Unraveling the complexity of geophysical systems

using idealized analogue configurations

Cyril Gadal

Institut de Mécanique des Fluides de Toulouse (IMFT), France

Academic background in short

PhD on sand dunes (IPGP/PMMH, 2017–2020)

with Clément Narteau & Philippe Claudin

PostDoc on turbidity currents (IMFT, 2021–2022)

with Laurent Lacaze & Matthieu Mercier

PostDoc on the clogging of riverbeds (IMFT, 2023)

with Laurent Lacaze & Matthieu Mercier

PostDoc on the self-organization of cohesive granular flows (Manchester)

with Nico Gray & Chris Johnson

Common point

Apprehending complex geophysical systems using simple analogue configurations!

Fundamental knowledge

  • smaller scales
  • isolated process knowledge
  • …

→

Complex natural system

  • many entangled processes
  • wide range of spatial and temporal scales
  • difficult measurements

↓

Simpler analogue configurations

  • selected/controllable processes
  • experiments/numerical/analytical models

↓

Going back to the field

  • validation from observations
  • guide in the interpretation of field data

→

Fundamental knowledge

  • interaction between processes
  • analytical models
  • …

From a hydrodynamic instability to dune patterns shaping sand seas

Dunes gathering at the bottom of a small mountain in the Taklamacan desert, in China.

Sand dunes as a complex system

Window width: \(10^4\) km. @GoogleEarth

Sand dunes as a complex system

Window width: \(10^3\) km. @GoogleEarth

Sand dunes as a complex system

Window width: \(10^2\) km. @GoogleEarth

Sand dunes as a complex system

Window width: \(10^1\) km. @GoogleEarth

Regular patterns at all scales!

Sand dunes as a complex system

Dunes in the Rub’al-Khali desert, Yemen

Dunes in the Rub’al-Khali desert, Yemen

What controls the patterns/shapes, and associated dynamics?

credits: GeorgeSteimetz (main image), NASA (martian dunes), Jana Majk (underwater ripples), Chris M Morris (nebkha), Paul van Schalkwyk (sand storm)

A conceptual model for sand dunes emergence


  • Under a unidirectional wind:
    • periodic ridges
    • perpendicular to wind direction
    • \(\lambda_{\rm max} \sim 15~\textrm{m}\), \(\lambda_{\rm c} \sim 10~\textrm{m}\) (eolian, earth)

\(\rightarrow\) Direct validation?

Direct validation from field data

Tenger desert, China

White Sands dune field, USA

Hardly controllable \(\rightarrow\) difficult to study specific parameters \(\rightarrow\) need for controllable analogue systems!

Gadal et al. (2020) “Spatial and temporal development of incipient dunes”, Lü et al. (2021) “Direct validation of dune instability theory”

An analogue subaqueous experiment

  • aeolian dunes: \(\lambda_{\rm min} \sim 10~{\rm m}\) \(\rightarrow\) impossible in the lab!
  • \(L_{\rm subaqueous} \sim \frac{\rho_{\rm air}}{\rho_{\rm water}} L_{\rm eolian}\) \(\rightarrow\) possible!

Experimental set-up (@Sylvain Courrech du Pont, MSC)

Parallel ridges emerging from a randomly perturbed bed.

only analogue to eolian dunes, i.e fluid viscosity is different (hydrodynamic, \(\mathcal{R}e_{\rm p}\), transport modes)!

Gadal et al. (2019) “Incipient bedforms in a bidirectional wind regime”

An analogue subaqueous experiment

\(\rightarrow\) Pattern orientation as a function of the flow orientations:

\(\rightarrow\) Pattern wavelength as a function of the flow velocity:

Gadal et al. (2019) “Incipient bedforms in a bidirectional wind regime”

An analogue cellular automaton model for more complex configurations

Statistical state transitions in the ReSCAL dune model [Gao et al. 2015]

Barchan and star dune in the ReSCAL dune model [@Clément Narteau]
  • global dynamics from nearest neighbor interactions
  • non-linearities of flow and granular physics
  • able to reproduce many different dune patterns

An analogue cellular automaton model for more complex configurations

\(\rightarrow\) Shape of a sand pile under unimodal wind regimes

\(\rightarrow\) Downwind side of a sand patch

Rub’al-Khali desert, Yemen @George Steinmetz

Gao et al. (2018) “Morphodynamics of barchan and dome dunes under variable wind regimes”, Gadal et al. (2020) “Periodicity in fields of elongating dunes”

In a nutshell

Analytical instability model for more complex situations

  • boundary conditions: spatio-temporal instability, convective

  • from unidirectional to any wind regimes: 3D model

Non-linear dune patterns characterization

Linear dune properties

Orientation = \(\mathcal{F}({\rm wind~sequence}, {\rm sediment~properties}, {\rm sand~cover})\)

Using dune physics to interpret desert systems

Modern winds can explain all dune orientations!

