1. Flow in Curved Tubes
Over twenty years, I and a colleague (L. Talbot)
established at Berkeley one of the most active centers of research
on flow in curved tubes and pipes, studies which have application
ranging from biofluiddynamics to any situation involving complex
piping systems. I directed the analytical and numerical studies.
We studied both fully-developed and developing flow, steady and
unsteady, including heat transfer effects.
Representative publications:
(Other publications: #50, 65-66, 69-70, 73-6, 79, 81, 83-5, 87)
2. Vortex Breakdown
Vortex breakdown is the abrupt change in the structure
of the concentrated core of a strongly swirling flow, resulting
in a recirculation bubble or a spiral about the axis. Various
mechanisms have been proposed as responsible for breakdown, but
none is yet universally accepted. We were the first to carry out
a full numerical simulation of breakdown, solving the full axisymmetric
Navier-Stokes equations. This was a seminal paper, leading to more complex simulations, non-axisymmetric
and unsteady, as computers became faster and more powerful. My
work also addresses the cause of the suddenness of breakdown and its
tendency to move upstream, as observed experimentally and in numerical
simulations.
A measure of the recognition that I have achieved
in this area of research is that I was invited to prepare an article
on vortex breakdown for the McGraw-Hill 1997
Yearbook of Science and Technology (#105)
Representative publications:
"Vortex Breakdown Incipience: Theoretical Considerations,"
Physics of Fluids, 7, 1995, 972-982.(#96) (Other publications: #91, 94)
3. Vortex/Free-Surface Interaction
When the vortex wake system produced by a lifting
or thrust-producing surface on a ship or submerged vessel interacts
with a free surface it produces a very complex disturbance of
the free surface, and leaves a characteristic signature on the
free surface. I have studied the resulting inviscid interaction
and explored the effect of turbulence, in particular
how to model the turbulent vortex/free-surface interaction using
turbulence models, such as the Reynolds-averaged Navier-Stokes
equations.
Representative publications:
4. Hydrodynamic Stability
Over my research career I have often returned to one of the ubiquitous
subject areas in fluid mechanics: hydrodynamic stability in various contexts.
Some of the problems I have looked at, with my students or alone, are:
(a) Towards understanding the separation and containment problem in a gaseous
core nuclear rocket, we studied the stability of a two-fluid vortex, in particular
the linear hydrodynamic stability of two incompressible, immiscible, viscous
fluids of different densities and viscosities occupying separate annular regions
of a cylindrical Couette apparatus. While most of our results appeared to be
manifestations of the Taylor-Couette instability phenomenon, evidence was presented
for the existence of additional "hidden" eigenvalues attributable
to the Kelvin-Helmholtz and/or the Yih viscosity-stratification instability
phenomenon. (#33)
(b) In #46 we presented an extensive critical review of the literature on the
stability and transition of laminar boundary layers, particularly on the strengths
and limitations of the well-known empirical e9 transition criterion.
