Two-Phase Continuum Models for Geophysical Particle-Fluid Flows

Two-Phase Continuum Models for Geophysical Particle-Fluid Flows

March 14 – April 15, 2016

Coordinators:  Greg Bewley, Jim McElwaine, and Alexandre Valance

A. Program Goals

Progress in the study of granular materials, improvements in field measurements, and the increased capabilities of large-scale computer simulations have led to a better quantitative understanding of particle transport by a turbulent fluid, the interaction between transported grains and the bed, the development of surface feature on the bed, and their subsequent motion and interaction. Further progress requires advances in our understanding of particle-fluid interactions and the modification of particle-particle interactions in the presence of a fluid. This program attempted (i) to accelerate these advances by bringing together physicists and geophysicists with an interest in geological processes that involve the interaction between particles and fluids and (ii) to consolidate the development of a multi-disciplinary culture devoted to the description and prediction of geophysical flows that was initiated at a program entitled Fluid-Mediated Particle Transport in Geophysical Flows held at the Kavli Institute for Theoretical Physics in the fall of 2013.

Fluid-particle flows on or near the Earth's surface include wind-blown sand, turbidity currents, transport sediment in rivers and along coastlines, debris flows, snow avalanches and pyroclastic flows. Such flows cover a wide range of particle volume fraction, particle-to-fluid density ratio and Reynolds number. The program attempted to determine common organizing principles in these flows across the range of parameters in which fluid turbulence makes an important contribution to the particle motions. The systems of interest involve turbulent fluid flow, modulated by dilute concentrations of particles in the upper regions of the flow, important particle-particle and particle-fluid interactions in denser concentrations near the bed, and mobile beds that may be eroded, or built up by deposition. The program, between March 14 and April 15, 2016,  started with a one-week workshop and was followed by a four-week seminar. The workshop and the seminar involved 41 and 28 participants, respectively.

            One goal was the development of a better understanding of how phenomena seen in the field are related to those studied in the laboratory; another was the determination of the appropriate models and computational schemes for the description of fluid-particle flows in the laboratory and in Nature. This discussion necessarily raised the issue of scaling, which is also central to understanding the relationship between Aeolian and aquatic transport and bed forms. It became clear that there are important systems that can be described by existing models and computational schemes and that it is possible to build from these. The development of realistic descriptions of natural flows require the development of continuum models whose elements are based on large-scale numerical simulations of fluid-particle flows and tested in well-controlled laboratory experiments.

B.  Workshop structure

The workshop took place during the first week of the program, from March 14^th through 18^th. The workshop served two purposes: it provide an opportunity  to review what progress had been made since the Kavli program in 2013 and it gave researchers who could not participate in the seminar session an opportunity to present their work. The workshop consisted of 38, thirty-minute talks, each followed by ten minutes of discussion.

C.  Seminar structure

 The backbone of the seminar program was a daily presentation by a participant concerning his or her relevant research. The talks were informal, often interrupted by questions from the audience, and, as a consequence, lasted for as long as two hours. Participants were scheduled to talk early in their visits. Extra, topical discussions were sometimes arranged and announced in the daily meetings.

Funding from the U.S. National Science Foundation was obtained for both the workshop and seminar. The funds were used to support the participation of US  based scientists and included senior and junior scientists.

D. Program Outcomes: State of the Art and Future Research Directions

The program dealt with various fluid-particle systems including Aeolian transport, turbidity currents, snow avalanches, clouds (i.e, liquid droplets in turbulent air flow), fluidized granular flows, debris flows, dense suspensions and pyroclastic flows.  Issues related to erosion and deposition processes, segregation phenomena and bedform instability in aeolian, river and marine environment were also discussed.

 The program evolved from proposals that focused on turbidity currents and Aeolian transport. The latter are dilute systems of particles in turbulent flows of water and air, respectively, that  that we can describe accurately without considering the interactions between particles. The Navier-Stokes equations in their Boussinesq approximation provide a reasonable basis for numerical modeling of turbidity currents. Existing continuum and particulate descriptions of Aeolian sand transport can predict the steady-state profiles over flat beds of particle and wind velocities and particle concentration as a function of the strength of a steady wind. These are two examples of fluid-particle systems, one in water, the other in air, and both involving a turbulent shearing flow that are relatively well understood. The challenge was to build from these.

Sand particles in air are the simpler system. The flows are typically so dilute that collisions between particle above the bed are rare and the significant interaction is the drag between the wind and the particles saltating (jumping) above the bed. Because of the great difference in the mass density of the particles relative to that of the air, collisions of particles with the bed (the splash) are not influenced by the wind and the measured mass and momentum transfers in them can be employed to derive continuum boundary conditions. These features make Aeolian transport a model system. The issues that remain are:

1) to describe the transient evolution of flows in time and their development along the flow and, in particular, to understand the mechanisms that drive relaxation towards steady flows. This relaxation plays a key role in the development of sand patterns. Drag, splash, and mid-air collisions are expected to play a role, but their relative importance in winds of different strengths has not yet been identified.

