Turbidity current flow over an obstacle and phases of sediment wave generation

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Corey Gibson
5 years ago
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Glinsky (CEO Science Leader) Moshe Strauss (Nuclear Research

1 Turbidity current flow over an obstacle and phases of sediment wave generation Michael E. Glinsky (CEO Science Leader) Moshe Strauss (Nuclear Research Center, Israel) Three Sisters -- aboriginal womans place for doing business, near BHPB Yandi iron ore mine 1

2 Roadmap description of the system & computations what is a physical phase and phase diagram (example of water) self sustainment of single flow, single grain two phases of flow and phase diagram sediment wave formation with multiple flows three phases of erosion/deposition relationship to self sustainment wavelength structure of deposited substrate (geologic facies) conclusion it s the physics self sustainment ==> phases of SW ==> geologic facies one-to-one correspondence between geologic facies and phases of physical self organization of system 2

3 A real example of a sediment wave Monterey Channel, offshore California USA levee channel splay breached channel levee (splay) depth of sea bottom deep shallow 3

4 Parts of the computer simulation Simulation of the fluid + suspended grains Interaction between the fluid and the bottom Keeping track of what is deposited on or eroded from the bottom 4

5 Simulation of the fluid and suspended grains mass continuity equations for each grain size c i t + ( u r + u si ĝ) c i = 1 2 c i S c R e settling velocity particle diffusion momentum continuity equation, ma=f incompressibility, EOS r u t + r u ( ) r u = p + 1 R e 2 r u + cĝ pressure force gravity force viscous drag force r u = 0 x and c y L 0 c 0 u scaled by u b gr * L 0 c 0 t scaled by scaled by scaled by L 0 / u b = 250 m = 0.8 % = 46 s = 5.4 m/s d i scaled by 3 d 0 ν 2 / R * g R pi d i / d 0 scale of particle dissipation = 41 µm = 42 R * ρ g ρ f ρ f ( ) 3/2 R e u b L 0 / ν = L 0 / d e d e ν 2 / R * c 0 g ( ) 3/2 u si = f (R pi ) = 10 9 = 200 µm scale of fluid dissipation 5

6 Simplified equations eliminate pressure, set Sc=1 (particles transported as fluid) and write in terms of stream function and vorticity where c i t + r u + u si ĝ ( ) c i = 1 R e 2 c i ω t + ( u r )ω = 1 2 ω + ( ĝ c) R z e ω = 2 ψ = F(ψ ) r u ˆx y ŷ x ψ = G(ψ ) ω ( u r ) z only {c } and ψ i to solve for d i θ 0 X HW = HL 0 : H parameters are: ({u },ĝ, R ;ψ ) si e 0 (d,θ, H ) 0 6

7 Resuspension brings initial concentration back into problem Garcia and Parker resuspension model J i = u si (ĝ y c ε si ) settling resuspension ε si = a c 0 z i 5 1+ a 0.3 z 5 i c 0 explicit dependance on u * = u z i α * α 1 R 2 pi = f (u *, R pi ) u si 1 u x R e y limit to u * = ω b f shr R e turbulent closure parameters are: (d,θ 0, H,c 0 ) since Re simulated is 10 3 instead of real value of

8 Interaction between the fluid and the bottom Resuspension of grains from the bottom is described using Garcia-Parker empirical relationships Resuspension flux finer grains coarser grains Velocity of fluid near the bottom For grains of different sizes 8

9 Boundary conditions on the fluid no-slip slip Turbidite flow slip immediate transport through boundary layer deposition no-slip resuspension L a 9

10 Phases of water P system parameters: (a) temperature, T (b) pressure, P T : m v 2 / 2 f(r) solid liquid gas f(r) f(r) r r r phases: (a) solid (b) liquid (c) gas correlation properties 10

11 Phase diagram of water P liquid solid gas phase is determined by the value of the system parameters, system parameter space is divided into regions for each phase T 11

What are the phases of turbidite deposition in a channel W H 2D θ 0 system parameters: (a) initial lock particle concentration, (b) average particle diameter, (c) slope angle, θ 0 (d) current