(c) In connection with work for IBM on drop-on-demand ink jet printers, I studied
the stability of a thin cylindrical liquid jet, a study initiated by Rayleigh,
who is also credited with many of the principal results. All previous investigators
treated this problem using a normal-mode type of analysis. As for a number of
other stability problems, there were good reasons for reconsidering the jet
stability problem as an initial-value problem. I did so, in what turned out
to be a substantial analytical analysis. The solution in the limit as time approaches
infinity contains all the previously known normal-mode results. The new results,
particularly for the sizes of the drops that result from the instability, agree
well with experiments. (#64, 68, 77)
(d) In connection with our studies of vortex breakdown, we investigated the stability of the velocity profiles in the flow field behind bubble-type vortex breakdowns, particularly to see whether such flows were themselves unstable, potentially leading to other vortex breakdowns. This required our carrying out a state-of-the-art linear hydrodynamic stability analysis, using techniques for regularizing the solution, and allowing for the presence of non-axisymmetric disturbances. The results confirmed that the flow fields were stable to axisymmetric modes, so a second bubble-type breakdown would not occur, but were unstable to certain nonaxisymmetric modes, which could manifest themselves as spiral or helical breakdowns. These results are consistent with what is known experimentally about single bubble breakdowns, and bubble-followed-by-spiral breakdowns. (#89)
5. Boundary Layer Control
The variation of viscosity with heating for liquids, in contrast with that of gases, presents opportunities for boundary control in water that are very much different than what we know from our more common experience in aerodynamics. The potential to dramatically raise the transition Reynolds number or delay separation for submersible bodies makes the heating of water boundary layers an exciting issue to explore. In our work we first developed approximate methods to calculate the properties of heated water laminar boundary layers (#48, 49), and then carried out an asymptotic analysis of the behavior of these boundary layers near the point of separation and compared the efficacy of heating in delaying separation vs. the use of suction to accomplish the same task (#47)
6. Simulations of Three-Dimensional, Unsteady Flows in Normal
and Stenotic Blood Vessels - Applications to MR Angiography
In MRI/A (Magnetic Resonance Imaging/Angiography) of blood flow fluid particles are tagged by complex spatially and temporally varying magnetic fields and then detected at some later time. Construction of the image requires that a model of the flow be used. Traditionally, the model used was a simple one, such as Poiseuille flow. The resulting images of the flow in complex geometries then show areas where it is not clear whether or not the vessels are blocked, and if not, the nature of the flow, laminar or turbulent, in the vessels. Clearly what is called for in constructing these images is a detailed knowledge of the three-dimensional unsteady flows in normal vessels and the greatly more complex flows in vessels with vascular stenoses. My students and I have been successfully numerically simulating these fully three-dimensional unsteady flows in complex arterial geometries. A focus of our work has been on flow in the carotid bifurcation, the carotid arteries being principal arteries supplying blood to the brain, impairment of which is the leading cause of strokes. Our studies have been implemented in the diagnostic studies conducted by our MRI colleagues at the Veterans Administration Hospital/UCSF, principally Dr. Saloner and his associates, our decade-old collaborators in this research. The vessel geometries we study are patient specific and supplied to us by our VA/UCSF colleagues, so our calculations can be directly compared to their MRI, CT, and Doppler diagnostic measurements, as well as to experiments being conducted on the very same geometries at Berkeley by an allied researcher. Our results when incorporated into MRI reconstructions help to resolve many imaging artifacts and to give a more accurate picture of the flow fields in stenotic vessels, crucial to informed clinical diagnosis and planning. Interesting fluid mechanical issues arise in these flows, particularly for severely stenotic vessels. The thin jet that issues from the throat formed at the location of maximum flow narrowing shows signs of instability, as evidenced by unsteadiness of the jet and vortex shedding. Also, although the Reynolds numbers of these flows are not large, of the order of hundreds, there is evidence of disturbed flow, what might be described either as a highly complex vortical flow, or what is sometimes called "chaotic" turbulence (to distinguish it from the more familiar fully-developed high Reynolds number turbulence). Much of our current efforts are directed to numerically capturing this instabiliy, as manifested by unsteadiness and chaotic behavior, by carrying out Reynolds-Averaged Navier-Stokes (RANS) calculations, and Large Eddy (LES) and Direct Numerical Simulations (DNS).
A recent offshoot of my work on the flow in diseased vessels was to begin research on stents, the mechanical scaffolds used to maintain the patency of blood vessels, often following angioplasty, or to reduce aneurysms. In connection with the use of stents placed post-operatively in vessels following angioplasty a major stimulus for calculating the flows in such vessels is a widely held belief that the flow plays a role in restenosis, the re-growth of the vascular wall into the lumen of the vessels, that occurs in roughly 30% of stented vessels (this statement does not hold for the recently introduced drug-coated stents, introduced specifically to overcome this problem).
