous supply of nutrients from near-bottom waters up to the euphotic zone. Permits phytoplankton production to continue at a good level throughout the summer

Different in stratified waters, where supply of nutrients tends to become depleted after the spring bloom

(Tidally mixed areas like George's Bank, near Gulf of Maine, and Dogger Bank in the North Sea have levels of primary production considerably higher than adjacent stratified areas of the shelf. These sites often selected as breeding grounds for commercially important fish)

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Seasonal Stratification and Tidal Mixing Fronts

  • Turbulence generated by tide is strong enough to destroy stratification. Heating < tide-mixingHigh u and/or low H
  • Turbulence generated by tide NOT strong enough to prevent thermal stratification. Heating > tide-mixing. Low u and/or high H

(Can predict h/u^3 critical value)

Rate of change of PE of shelf sea water column, driven by surface heat flux:

△P.E / △t = b.h.q   (Q = Rate of heat flux through surface (Wm^-2)

Range of increase of PE of shelf sea water column, driven by surface heat flux:

1 / H △P.E / △t = c. uo^3 / H (H = depth (m). Establishes critical value for location of the shelf sea front. uo = Tidal current amplitude (ms-1)

Front separates mixed and stratified zones. Occur at same location each year due to location determined by tidal current strength

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Physics of Tidal Fronts

Key Idea:

Turbulence generated by high tidal currents keeps water over some shallow regions mixed all year while the quieter regions, in the deeper waters, become stratified in summer

Dietrich (1950) suggested that summertime front across the western end of the English Channel exists because of increase in turbulent mixing in the shallower regions of the channel

Extensive areas of tidal mixing occur in the southern North Sea, the English Channel and the southern Irish Sea.

The Celtic Sea is a stratified region. Development of spring bloom in this region shows thermocline establishing first in region of weakest tidal currents, then gradually spreading to areas of stronger tidal currents

In shallow water, models incorporating wind mixing effects are most accurate. In deeper waters, the wind effects decline in importance

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The Biology of Upwelling Fronts

(Front is where the pycnocline intersects the surface of the ocean)

  • During upwelling event, front first forms close to shore, then moves offshore
  • Equilibrium reached at which front ceases to move offshore
  • Upwelled waters, as they continue to move offshore, driven down beneath offshore waters
  • At surface there is a convergence of waters (buoyant biological material accumulation)
  • When wind stress decreases, and upwelling ceases, the front retreats landward and may disappear

Presence of the front marked by sharp temperature transition from cold, nutrient-rich upwelled water inshore to the warmer, less nutrient-rich stratified water offshore

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Mesoscale Residual Flow

(Moving particles, such as zooplankton, around shelf sea fronts)

Drivers of flow:

  • Wind-driven
  • Density-driven (Residual circulation is mainly density-driven)
  • Boundary-forced

Residual Currents:

  • Residual currents in a tidal front are primarily along the front
  • However, a weak cross-frontal circulation induced by internal friction is also expected
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Vertical Exchange


  • Water column structure predicted by water depth and tidal current speeds
  • Vertical exchange processes dominate
  • Varying rates of warming of isolated deep water is a result of varying levels of mixing across the thermocline


  • Rate parameterised by diffusion coefficient
  • Magnitude of the diffusion coefficient determines magnitude of the vertical flux
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Subsurface Chlorophyll Maximum

(Nutrient fluxes sustaining primary productivity through subsurface chlorophyll maximum)

  • Consequence of vertical mixing (across seasonal thermocline) is injection of deep water nutrients into nutrient deplete surface layer (euphotic zone)
  • Upward vertical flux, Fv, production can be inferred using Redfield Ratio

Fv = -Kz N / (Kz = Calculated from profiles of E - efficiency of tidal stirring. △N Diff. in nitrate between surface and deep water. △Z Thickness of pycnocline)

English Channel:

  • Persistent chlorophyll maximum from the surface down to the pycnocline on the stratified side of the front
  • Subsurface chlorophyll maximum in pycnocline some distance behind the front (Result of vertical transport of nutrients across the pycnocline during the passage of internal waves)

Promotes phytoplankton at deepest point of sufficient light. Resulting blooms known as subsurface chlorophyll maximum. Vertical nutrient flux into post blooms euphotic zone promotes new production

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Enhanced Primary Production at Fronts

Separate low nutrient stratified water from higher nutrient mixed water:

  • Often observed to be regions of high chlorophyll biomass
  • Fronts are regions of enhanced primary production, where nutrients go across front, making them productive waters

Increased biological activity at tidal fronts:

  • Current speeds increase during spring tides
  • Level of turbulence generated at bottom increases
  • Leads to increased mixing in water column and area of mixed water increases
  • Boundary between mixed and stratified water moves toward deeper water
  • When tidal currents decrease during neap tides, turbulence declines and front moves toward shallower water, allowing area of stratified waters to move into region of unstratified water
  • As front advances, newly stratified water will contain nutrient levels characteristic of previously mixed waters, presumed to be depleted by biological activity
  • Thus, newly formed part of the front should contain higher concentrations of nutrient than the water that has been stratified for a long time
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How Fronts Enhance Biological Productivity

(In upper mixed layer of stratified water in summer, phytoplankton growth is usually nutrient-limited because the presence of a pycnocline restrict upward movement of nutrients from lower regions, where they are more plentiful. Any mechanism causing transfer of nutrients to surface layer is likely to lead to enhanced biological production)

1. The Spring-Neap Tidal Cycle - Water may be tidally mixed at one stage of tidal cycle, and stratified at another. Nutrients brought up during mixing phse and utilized in upper mixed layer during stratified phase.