  • Orientation = \(\require{cancel} \mathcal{F}(\underbrace{\rm wind~sequence}_{?}, \cancel{\rm sediment~properties}, \underbrace{\rm sand~cover}_{\rm 2~orientations})\)

Three dune orientations?

Paleo-winds (big dunes) vs Modern winds (small dunes)

Gadal et al. (2022) “Local Wind Regime Induced by Giant Linear Dunes: Comparison of ERA5-Land Reanalysis with Surface Measurements”

From sand dunes to particle-laden gravity currents

Sand storm over dunes, Sahara @EUMETSAT

Particle-laden gravity currents

Powder snow avalanche at the Zinal ski station, in Switzerland @Zacharie Grossen

Particle-laden gravity (turbidity) currents

  • gravity-driven flow
  • excess density = suspended particles (maybe combined with temperature, salinity or humidity differences)
  • ubiquitous in many planetary environments

Snow avalanche, Zinal, Switzerland @Zacharie Grossen

Pyroclastic flow, Sinabung, Indonesia @Jean-Guillaume Feignon

Dust storm, Phoenix, USA @Alan Stark

Particle-laden gravity (turbidity) currents

Almost always destructive natural hazards.

Power transmission overturned by a powder snow avalanche, Switzerland. Caviezel et al. 2021

Dammages by pyroclastic flow after the Merapi eruption, Indonesia. @Noer Cholik

Dust storm, Phoenix, USA. @Mike Olbinski

Hence, reliable modeling is needed!

\(\rightarrow\) determination of relevant processes and associated regimes

Particle-laden gravity currents as a complex system

A simple analogue subaqueous experiment: lock-release devices

Particles: glass beads (\(d \sim 120 \mu\)m). Ambient: fresh water. Inclination: \(\theta = 7^\circ\)

Gadal et al. (2023) “Slumping regime in lock-release turbidity currents”

Many processes to investigate

Processes and regimes:

  • global slope: \(\alpha\)
  • settling: \(\mathcal{S}t = \displaystyle\frac{\rm settling}{\rm inertia}\)
  • bottom roughness

  • particle/particle interactions: \(\phi\)

  • dissipation: \(\mathcal{R}e = \displaystyle\frac{\rm inertia}{\rm viscosity}\)

  • bottom topography

  • internal structure

  • interfacial mixing

  • …

Systematic exploration of the parameter space

\(\rightarrow\) collaboration between IMFT, LEGI and LEMTA

Gadal et al. (in review) “Chapter 16: Particle-laden gravity currents: the lock-release slumping regime at the laboratory scale”

One example: the influence of the global slope

\(\bullet\) PMMA particles, \(\phi \sim 1~\%\)

\(\alpha = 0^\circ\)

@Marie Rastello, LEGI

\(\alpha = 45^\circ\)

@Marie Rastello, LEGI

One example: the influence of the global slope

\(\rightarrow\) not yet reproducible by current depth-averaged models

In a nutshell

Front dynamics

  • general slope
  • settling
  • volume fraction
  • viscosity

Current shape, fluctuations, and link with the dynamics

Internal structure, particle buoyancy and particle/turbulence interaction

Gadal et al. (2023) “Slumping regime in lock-release turbidity currents”, Gadal et al. (in review) “Chapter 16: Particle-laden gravity currents: the lock-release slumping regime at the laboratory scale”

Back to the field: depth-averaged models

Pyroclastic flow, 2010 Merapi eruption (Jelfoun et al. 2017)

Turbidity current on a real topography. @Hajime Naruse

Back to the field: depth-averaged models





  • mass: \(\displaystyle\frac{\partial h}{\partial t} + \displaystyle\frac{\partial}{\partial x}[h u] = E\vert u\vert - V_{\rm s}\)
  • particle: \(\displaystyle\frac{\partial \phi h}{\partial t} + \displaystyle\frac{\partial}{\partial x}[h u \phi] = - V_{\rm s} \phi\)
  • momentum: \(\displaystyle\frac{\partial}{\partial t}[h u] + \displaystyle\frac{\partial}{\partial x}\left[ h u^{2} + \displaystyle\frac{g'}{2}h^{2} \right] = -g'h\displaystyle\frac{\partial Z}{\partial x} - \mathcal{C}\vert u \vert u\)



  • front shock condition: \(\displaystyle\frac{u_{\rm f}}{\sqrt{g'_{\rm f} h_{\rm f}}} = \mathcal{F}(??)\)