A measure of the recognition this work has received was the invitation
to contribute an article on Flows in Stenotic Vessels for Vol. 32 of Annual
Review of Fluid Mechanics, published in January 2000.
Representative publications:
7. Flow of Sickle-Cell Blood in the Microcirculation
The clinical symptomology of sickle cell disease is primarily
a manifestation of abnormal events in the capillaries. In a series of papers
I developed a quantitative theoretical model that coupled oxygen transport to
the motion of the red blood cells in the capillaries, and that incorporated
the most important characteristics of sickle blood. The model predicts conditions
conducive to the development of the deleterious effects associated with sickling.
This is most likely to occur when there is vasoconstriction of the arterioles.
This theory provided the first quantitative explanation of the cause of sickle-cell
"crisis". Recently, one of my students (Brian Carlson) has extended
the single capillary model to microcirculatory networks. Results for randomly
generated distributions of capillaries suggest that capillary blockage is not
less than for single capillaries, but even more likely, with significant ramifications
for persons with sickle cell disease.
Representative publications:
(Other publications: #51, 52, 61, 62)
8. Motion of Microorganisms and Rheology of Biological
Fluids
Over many years we developed at Berkeley one of the leading centers
for research on the motion of microorganisms, particularly self-propelling flagellated
organisms such as spermatozoa. Our studies concentrated on the analysis of these
when the flagella are of finite length and the waves along the flagella are
of finite amplitude. These analyses, which were both analytical and numerical,
provided more accurate simulations of the actual motion of such microorganisms.
These studies led to investigations of the effects on these motions of nearby
solid boundaries, and non-Newtonian behavior of the media in which they were
propelling themselves.
Representative publications:
9. Wake Flows
My early research was on wake flows, both the near wake and the
far wake behind bluff and thin bodies, generally for laminar flow conditions,
for both small and large Reynolds numbers. I wrote a monograph providing a comprehensive,
critical review and survey of the research in this field.
Representative publications:
(Other publications: #15, 19, 20, 21, 23, 26, 29,
31)
10. Explosions
Beginning with my doctoral thesis and continuing
for some years, I studied the fluid dynamics of explosions, both
analytically and numerically. The earlier work was on inviscid
finite-charge blast waves in water where the flow field behind
the leading shock is complicated by the presence of a secondary
shock which initially propagates outward, then implodes towards
the center, and reflects. Subsequent work concentrated on explosions
in heat conducting and viscous gases, including the effects of
radiation.
Representative publications:
(Other publications: #1, 2, 3, 5, 39)
11. Magnetohydrodynamics and Flow of Ionized Gases
The MHD equations governing the flow of a conducting
gas interacting with a magnetic field are nonlinear and so exact
solutions are rare. When the gas is infinitely conducting and
flows in such a way that the velocity and magnetic fields are
aligned, the governing equations may formally be reduced to those
of ordinary gas dynamics. If one restricts attention to plane
flows then the hodograph technique may be employed, and the equations
solved exactly. The problem remains of satisfying the boundary
conditions. In a series of papers (#10, 16-18) I solved this problem
exactly for an important and realistic geometry, the flow of a
jet of gas out of a slit in a rectangular channel. The method
used is a modification of the method of Chaplygin for nonconducting
gas jets. Like exact solutions in non-MHD flows, such exact solutions
are important in themselves, exhibiting the full interplay of
nonlinear effects, and as generic problems against which to evaluate
approximate and numerical solutions. [These papers appeared only
as RAND Research Memoranda because they are widely distributed
to depository libraries around the world and therefore considered
by many technical journals as archival publications
and thus not "re-publishable" in such journals.]
In an important contribution to hydromagnetics (#30), we analyzed the structure of a hydromagnetic ionizing shock wave and showed how an analysis of the structure resolves a well-known indeterminacy in the solution of the shock jump conditions arising from the inability to fix the upstream electric field for ionizing shock waves.
