My overall research
objective is to better understand the dynamical processes that govern the
behavior of the stratified and rotating fluid that comprise the Earth's
oceans, so as to improve upon existing capacity to predict evolution of
complex geophysical fluid dynamical processes. In pursuing this goal I have
come to rely upon an approach combining theoretical, experimental and
numerical techniques. This is an exciting area of research, as it gives us insight
into fundamental oceanic and atmospheric physics, and also has relevance to
our interaction with the environment.
The 2nd edition of the
textbook Physical Oceanography: A short course for beginners by Y.
Oceanography is a vast science, and beginners
often feel overwhelmed by the number and variety of different topics. This
book presents a distilled version of physical oceanography by providing
physical insight into the circulation of the Earth�s
oceans. A consistent view of the circulation is presented using only simple
mathematics and an intuitive approach; however, hints to various phenomena
are given for those who are willing to explore beyond this book. The book
also contains an elementary introduction to fluid mechanics.
This book is written at a mathematical level appropriate for
undergraduate students in oceanic and climate science.
Picture above shows evolution of
thermally induced turbulence on a polar beta-plane, as seen from above the
North pole (the center). Color shows the surface elevation field. The bottom
is heated along a radius, and the convective turbulence generates zonal
circulation in turbulent beta-plumes, which involve Rossby-wave signalling westward from the energy source. Visualized
with optical altimetry which displays surface height variations of a few
microns (millionths of a meter). Physics Today inside back cover, October
2011. Ocean/atmosphere experiments on a rotating table use the parabolic
water surface to simulate the polar cap of the planet.
I am creating a library of videos
which can be used for demonstrations in oceanography or geophysical fluid
dynamics. Check them out at Youtube:
ALTIMETRY: IMAGING THE PRESSURE, VELOCITY AND VORTICITY IN A ROTATING FLUID
complete software package for analysis of AIV (color altimetric images) is
now available. Once the system is assembled (involving a color transparency
and a light source and camera mounted above the rotating table, or with
mirror mounted halfway above the fluid in the
laboratories with low ceiling), this software makes efficient calculations of
surface height field, geostrophic and ageostrophic pressure and velocity, and
vorticity and potential vorticity. Contact email@example.com
am back from sabbatical where I was working with Peter Rhines at the
University of Washington . Here are a few movies and
pictures of our recent results:
"Designer planets" Atmosphere (ocean) in a soap bubble:
The iris of this eye
is an experimental image of a large soap bubble (diameter 30 cm). The
soap bubble when placed on a rapidly rotating platform
can model a planetary atmosphere or an ocean. Convective motions
within the bubble create color pattern due to interference of light.
For 10mbwmv movie (with sound) of rotating soap
bubbles click here.
Experimental image of a phenomenon
which occurs often in oceans and atmosphere. This phenomenon is called
baroclinic instability. The image is obained by a new method of color altimetry developed
recently in collaboration with the University of Washington.
For 2mbwmv movie of
a rotating flow over a mountain illustrating Rossby and inertia waves click here.
behind towed and self propelled bodies in 2D and 3D
Theoretical, numerical and laboratory investigation of wakes behind moving
forcing of different configurations. Applications include flying insects and
birds, swimming microorganisms and fish, wakes behind submarines and bluff
Flight in a viscous
Experimental image of a flow modelling the vortical wake behind a
hydrodynamic model of a small insect. This image won
1st prize at the recent Art of Physics competition of Canadian Association of
This picture shows the wake behind a “virtual” insect flying in
fluid. The model of the insect is translated in water horizontally. It has a
permanent magnet in its rear end which provides a magnetic field in the
direction of motion. At the same time the electric current flows between two
electrodes in a perpendicular direction in the horizontal plane. The
resulting Lorentz force on the fluid is perpendicular to both the current and
the magnetic field and acts in the vertical direction. This force, if applied
impulsively during some time intervals, simulates the lift force applied by
the flapping wings of an insect during downstrokes.
This force transfers momentum downwards while the reaction to this force
supports the insect in the air. Momentum transfers in the form of vortex
rings. These “rings” look like a Greek letter W and
are connected to each other. The insect is small and the viscosity of the
fluid is important. As a result the vortex tubes diffuse in the
flows, mixing and transport in fjords
Recent interests have included
numerical modeling of unstable internal gravity waves, using a fully
three-dimensional ``state-of-the-art'' numerical model on various Cray vector
supercomputers. The most interesting and dynamically significant effect of
internal wave propagation in a stratified fluid arises when the wave achieves
such amplitude that it becomes subject to a local convective instability.