2) to describe saltation transport over rippled surfaces. This issue is important in practice, because sand beds in Nature are rarely flat. Experimental and numerical investigations suggest that there is a phase-locking between the length of the saltation hop and the spatial modulation of the ripple. Further studies are needed to capture the relevant mechanisms that are responsible for this.

3) to understand the transition between pure saltation and flows in which mid-air collisions are important. Several theoretical and numerical studies emphasize the role of mid-air collision in sand transport at higher wind speeds. Unfortunately, there is a lack of experiments to evaluate the importance of collisions and a clear need for further investigations in wind tunnels.

4) to describe polydisperse flows. Most theoretical approaches for modeling Aeolian sand transport assume particles of a single size. Wind-tunnel experiments and field observations indicate that the polydispersity of natural sand influences its transport and play a major the role in the formation of mega-ripples.

5) to understand mechanisms for the development of steady bed forms, such as ripples and dunes. The origin of the instability of a planar sand bed is now well understood, but the mechanisms responsible for the wavelength selection of steady forms remain to be identified. Is such selection a linear process or is there a nonlinear mechanism at work? Further investigations that couple theory and experiment are necessary.

Sand particles are some three orders of magnitude denser than air. For systems in which the mass densities of the particles and fluid are not so different, such as sand in water, the situation is not so simple since much higher concentrations are enountered. Computational schemes to resolve individual particles in a realistic turbulent shearing flow are beginning to be developed. However, because of the length scales involved in a wide range of natural flows, fully-resolved simulations are unfeasible. Two-phase continuum models, with some averaged description of the turbulence, provide the best hope for describing natural, fluid-particle flows in the foreseeable future. However, the development of such descriptions requires modeling of the interaction between the particles and between particles and the flow and closure of terms that result from the averaging.

The power of modern computational schemes was made clear during the program, as was their present limitations. Direct numerical simulations and/or large eddy simulations that involve a discrete particle phase presently have the capacity to assist in the development of two-phase continuum models. Integration over the expertise expressed during the program indicates that something like this should be done. The activity should be carried out in conjunction with a program of laboratory experimentation, to test both the computations and modeling, and it should, of course, be informed by the phenomena in the field that it eventually hopes to describe.

Research results presented during this program promoted in-depth discussions concerning particle/turbulence interactions, particle/fluid and particle/particle interactions in dense suspensions, particle and fluid interactions at the bed, mechanisms of erosion and deposition, bed form dynamics and wavelength selection. These discussion resulted in the identification of several important challenges for aquatic particle-laden flows. Among them are:

1) the most important challenge for fluid-particle flows in water is to develop a better understanding of the interaction between the particles and the turbulent shearing flow over a range of different particle/fluid density ratios and particle volume fractions. Currently it is unclear what a minimal set of variables is that can accurately describe the flow. This can be done in laboratory experiments and, more and more, by direct numerical solution of turbulent shearing flows that include particles. Laboratory experiments and the further development of direct numerical schemes with this focus should be encouraged.

2) Most of theoretical approaches for modeling particle-laden flows deal with spherical particles of a single size while the poly-dispersity in size and shape is a  common feature of natural flows. How do known results for mono-disperse suspensions of spherical particles need to be modified to be applicable to poly-disperse suspensions of irregularly shaped particles?

3) because the relevant physics near the particle bed are not known, ways must be found to study the particle-fluid interactions near, at, and in the particle bed during erosion and deposition. These are the regions of densest particle concentration and, as a consequence, they are, typically, opaque, so difficult to access experimentally. However, because the particle concentrations are so high, the fluid dynamics may be simplified. An elucidation of the appropriate physics will facilitate the development of continuum formulations for the transfer of mass, momentum, and energy at particle beds and provide the basis for the derivation of boundary conditions and the description of bed forms.

4) important challenges concerning bed forms dynamics are still to be addressed. Are there common morphodynamic organizing principles active across the entire range of particle/fluid density ratios and particle volume fractions, and between gas- and liquid-mediated flows? Which mechanisms dominate the wavelength selection of bed forms in different parameter regimes?

5) what is learned in physical and numerical experiments about the particle-turbulence interaction should be employed to develop closures in continuum models. Such models will be employed to predict the evolution in time and space of the relevant particle and fluid variables. At the present time, two-phase continuum theories offer the best, and perhaps only, hope for treating geophysical fluid-particle flows over the time and space scales found in nature.

6) the predictions of two-phase continuum models must be tested against the results of physical experiments and direct and numerical simulations. This is the second role to be played by laboratory researchers and computational fluid dynamicists in the description of natural, fluid-particle flows.

7) the interaction between laboratory researchers, computational fluid dynamicists, theoreticians and those researchers working in the field must be facilitated and encouraged. A better understanding must be developed of how phenomena seen in the field are related to those studied in the laboratory – that is, an understanding of how geophysical fluid-particle flows scale. This should lead to field measurements that are informed by theory and field tests of theoretical prediction.

We are convinced that the cooperative venture between computational, theoretical, experimental and observational fluid dynamicists with the long-term goal of describing fluid-particle flows that occur in Nature is essential to conceive and launch novel research directions for advancing the field of two-phase flow modeling. We believe that the present program and the previous Kavli program provided an important step in this direction that we intend to pursue by seeking financial support from government and industry.