12. The Application of Fluid Mechanics to Materials Processing
Materials processing often involves very complex
fluid mechanical phenomena, long recognized by material scientists
and acted upon accordingly. It is more recently that fluid mechanicians
have recognized this, and it has not escaped the attention of
industry and government agencies that interaction between these
two groups could lead to dramatic improvements in materials quality
and cost, lead to the development of new processes, improvement
of current processes, etc. (#78). In particular, I looked at the
problem of melt spinning in the aluminum industry, as part of my
long association with Alcoa as a consultant and grant recipient.
A model which allowed an overall evaluation and optimization of
the planar flow casting melt-spinning process was presented in #80. (Many
of my contributions to this process as used by industrial leaders
such as Alcoa were in the form of informal and formal technical
discussions with the engineers supervising the operations.)
(A measure of the recognition I received for work in this area was the invitation to organize and chair an NSF Workshop on the Application of Fluid Mechanics to Materials Processing. The Workshop was held at NSF Headquarters in Washington, D.C. in March, 1988, and included some of the most respected figures in fluid mechanics and materials science.)
13. Miscellaneous Research:
(a) Mathematical Ship Lofting
Our work was the first major attack on the problem of how
to eliminate the full or tenth-scale manual loft to draw ships' lines by using
instead sophisticated mathematical and computational techniques. We came up
with an innovative linear programming approach to fit two-dimensional splines
to waterlines and three- dimensional splines to ships' surfaces. Using linear
programming allows one to impose requisite smoothness and other, overall constraints
on the fitted curves and surfaces. Our work (#6, 22) was seminal, followed often
in later years by less powerful and less innovative alternative approaches.
(b) Unsteady Compressible Boundary Layers
We addressed and treated a few important and interesting topics and problems
in compressible boundary layers, one a general procedure for obtaining approximate
unsteady one-dimensional solutions based on expansions in Mach number (#24),
and the other an analysis of compressibility effects in the boundary layer ahead
of an accelerating flame (#28)
(c) Analytical Studies of Sails
In a series of papers (#27, 32), one of which appeared in the Proceedings of
the Royal Society, communicated by Sir James Lighthill, we treated for the first
time analytically the interaction of a mainsail and a jib, to investigate how
and when the jib interacts with the flow about the mainsail, namely whether
the main effect of the jib is to create a "slot" between it and the
mainsail, or to act as a second, albeit smaller, sail. Our analysis was a complex
study of two flexible, thin, lifting surfaces, assumed to be two-dimensional,
leading to coupled linear integral equations. The solution of these equations
is exceedingly complex. The resulting solution shows that both of these mechanisms
can occur, depending on the separation distance and the angle between the jib
and the mainsail.
BOOKS:
1. LAMINAR WAKES, S. A. Berger, Elsevier. New York, 1971. This was a critical treatise covering work on incompressible and compressible, subsonic and supersonic wakes. Wakes flow are a classical topic in fluid dynamics. In the nineteen fifties and sixties, because of military considerations, there was an enormous effort in investigating complex wake flows behind slender and bluff bodies, compressible in general and, particularly, high-speed flows. This book was the first and most comprehensive treatise covering the classical work and the modern investigations.
2. INTRODUCTION TO BIOENGINEERING, S. A. Berger, W. Goldsmith, E. R. Lewis, Editors, Oxford University Press, Oxford, 1996. This is a first-year graduate or senior-level undergraduate text on bioengineering. Unlike other multi-authored books, preparing this book was far different than putting together a set of chapters. It required a great deal of oversight and involvement of the editors. The major contributions were by myself and Goldsmith (E.R. Lewis took early retirement after agreeing to be one of the editors), myself as the principal person in synthesizing and putting together the book, Goldsmith in preparing the first and largest chapter of the book, on biomechanics. (I also wrote one of the longest chapters, on physiological fluid mechanics.)
REVIEW ARTICLES, CONTRIBUTIONS TO HANDBOOKS, YEARBOOKS,
ETC.:
Latest update: November 19, 2004
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