Annual Review of Fluid Mechanics - Volume 40, 2008

We review flows of dense cohesionless granular materials, with a special focus on the question of constitutive equations. We first discuss the existence of a dense flow regime characterized by enduring contacts. We then emphasize that dimensional analysis strongly constrains the relation between stresses and shear rates, and show that results from experiments and simulations in different configurations support a description in terms of a frictional visco-plastic constitutive law. We then discuss the successes and limitations of this empirical rheology in light of recent alternative theoretical approaches. Finally, we briefly present depth-averaged methods developed for free surface granular flows.

This article reviews the main established ideas on the influence of a magnetic field on turbulence in electrically conducting fluids. We limit our discussion to the asymptotic range of very small values of the magnetic Reynolds number, characterized by the fact that the induced magnetic field remains very small in comparison with the applied magnetic field. We consider three kinds of flows here. The simplest one is freely decaying homogeneous turbulence, which serves as a test bed to analyze the development of anisotropy resulting from the linear damping by the Lorentz force. We then discuss flows between walls perpendicular to the magnetic field and emphasize the influence of the Hartmann layers that develop in their vicinity. We then review the main features of the possible quasi-two-dimensional regime that can arise in that context. Finally, we consider magnetohydrodynamic turbulent shear flows. These are frequent in industrial applications involving molten metals, such as in metal processing or in the blanket of future nuclear fusion reactors. We pay particular attention to recent attempts to develop specific RANS (Reynolds-averaged Navier-Stokes) models for these flows.

Gas-solid fluidized beds are widely applied in many chemical processes involving physical and/or chemical transformations, and for this reason they are the subject of intense research in chemical engineering science. Over the years, researchers have developed a large number of numerical models of gas-fluidized beds that describe gas-solid flow at different levels of detail. In this review, we discriminate these models on the basis of whether a Lagrangian or a Eulerian approach is used for the gas and/or particulate flow and subsequently classify them into five main categories, three of which we discuss in more detail. Specifically, these are resolved discrete particle models (also called direct numerical simulations), unresolved discrete particle models (also called discrete element models), and two-fluid models. For each of the levels of description, we give the general equations of motion and indicate how they can be solved numerically by finite-difference techniques, followed by some illustrative examples of a fluidized bed simulation. Finally, we address some of the challenges ahead in the multiscale modeling of gas-fluidized beds.

I present a brief review of tsunami simulations, first introducing the subject with an overview of notable tsunamis. Then I discuss modeling strategies and philosophies, describing the use of shallow-water equations and Navier-Stokes and Euler equations for various phases of tsunami development. Recent developments have made possible the real-time forecasting of impending tsunami dangers, which I briefly describe. Finally I focus on modeling in the generation phase, during which rock meets water, often violently and sometimes explosively, and discuss why I believe this phase (at least) must be modeled using fully compressible hydrodynamics. I then describe some illustrative simulations with the Los Alamos/SAIC code SAGE of underwater earthquakes and underwater landslides and demonstrate how these couple to surface waves.

The polar oceans of Earth are covered by sea ice. On timescales much greater than a day, the motion and deformation of the sea ice cover (i.e., its dynamics) are primarily determined by atmospheric and oceanic tractions on its upper and lower surfaces and by internal ice forces that arise within the ice cover owing to its deformation. This review discusses the relationship between the internal ice forces and the deformation of the ice cover, focusing on representations suitable for inclusion within global climate models. I first draw attention to theories that treat the sea ice cover as an isotropic continuum and then to the recent development of anisotropic models that deal with the presence of oriented weaknesses in the ice cover, known as leads.

In this review, we present control methods for flow over a bluff body such as a circular cylinder, a 2D bluff body with a blunt trailing edge, and a sphere. We introduce recent major achievements in bluff-body flow controls such as 3D forcing, active feedback control, control based on local and global instability, and control with a synthetic jet. We then classify the controls as boundary-layer controls and direct-wake modifications and discuss important features associated with these controls. Finally, we discuss some other issues such as Reynolds-number dependence, the lowest possible drag by control, and control efficiency.

This review surveys the large variety of mechanical interactions between wind and plants, from plant organs to plant systems. These interactions range from leaf flutter to uprooting and seed dispersal, as well as indirect effects on photosynthesis or insect communication. I first estimate the relevant nondimensional parameters and then discuss turbulence, plant dynamics, and the mechanisms of interaction in this context. Some common features are identified and analyzed in relation to the wind engineering of manmade structures. Strong coupling between plants and wind exists, in which the plant motion modifies the wind dynamics. I also present some related biological issues in which the relation between plant life and wind environment is emphasized.

[V]oici la lourde nappe/Et la profonde houle et l’océan des blés

[Like a sheet/The deep swell on a sea of wheat]

Charles Péguy (1873–1914)

We examine observations of turbulence in the geophysical environment, primarily from oceans but also from lakes, in light of theory and experimental studies undertaken in the laboratory and with numerical simulation. Our focus is on turbulence in density-stratified environments and on the irreversible fluxes of tracers that actively contribute to the density field. Our understanding to date has come from focusing on physical problems characterized by high Reynolds number flows with no spatial or temporal variability, and we examine the applicability of these results to the natural or geophysical-scale problems. We conclude that our sampling and interpretation of the results remain a first-order issue, and despite decades of ship-based observations we do not begin to approach a reliable sampling of the overall turbulent structure of the ocean interior.