This is commonly referred as ``wave breaking'' and it is thought to be
associated with the transfer of momentum from the wave field to the main
flow. The oceanographic examples include flows in coastal inlets subject to
gradually changing tidal currents (e.g. Newman Sound, NF; Knight Inlet, BC).
Such fjords are typical features of the Newfoundland coast and many of them
are used for aquaculture. Thus the study of mixing and forcing of circulation
is also of great importance for biological applications. A significant new
study devoted to understanding this interesting oceanic nearshore process is
currently under way and will be continued. A field study will be considered
at a later stage of the project.
and transport by vortices in a rotating stratified fluid
Vortex structures such as monopoles,
dipoles as well as more complex structures are fundamental elements of geophysical
turbulence. Because they can effectively transport momentum, heat, salt and
biochemical products, they play an essential role in ocean dynamics,
determining the instantaneous fields of velocity, temperature and salinity,
i.e. so-called internal oceanic weather. A very efficient tool for the
investigation of vortices clearly consists of laboratory experimentation. The
following specific projects are under way: vortex formation in coastal flows;
stability of barotropic vortices in a rotating stratified fluid; dynamics and
interactions of vortex structures on a ``beta-plane''. The experimental part
of these projects includes setup of PIV (Particle Image Velocimetry) system
for the computerized measurements of flow fields. In the framework of this research
stream I also plan to initiate a project in collaboration with colleagues
from the P.P.Shirshov Institute on thermal
variability of the waters of the Newfoundland shelf using satellite SST data.
turbulence can be modified significantly when the Coriolis parameter varies
with latitude such as that on the rotating Earth. The vortices that comprise
the turbulent flow are found to distribute themselves in such a way that they
form zonal jets. Such zonal jets have been observed in many geophysical
systems and are a common feature in the atmospheres of Jupiter, Saturn and
the Earth. This picture shows vorticity (color) and velocity (arrows)
fields measured during a laboratory experiment on quasi-two-dimensional
turbulence on a polar beta-plane. A well-defined polar vortex can be clearly
seen in the center of the picture surrounded by an intense cyclonic jet that
is subject to Rossby waves.
Afanasyev, Y. D. and Wells, J., "Quasi-two-dimensional turbulence on the
polar beta-plane: laboratory experiments", Geophys.
Astrophys. Fluid Dynamics, 99 (1), 1-17 (2005).
picture shows the baroclinic instability of a coastal gravity current
visualized by dye. Our experiments were carried out using a scaled model of
the Black Sea mounted on a rotating table
to simulate the effects of the Earth’s rotation. The tank was filled
with saline water while the source of fresh dyed water was located in the
lower right hand corner of the model. The source allowed us to simulate the
supply of fresh water by rivers in the western part of the Black
Sea. The fresh water is then transported in cyclonic direction
around the sea forming the so-called Rim Current. The current becomes unstable
due to the baroclinic instability and forms meanders and vortices. Arrow in
the picture indicates the pairing of two vortices. <>(Blokhina, M. D. and Y. D. Afanasyev: Baroclinic
instability and transient features of mesoscale surface circulation in the Black
Sea: laboratory experiment, J. Geophys.
Res. Oceans, 2003, 108 (C10), 3322, doi:10.1029/3003JC001979).
Winter 2015: p2820 - Computational Mechanics The
goal of this course is to integrate computational techniques with some
fundamental classical mechanics. The student will use computational
techniques to solve mechanics problems. The primary programming tools will be
Mathematica and to a lesser extent Matlab.
Prerequisite(s): Physics 1051 and math 2000. Math 2000 may be taken
concurrently. Lectures: Three hours per week.
2300 - - Introductory Oceanography. This course will provide an
introduction to the physical ocean. Ocean characteristics studied will include:
the properties of seawater, key features of ocean circulation, wind forcing
in the ocean, tides and shoreline processes as well as ocean coupling with
the atmosphere. Prerequisite(s): Any two first-year courses in Physics.
