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GE0-3112 Sedimentary processes and products Lecture 2. Fluid flow and sediment grains. Geoff Corner Department of Geology University of Tromsø 2006 Literature: - Leeder 1999. Ch. 4, 5 & 6. Sedimentological fluid dynamics.

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Contents ► 2.1 Introduction - Why study fluid dynamics ► 2.2 Material properties ► 2.3 Fluid flow ► 2.4 Turbulent flow ► Further reading

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2.1 Introduction - Fluid dynamics ► Concerns how fluids transport sedimentary particles. (NB. Fluids are liquids and gasses) ► Fluid flows can be described using basic physics, although sedimentary particles add complication.

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Why study fluid dynamics? ► Examples of practical problems Pebbles on a sandy surface Slidden boulder in Death Valley Deformation structure

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Notes on scientific notation ► Fundamental units of physical dimension (dimensional analysis): M (mass), L (length), T (time). ► System of units of measurement: Metre-kilogram-second (SI, Systèm Internationale d’Unités). CGS, centimetre-gram-second (informal) ► Greek letters (used in formulas).

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2.2 Material properties ► Three states of matter (solid, liquid, gas); have different properties and behaviour. ► Solids (e.g. rock, ice): have strength and resist shear (limited...deformation). ► Liquids (e.g. water): deform readily under shear stress; incompressible. ► Gasses (e.g. air): deform readily under shear stress; compressible ► NB. Some substances have behaviour intermediate between liquid and solid (e.g. mud-water mixtures).

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Material properties of fluids ► Density ► Viscosity Density and viscosity are temperature dependent.

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Density ► Density (ρ) is mass (m) per unit volume [ML-3; kg/m 3 ]. ► Solids (rock, ice, sediments) have strength and resist shear (limited...deformation). ► Liquids (water) deform readily under shear stress but are incompressible. ► Gasses (air) deform readily under shear stress and are compressible. ► NB. Some substances have behaviour intermediate between liquid and solid (e.g. mud-water mixtures). ► Density affects:

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Fluid momentum Buoyancy (density ratio)

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Density vs. temperature and pressure ► Water density decreases with temperature (above 4 o C) and increases with pressure. ► Air density decreases with temperature and increases with pressure. WaterAir

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Example 1: thermal stratification in lakes

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Density vs. salinity ► Water density inceases with salinity. ► Salinity examples: Freshwater lakes Norway: Freshwater lakes Norway:

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Example 2a: saline stratification in fjords Syvitski 1987

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Example 2b: density driven thermohaline circulation in the ocean ► Example of flow generated by density and temperature differences: thermohaline flow

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Density vs. sediment content ► Density increases with sediment content

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Example 3: Hypo- and hyperpycnal flows beyond river mouths ► Hypopycnal = less dense ► Hyperpycnal = more dense ► Density differences between the inflowing and ambient water can be caused by a combination of temperature, salinity and sediment concentration differences.

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Viscosity ► Dynamic (or molecular) viscosity (μ): [ML -1 T -1 ; kg/m s, or N s/m 2 ] (A measure of a fluid’s ability to resist deformation) ► Kinematic viscosity (ν): v=μ/ [L 2 T -1 ; m 2/ s] (Ratio between a fluid’s ability to resist deformation and its resistance to acceleration)

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Dynamic (molecular) viscosity ► Viscosity controls the rate of deformation by an applied shear, or: ► Viscosity is the proportionality factor that links shear stress to rate of strain: ► Dimensions are: [ML -1 T -1 ; kg/m s] ► Viscosity is much higher in water than in air. Shear stress (tau) Viscosity (mu) Strain rate

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Viscosity vs. temperature ► Viscosity varies temperature: In water it decreases. In air it increases.

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Viscosity vs. sediment concentration ► Fluid viscosity increases with sediment content.

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Viscosity vs. shear rate ( Newtonian and Non-Newtonian behaviour ) ► Newtonian fluids: Constant viscosity at constant temperature and pressure. Continuous deformation (irrecoverable strain) as long as shear is maintained. ► Non-Newtonian fluids: Viscosity varies with the shear rate. Various types of Non-Newtonian behaviour/substances: ► Pseudoplastic, Dilatant, Thixotropic, Rheopectic.

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Non-Newtonian behaviour ► Pseudoplastic: μ decreases as rate of shear increases. ► Dilatant: μ increases as rate of shear increases. ► Thixotropic: μ decreases with time as shear is applied. ► Rheopectic: μ increases with time as shear is applied.

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Examples from nature Newtonian viscous fluid Non- Newtonian Increasing viscosity

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2.3 Fluid flow ► Flow types ► Controlling forces ► Dimensionless numbers ► Flow steadiness and uniformity ► Flow visualisation and flow lines ► Laminar and turbulent flow (Reynolds number) ► Turbulent flow

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Flow types ► Newtonian: continuous deformation (irrecoverable strain) as long as shear stress is maintained (linear stress-strain relationship). ► Plastic: initial resistance to shear (yield stress) followed by deformation. Bingham plastic: constant viscosity Non-Bingham plastic: viscosity varies with shear ► Non-Newtonian pseudo-plastic ► Non-Newtonian thixotropic ► Non-Newtonian dilatant

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Fluid flow – driving forces ► Momentum-driven flows (externally applied forces) (Gravity and pressure differences drive flows) ► Buoyancy-driven flows (Density difference drives flows) (Density difference drives flows)

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Controlling forces ► Buoyancy forces (density controlled) ► Viscous forces (viscosity controlled) ► Inertial forces (momentum controlled) ► Gravitational forces