12 What are the phases of turbidite deposition in a channel W H 2D θ 0 system parameters: (a) initial lock particle concentration, (b) average particle diameter, (c) slope angle, θ 0 (d) current size, HW : H (e) initial aspect ratio, H / W (insensitive) c 0 d 0 d 0 c 0 What are the phases of: (a) single flow? (b) multiple flow substrate surface? (c) multiple flow deposited substrate? 12

13 Two phases of single flow slope = 3 degrees, deposition outweighs erosion, decaying turbidity current ( depositing phase) collapsing building slope = 4 degrees, erosion outweighs deposition, growing turbidity current ( self sustaining phase) avalanche 13

14 Closer look at evolution of single flow self sustaining self sustaining depositing depositing 14

Characteristics of phases of single flow depositing (a) monotonically decreasing mass to 0 (b) suppressed and decaying front velocity (c) ill-defined head of current with

15 Characteristics of phases of single flow depositing (a) monotonically decreasing mass to 0 (b) suppressed and decaying front velocity (c) ill-defined head of current with un-elevated density self sustaining (a) exponentially increasing mass (b) elevated front velocity, asymototing to constant (c) well-defined head of current with elevated density 15

16 The phase diagram of single flow current size (solid) H slope critical angle (degrees) θ 0 resuspension (dashed) slope angle (solid, degrees) θ 0 particle concentration (dashed) c 0 average particle diameter d 0 16

17 Three phases of multiple flow turbidite deposition H=0.5, slope=0.5 A no sediment waves, no SW H=1.0, slope=0.5 B buildup of sediment waves, SW buildup C H=1.5, slope=1.5 growing sediment waves, SW growth 17

18 Closer look at evolution of turbidite deposition (no SW) A (SW buildup) B particle concentration 0% 1.5% F2, kinetic/potential velocity concentration resuspension (SW growth) height C 0 x (m)

19 Closer look at evolution of turbidite deposition (continued) C B C B A A 19

20 Characteristics of multiple flow turbidite deposition no SW slope never unstable to SW growth SW buildup slope sometimes unstable to SW growth SW growth slope always unstable to SW growth (a) no development of SW (b) no periodic structures in flow (c) monotonically decreasing mass (d) no significant erosion (e) suppressed front velocity (f) no evidence of individual flows in bedding (g) one massive bed fining downslope, coarsing from bottom to top (a) rapid local SW development to steady state profile (b) periodic flow structure (c) relatively constant mass with maximum (d) no appreciable erosion (e) reference front velocity (f) little evidence of individual flows in bedding (g) one massive bed fining downslope, oscillatory bottom to top structure (a) initially exponential growth of global SW (b) periodic flow & erosion structure (c) monotonically increasing mass (d) significant erosion, exponentially growing updip within flow (e) enhanced front velocity (f) evidence of individual flows in bedding (g) complex bed structure 20

21 Phase diagram of multiple flow turbidite deposition in (θ 0, H,c 0,d) space A B C 21

22 Resuspension is driving phase boundary as for single flow resuspension W=2 phase boundary 22

23 Study of dependance of SW wavelength on particle concentration y (m) concentration = concentration = 1.2 x (m) 5500 average grain size (µm)

24 Dependance of particle concentration on wavelength : 1 / c 0 wavelength is insensitive to other parameters 24

25 Geologic facies are physical phases single flow multiple flow substrate surface deposited substrate physics self sustainment geologic facies! sediment wave phases 25

The future: phases could be identified by new texture attributes path integral formulation of data assimilation monte carlo eliminate implicit time

organisation, based on iterative wavelet transformation data assimilation or synchronisation of fundamental variables leading to prediction of

26 The future: phases could be identified by new texture attributes path integral formulation of data assimilation monte carlo eliminate implicit time step fundamental coordinates of dynamics (related to fundamental excitations of physical system) best coordinates to identify phase of self organisation, based on iterative wavelet transformation data assimilation or synchronisation of fundamental variables leading to prediction of effective parameters of texture unique fingerprint of texture excitation of order 3 p N s independent of chaotic phase p = (N s ;s 1,s 2,,s Ns ) N s = order of exitation 26

27 Conclusion It s the physics Geologic facies are physical phases 27

Uniform Channel Flow Basic Concepts. Definition of Uniform Flow

Uniform Channel Flow Basic Concepts Hydromechanics VVR090 Uniform occurs when: Definition of Uniform Flow 1. The depth, flow area, and velocity at every cross section is constant 2. The energy grade line,