Differential heating along one horizontal boundary of a fluid-filled volume establishes an overturning circulation (horizontal convection) in the volume. The governing dynamics in this type of convection are fundamentally different from those in other more commonly studied forms of convection in which the thermal forcing is applied at more than one level. The study of horizontal convection has been motivated largely by the need to understand the role of surface buoyancy forcing of the global oceans, and with this in mind we review a number of extensions to idealized convective flow in a simple box.

The review deals with applications of magnetic resonance imaging (MRI) techniques to study flow. We first briefly discuss the principles of flow measurement by MRI and give examples of some applications, such as multiphase flows, the MRI rheology of complex fluid flows, and blood flows in the human body.

This article provides a review of recent progress in understanding and predicting polymer drag reduction (DR) in turbulent wall-bounded shear flows. The reduction in turbulent friction losses by the dilute addition of high–molecular weight polymers to flowing liquids has been extensively studied since the phenomenon was first observed over 60 years ago. Although it has long been reasoned that the dynamical interactions between polymers and turbulence are responsible for DR, it was not until recently that progress had been made to begin to elucidate these interactions in detail. These advancements come largely from numerical simulations of viscoelastic turbulent flows and detailed turbulence measurements in flows of dilute polymer solutions using laser-based optical techniques. This review presents a selective overview of the current state of the numerics and experimental techniques and their impact on understanding the mechanics and prediction of polymer DR. It includes a discussion of areas in which our understanding is incomplete, warranting further study.

This review presents recent technological advances in charge-coupled-device ultrahigh-speed video cameras and their applications in experimental fluid mechanics. Following a brief review of the various high-speed camera types, we point out the advantages of the new technology. Then we show examples of how these cameras are leading to new discoveries in the study of free-surface flows, emphasizing the dynamics of drops and bubbles. We specifically review work on the basic singularities occurring when liquid masses come into contact and coalesce, or break apart during the pinch-off of drops or bubbles from a vertical nozzle. We briefly discuss the imaging of cavitation bubbles and finish by outlining future prospects for these sensors.

Oceanic rogue waves are surface gravity waves whose wave heights are much larger than expected for the sea state. The common operational definition requires them to be at least twice as large as the significant wave height. In most circumstances, the properties of rogue waves and their probability of occurrence appear to be consistent with second-order random-wave theory. There are exceptions, although it is unclear whether these represent measurement errors or statistical flukes, or are caused by physical mechanisms not covered by the model. A clear deviation from second-order theory occurs in numerical simulations and wave-tank experiments, in which a higher frequency of occurrence of rogue waves is found in long-crested waves owing to a nonlinear instability.

This article reviews the physical processes responsible for the transport and deposition of particles and their theoretical modeling. Both laminar and turbulent processes are considered, emphasizing the physical understanding of the various transport mechanisms. State-of-the-art computational methods for determining particle motion and deposition are discussed, including stochastic Lagrangian particle tracking and a unified Eulerian advection-diffusion approach. The theory presented includes Brownian and turbulent diffusion, turbophoresis, thermophoresis, inertial impaction, gravitational settling, electrical forces, and the effects of surface roughness and particle interception. The article describes two example applications: the deposition of particles in the human respiratory tract and deposition in gas and steam turbines.

This review concerns recent progress in primary atomization modeling. The numerical approaches based on direct simulation are described first. Although direct numerical simulation (DNS) offers the potential to study the physical processes during primary atomization in detail, thereby supplementing experimental diagnostics, it also introduces severe numerical challenges. We outline these challenges and the numerical methods to address them, highlighting some recent efforts in performing detailed simulation of the primary atomization process. The second part is devoted to phenomenological models of primary atomization. Because earlier conventional models of breakup are well reported in the available literature, we highlight only two recent developments: (a) stochastic simulation of the liquid jet depletion in the framework of fragmentation under scaling symmetry and (b) primary atomization in terms of Reynolds-averaged Navier-Stokes (RANS) mixing with a strong variation of density.

Blood flow in end-to-side autogenous or prosthetic graft anastomoses is of great interest to biomedical researchers because the biomechanical force profile engendered by blood flow disturbances at such geometric transitions is thought to play a significant role in vascular remodeling and graft failure. Thus, investigators have extensively studied anastomotic blood flow patterns in relation to graft failure with the objective of enabling the design of a more optimal graft anastomotic geometry. In contrast to arterial bifurcations, surgically created anastomoses can be modified to yield a flow environment that improves graft longevity. Understanding blood flow patterns at anastomotic junctions is a challenging problem because of the highly varying and complex three-dimensional nature of the geometry that is subjected to pulsatile and, occasionally, turbulent flow.

Biomedical acoustics is rapidly evolving from a diagnostic modality into a therapeutic tool, and acoustic cavitation is often the common denominator in a wide range of new therapeutic applications. High-intensity focused ultrasound (HIFU) waves generated outside the body can be used to deposit heat deep within the body. Through a quantitative analysis of heat deposition by ultrasound, it is shown that inertial cavitation can help address some of the major challenges of HIFU therapy by providing a means of enhancing and monitoring treatment noninvasively. In the context of drug delivery, both inertial and stable cavitation play roles in enhancing drug activity and uptake. In particular, shape oscillations arising during stable cavitation provide an effective micropumping mechanism for enhanced mass transport across inaccessible interfaces.