2. Cross-frontal transport Baroclinic eddies, in which parcels of nutrient-rich water break through to the stratified side, have been observed by remote sensing

3. Vertical Transport - Some evidence suggests conditions in frontal zone favorable for the vertical transport of nutrients through front to the stratified water above. Movement could result in enhanced phytoplankton in the immediate vicinity of the front

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Regions of Freshwater Influence

Characterised by salinity gradient producing a density gradient

Horizontal density gradient advected by tide.

Surface layers moved further than bottom layers (Vertical shear in tidal current)

Ebb Tide:

  • Produces stratification (Light FW pushed out over heavier water. Occurs due to shear)
  • Takes lighter water offshore (Periodic stratification over tidal and spring-neap cycles)

Flood Tide:

  • Produces instability (Heavier, saltier water goes over lighter water)
  • Sinks, resulting in overturning (Convection)
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Aspects of Tidal Flow

Tidal Advection:

Tidal currents move back and forth with little net movement

Vertical Structure:

Tidal current sheared near seabed on account of feeling effects of friction at the seabed

Distance moved in tidal stream (km) is equal to maximum tidal current (m/s) x 14

Spring-neap tidal cycle:

  • During spring tides the tidal currents are at their maximum strength (tidal mixing extends to deeper water regions)
  • Nutrients from below the thermocline will be brought to surface in area covered by the excursion of the front
  • As tidal currents relax towards the neaps, the area of tidally mixed water decreases, permitting stratification to return in that same area covered by excursion of the front
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Tidal Straining

  • Differential advection of horizontal density gradient due to shear in tidal flow
  • Surface water pushed further than deep water because of velocity shear, the tidal excursion is greatest near the surface

Ebb Tide:

  • Near shore, light water will travel offshore further at surface, which induced stratification
  • p1 < p2

Flood Tide:

  • Offshore water will travel further at the surface
  • Pushing heavy water onto light water
  • Results in instability (thus convection)
  • Results in a mixed water column
  • p1 > p2
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Frontal Dynamics


  • Barrier separating two water masses of different densities
  • Presence of horizontal gradient results in the formation of strong, residual current known as a frontal jet


  • Take water from one side of front to the other
  • Geostrophic balance 'departures' result in formation of instabilities that drain energy into eddies, transferring water across the front
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Spring-neap Frontal Adjustment

Tidal current varies over lunar month between spring-neap tides (Front thus moves)

Current increase:

  • Turbulence increases
  • Energy available for mixing increases
  • Depth of water (Turbulence energetic enough to breakdown stratification will increase)

Current decrease:

  • Turbulence decreases
  • Front moves towards shallower regions
  • Area of stratified water can then increase again

Newly stratified water behind advancing front will contain nutrient characteristics of previous mixed water (promoting primary production)

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Extra Information - Sensible Heat

Direct contact between atmosphere and ocean enables energy exchange between them by conduction (Occurs because molecule collisions at interface transfer energy from faster moving (warmer) molecules to slower moving (cooler) particles)

Turbulence accelerates exchange process (increases collision rate)

Qh = PacHw (Tsea - Tatmos) (Brackets = temperature difference. Pa = Air density, w = wind speed, cH = Dalton number - function representing atmospheric turbulence)

(Values range from 0.83 x 10^-3 in a CALM atmosphere)

(Values range from 1.1 x 10^-3 in a TURBULENT atmosphere)

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Extra Information - Latent Heat

Water evaporating results in energy supplied from ocean surface energy to free these molecules from intermolecular bonds within the liquid (i.e. energy is lost)

Difficult to measure at sea, so is estimated empirically:

QE = cEPaw(qs = qa) (qs = Saturated specific humidity at sea surface, qa = Specific humidity at 10m above the sea bed)

Usually Qs << Qe

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Extra Information - Momentum

Wind blowing across ocean surface feels a drag force and induces shear stress on the surface

(Results in transfer of momentum from wind to the ocean)

Difficult to measure so is represented by a quadratic drag law (Bulk Parameterisation)

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Extra Information - Energy Inputs to Turbulence

Wind stress at sea surface:

Tidal stress at seabed:

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Extra Information - Ocean Tides

  • Moons gravitational force acts on all parts of the Earth
  • Strength of force is always proportional to inverse square of distance of the moon
  • Causes ocean to 'bulge' directly under moon (i.e. where Earth-moon distance is shortest, and so force strongest)
  • Second 'bulge' will form on opposite side of Earth (i.e. where Earth-moon distance is largest, and so force weakest)

(As Earth rotates, the ocean 'bulge' will stay beneath the moon. Resulting in two 'high' tides per Earth's rotation)

Long Wave:

  • Semidiurnal (i.e. two tides per day)
  • Tidal Range - Difference between low and high water tidal levels
  • Tidal Amplitude - Half the tidal range
  • Tidal Phase - Time of high water relative to HW time at Greenwich (measured as an angle of 0-360 degrees)
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Extra Information - Tidal Friction

75% of tidal energy dissipated in shelf seas:

(Turbulence thus driven by dissipation of tidal energy)

(Brings about mixing)

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