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Dimensionless numbers ► Dimensionless ratios provide scale- and unit-independent measures of dynamic behaviour. ► Two important ratios in fluid dynamics are: Reynolds number: ratio of inertial to viscous forces Froude number: ratio of inertial to gravity forces

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Flow steadiness ► Relates to change in velocity over time Steady flow - constant velocity Unsteady flow – variable velocity Steady flow (e.g. steady turbulent river measured over hours) Unsteady flow (e.g. decelerating turbidity current)

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Flow uniformity ► Relates to change in velocity over distance Uniform flow - constant velocity (parallel streamlines) Non-uniform flow – variable velocity (non-parallel sls) Uniform flow (e.g. in channel) Non-uniform (diverging) flow (e.g. at river mouth)

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Flow visualisation - flow lines ► Streamline - line tangential to the velocity vector of fluid elements at any instant. ► Pathline - trajectory swept out over time (e.g. long exposure of a spot tracer). ► Streakline - instantaneous locus of all fluid elements that have passed through the same point in the flow field (e.g. short exposure of a continuously introduced tracer. Pathlines StreamlinesStreaklines

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Flow visualisation – reference frames Streamlines for flow pattern round an object moving to the left through a stationary fluid (Langrangian velocity field) Streamlines for flow past a stationary object (Eulerian velocity field)

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Laminar and turbulent flow ► Flow type changes with increasing velocity - from laminar to turbulent. from laminar to turbulent. ► The relationship is described by the Reynolds number. Rapid pressure drop/ change in flow type.

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Reynolds number ► Reynolds number (Re) is the the ratio of viscous forces (resisting deformation) to inertial forces (ability of fluid mass to accelerate). ► The transition from laminar to turbulent flow occurs at about Re = 500 – 2000. Inertial force Viscous force Molecular viscosity Velocity Density Depth

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Flow patterns ► Laminar flow: parallel flowlines (low Re). ► Turbulant flow: irregular flowlines with eddies and vortices (high Re). Laminar flow Transitional to turbulent flow Turbulent flow Streaklines

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Velocity distribution in viscous flows Parabolic Newtonian laminar flow velocity profile. Plug-like non- Newtonian laminar flow (e.g. debris flow). Flow retardation in a boundary layer

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2.4 Turbulent flow ► Turbulent eddies ► Bed roughness ► Flow separation

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Turbulent eddies Backwash/rip-current eddies at Breivikeidet Eddy movement in x-y space with time (t 1 -t 2 )

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Instantaneous velocity

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Bed roughness Turbulent stresses dominate Viscous sublayer Viscous forces dominate +η (Boussinesq’s eddy viscosity)

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Bed roughness Viscous sublayer (smooth bed) No viscous sublayer (rough bed)

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Shear velocity and skin friction Smooth Rough

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Turbulent eddies in air Streaklines viewed in the x-z plane (i.e. plan section) Streaklines viewed in the x-y plane (i.e. flow- parallel vertical section)

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Components of turbulent eddies Sweep (fast) Burst (slow) Streaks (close to bed)

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Turbulent eddies in water Flow at successively higher positions above the bed (a- d) Slow flow pattern in viscous sublayer Flow pattern in turbulent boundary layer Macroturbulence in outer regions of flow Sand particle flow in viscous sublayer shown at 1/12 s time intervals ’Sweep’ event

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Kelvin-Helmholz vortices ► Important mixing mechanism at junction of two fluids, e.g. at junctions of tributaries or mixing water masses, at fronts and tops of density currents, etc. Likely causes of K-H instability: a)-c) velocty differences across boundary layer or in density- stratified flows; d)-e) shear layers produced by pressure differences.

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Flow separation Boundary layer separation point Boundary layer reattachment zone (downstream)

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Accelerating flow, decreasing pressure Decelerating flow, increasing pressure, redardation and separation of flow closest to the bed

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2.5 Sediment grains in fluids ► Settling (Stokes velocity) ► Threshold velocity ► Rolling, saltation and suspension ► Bedload, suspended and washload

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Settling ► Fall velocity increases with increasing grain size Stokes equation applies: - Low Re (< 0.5) - No viscous flow separation - Low sed. concentration Silt-f.sand Velocity increase reduced: - Higher Re (>1) - Turbulent drag - Non-spherical grains - High sed. concentration NB! Clays flocculate

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Particle transport ► Critical threshold (shear) velocity Lift + drag forces = resisting (gravity) forces. ► Low pressure over grains (due to acceleration, cf. Bernoulli’s equation) causes lift.

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Particles above the bed ► Instantaneous local shear varies due to burst/sweep events. ► Once entrained, drag forces increase relative to lift forces. More drag More lift

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Threshold velocity ► Threshold velocity for motion increases with increasing grain size. SiltSand Pebbles

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Impact threshold in air ► Falling grains in air can induce grain motion on impact above the impact threshold velocity. ► Velocity for normal threshold is higher.

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Grain motion ► Rolling, saltation, suspension

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Types of transport loads ► Washload ► Suspended load ► Bedload

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Further reading ► Allen, J.R.L. 1970. Physical processes of sedimentation. Chapter 1 covers the same ground as Leeder and explains clearly the principles involved; good supplementary reading for aquiring a sound grasp of the physics of fluid dynamics and sedimentation. Alternatively consult the more encyclopedic: ► Allen, J.R.L 1984. Sedimentary structures: their character and physical basis. A more encyclopedic alternative to the above if it is unavailable.

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