A proposal for a third program on fluid-mediated particle transport in 2019 will be submitted to the Mathematical Isaac Newton Institute in Cambridge, England. The intent is to involve as many of the participants in the past programs as possible, in order to continue to develop the multi-disciplinary culture devoted to geophysical flows that was initiated at the program.

E. Diversity  

While substantial progress has been achieved in recent years through field observation, laboratory experiments, numerical simulations and theoretical modeling, this progress has occurred in different communities that commonly do not interact closely. Hence, the program served the important function of bringing together researchers whose primary expertise lies in the physics of granular flows, in multiphase fluid dynamics, and in the geosciences. Intensive collaborations at the intersections of these disciplines led to stimulation, insights, and cross-fertilization during the workshop. The organizers believe, supported by early evidence, that this laid the foundations for sustained long-term collaborations among the program participants.

Throughout the planning of the workshop and seminar the organizers attempted to contact a broad cross-section of researchers in the field, particularly with an eye toward inclusion of women.

Though many were invited, of the 28 participants in the seminar only three were women. At the workshop, six (including a keynote) of the 38 speakers were women. The program included many international participants who were from Europe (49), United-State (13), India (2) and Canada (1).

F. Planning issues

The staff of the Max Plank Institute was extraordinarily helpful in assisting the organizers and participants. The arrangement of accommodations and reimbursement and the organization of the program went very smoothly. Responses from participants to the organizers were very positive. The organizers thank Maria Pätzold and her colleagues  for making their job relatively easy.

A traditional hurdle is the length of stay requirement. We had only six participants who were able to attend for the entire four-week seminar session, including all of the organizers. We would have had  long-term participants if the invitations had been sent out earlier. We would suggest at least one year in advance.

G. Participant List

Aliseda, Alberto, University of Washington, USA

Arran, Matthew, University of Cambridge, United Kingdom

Berzi, Diego, Politecnico di Milano, Italy

Bewley, Gregory, Max Planck Institute for Dynamics and Self-Organization, Germany

Bodenschatz, Eberhard, MPI for Dynamics and Self-Organization, Germany

Bowman, Elisabeth, University of Sheffiled, United Kingdom

Colombini, Marco, Università di Genova, Italy

de Lozar, Alberto, Max-Planck-Institut für Meteorologie, Germany

Duran Matute, Matias, Eindhoven University of Technology, Netherlands

Eggenhuisen, Joris, University Utrecht, Netherlands

Fiorot, Guilherme, insa de Rennes, France

Fischer, Jan-Thomas, Austrian Research Centre for Forests, Austria

Fraccarollo, Luigi, Università di Trento, Italy

Govindarajan, Rama, Tata Institute of Fundamental Research, India

Gray, Nico, The University of Manchester, United Kingdom

Guazzelli, Elisabeth, CNRS Aix-Marseille University, France

Gustafsson, Kristian, University of Gothenburg, Sweden

Hewitt, Duncan, University of Cambridge, United Kingdom

Heyman, Joris, Institut de Physique de Rennes, France

Hill, Kimberly, University of Minnesota, USA

Hogg, Andrew, University of Bristol, United Kingdom

Hsu, Tian-Jian, University of Delaware, USA

Issler, Dieter, Norwegian Geotechnical Institute, Norway

Jenkins, James Thomas, Cornell University, USA

Johnson, Chris, University of Manchester, United Kingdom

Khosronejad, Ali, University of Minnesota, USA

Kostaschuk, Ray, Simon Fraser University, Canada

Kroy, Klaus, Universität Leipzig, Germany

Kumaran, V., Indian Insitute of Science, India

La Ragione, Luigi, Politenico di Bari, Italy

Lämmel, Marc, University Leipzig, Germany

Larcher, Michele, University of Trento, Italy

Lee, Sungyon, Texas A&M University, USA

Maurin, Raphael, IRSTEA Grenoble, France

McElwaine, Jim, Durham University, United Kingdom

Meiburg, Eckart, University of California at Santa Barbara, USA

Meninno, Sabrina, University of Trento, Italy

Nasr-Azadani, Mohamad, University of California Santa Barbara, USA

Nield, Jo, University of Southampton, United Kingdom

Nucci, Elena, University of Trento, Italy

Oger, Luc, University of Rennes 1, France

Ouellette, Nicholas, Stanford University, USA

Ould El Moctar, Ahmed, University of Nantes, France

Pham-Van-Bang, Damien, Laboratory for Hydraulics Saint-Venant, France

Revil-Baudard, Thibaud, Karlsruher Institut für Technologie, Germany

Rivera, Gustavo, Cornell University, USA

Rochinha, Fernando, Universidade Federal do Rio de Janeiro (UFRJ), Brazil

Turnbull, Barbara, University of Nottingham, United Kingdom

Valance, Alexandre, Université de Rennes 1, France

Vollmer, Jürgen, Georg-August-Universität Göttingen,

Vowinckel, Bernhard, UC Santa Barbara, USA

Vriend, Nathalie, University of Cambridge, United Kingdom

Wilkinson, Michael, The Open University, United Kingdom