Back to the field: depth-averaged models






Calibration and assessment from our experiments

  • mass: \(\displaystyle\frac{\partial h}{\partial t} + \displaystyle\frac{\partial}{\partial x}[h u] = \color{lightblue}{E\vert u\vert} - \color{peru}{V_{\rm s}}\)
  • particle: \(\displaystyle\frac{\partial \phi h}{\partial t} + \displaystyle\frac{\partial}{\partial x}[h u \phi] = - \color{peru}{V_{\rm s} \phi}\)
  • momentum: \(\displaystyle\frac{\partial}{\partial t}[h u] + \displaystyle\frac{\partial}{\partial x}\left[ h u^{2} + \displaystyle\frac{g'}{2}h^{2} \right] = -\color{yellowgreen}{g'h\displaystyle\frac{\partial Z}{\partial x}} - \color{salmon}{\mathcal{C}\vert u \vert u}\)


Front dynamics

  • settling
  • topography and slope
  • mixing and entrainment
  • dissipation
  • front shock condition: \(\displaystyle\frac{u_{\rm f}}{\sqrt{g'_{\rm f} h_{\rm f}}} = \color{orange}{\mathcal{F}(??)}\)

Correlation: dynamics and current front shape

From particle-laden currents to riverbed clogging

Photograph of the Sanmenxia Dam during silt flushing (@Imaginechina Limited/Alamy)

Particle flow in porous media: the example of riverbed clogging

Underwater view of the River Tara riverbed, in Montenegro. (@LiquiArt)

Riverbed clogging – General questions

  • Risks, Land management: flood, impacts of dam presence
  • Ecosystem preservation: life, transfer across the riverbed (pollution, nutrients)

Photograph of the Sanmenxia Dam during silt flushing. (@RolfMueller)

Salmon eggs buried in riverbed gravels. (@Olympic National Park)
  • Fundamental questions:
    • clogging and unclogging (if possible ?) thresholds
    • spatio-temporal dynamics
    • particle dynamics inside the porous media

Riverbeds as a complex system

Main factors affecting riverbed clogging. Modified from Dubuis & Cesare 2023.

A simplified analogue experiment

A simplified analogue experiment

  • injection:
    • flow rate, \(Q\)
    • volume fraction, \(\phi_{0}\)
  • particle properties:
    • density \(\rho_{\rm p}\)
    • size \(d_{\rm p}\)
  • porous matrix:
    • hydrogel bead size \(d_{\rm h}\)





  • Settling: \(\mathcal{P} = \displaystyle\frac{\textrm{settling}}{\textrm{turbulence}}\)
  • Infiltration: \(\mathcal{I} = \displaystyle\frac{d_{\rm p}}{d_{\rm h}}\)
  • …

One example: unimpeded infiltration \(d_{\rm p} \ll d_{\rm h}\)

An experiment (accelerated x5).

Suspended part

Porous matrix

Parameter space exploration remains to be done!

Future project: Evolution of consolidated surfaces under a flowing granular media

Ripples, waves, stripes

Wear pattern in a pipe [Karimi et al. 1992]

Ventifacts on Mars [Laity et al. 2009]

Yardangs in China [Wang 2020]

Channels

Debris-flow channel [Morino, et al. 2019]

Turbidity current channel [Deptuck et al. 2007]

Thank you!

Contact me: cyril.gadal@imft.fr

Dunes

  • Clément Narteau (IPGP) & Philippe Claudin (PMMH) for everything during my PhD
  • Olivier Rozier (IPGP) for his support with the numerical simulations
  • Sylvain Courrech du Pont (MSC - Univ. Paris) for his help with the experiments
  • Laurie Barrier (IPGP) for the great discussions on eolian landforms
  • Ryan C. Ewing (Texas A&M Univ.), Douglas Jerolmack (Univ. Pennsylvania) and Andrew Gunn (Univ. Pennsylvania) for providing the field data used in the study of White Sands.
  • Pauline Delorme (Univ. Southampton), Giles W.S. Wiggs (Univ. Oxford), Matthew Baddock (Loughborough Univ.) for their collaboration in the study of the Namib Sand Sea. and Jo M. Nield (Univ. Southampton)
  • Xin Gao (Chinese Acad. Sciences) for organizing and managing our field trip through the Taklamacan desert in China.
  • many others

Particle-laden gravity currents and Riverbed clogging

  • Laurent Lacaze, Matthieu Mercier (IMFT) for everything at IMFT
  • The PALAGRAM consortium, and more specifically Marie Rastello (LEGI), Julien Chauchat (LEGI) and Jean Schneider (LEMTA) for the help in creating our big inter-lab dataset
  • Jean-Dominique (IMFT) for the technical support on the experiments