6363 - - Laboratory Experiment in Geophysical Fluid Dynamics. The
objective of this course is to give the student the theoretical basis of the
laboratory experimentation in Geophysical Fluid Dynamics through lectures as
well as practical skills. This will include the development and
implementation of your own fluid dynamics experiment to study a problem that
interests you, the results of which will be reported in a paper and video
which you will create. Prerequisite(s): P4205 or AMAT 4180 Lectures: Three
hours per week.
Fall 2007, 2009:1051 - General
Physics II: Oscillations, Waves, Electromagnetism. is a calculus based introduction to oscillations,
wave motion, physical optics and electromagnetism.
Prerequisites: Physics 1050 or 1020 (with a minimum grade of 65%) and
Mathematics 1001. Mathematics 1001 may be taken concurrently.
Laboratories: Normally six laboratory sessions per semester, with each
session lasting a maximum of three hours.
covers kinematics and dynamics of a particle. Moving
reference systems. Celestial mechanics. Systems of particles.
Prerequisites: Physics 2820 and Applied Mathematics/Pure Mathematics 3260. Applied
Mathematics/Pure Mathematics 3260 may be taken concurrently.
Lectures: Three hours per week.
Winter 2001: 3230 - Classical Mechanics II.
Rigid body motion. Lagrange's equations. Hamilton's equations. Vibrations.
Special theory of relativity. Prerequisite(s): Physics 3220, Physics 3810 (or
AM/PM 3202) and AM/PM 3260. Lectures: Three hours per week.
Winter 2002: 2056 - General Physics VI: Modern
Physics. Special relativity, quanta of light, atomic structure and
spectral lines, quantum structure of atoms and molecules, nuclei and
elementary particles. Prerequisite(s): Mathematics 1001, Physics 1050 (or
1020 and 1021), and Physics 1054. Math 1001 and Physics 1054 may be taken
concurrently. Lectures: Three hours per week. Laboratory: Three hours per
Winter 2002: 3300 - - Introduction to Physical
Oceanography. The course deals with the physics of processes in the
ocean, but provides an integrated view of the whole field of oceanography.
The importance of physical processes to other aspects of oceanography is
treated. Prerequisite(s): Physics 2053 and Mathematics 2000. Lectures: Three
hours per week.
Winter 2003: 4205 - - Introduction to Fluid
Dynamics (same as AM 4180). Basic observations, mass conservation,
vorticity, stress, hydrostatics, rate of strain, momentum conservation (Navier-Stokes equation), simple viscous and inviscid
flows, Reynolds number, boundary layers, Bernoulli's and Kelvin's theorems,
potential flows, water waves, thermodynamics.. Prerequisite(s): Physics 3230
and either Physics 3821 or AM 4160.. Lectures: Three
hours per week.
Fall 2003, 2004: 3821 - - Mathematical Physics
III. Further topics on the partial differential equations of
mathematical physics and boundary value problems.
Prerequisite(s): Physics 3820.
Lectures: Three hours per week.
Fall 2003: 6323 - - Stability Theory. Kelvin-Helmholtz
and Rayleigh-Taylor instabilities, centrifugal instability, stability on f-
and beta- planes. Effects of viscosity: Orr-Sommerfeld
equation. Thermal instability, stability of stratified fluids, baroclinic
instability, transition to turbulence.
Winter 2013, 2012: P4300
(and parallel graduate course P6310) - -Advanced Physical Oceanography.
Fundamental properties of seawater and techniques of oceanographic
measurement. The dynamical equations of oceanography are derived and
solutions explored by comparison with oceanic observations. Properties of
waves in rotating and non- rotating fluids. Linear and non-linear wave theory are developed.
Prerequisites: Physics 3300 and 3820, or Engineering 7033, or the permission
of the instructor.
Lectures: Three hours per week.
Fall 2005: 6321 - -Coastal
Coastal circulation: observations and theory; coastal trapped waves;
wind-forced response; uniform density models;
effect of density stratification
Prerequisites: permission of the instructor.
Lectures: Three hours per week.
P2053 - Vortex streets
This is a new lab experiment in Physics 2053. This laboratory experiment is
designed to study regular arrays of vortices occurring behind an object in a
stream of fluid. This phenomenon is observed in industrial flows, flows in
the ocean and in the atmosphere. We consider the flow behind a circular
cylinder. In the second part of the experiment the effect of the body on the
fluid is imitated by using an appropriate force field when there is no real
body present in the fluid. The force field (virtual body) is created by a
permanent magnet located above the surface of water in combination with
electric current applied in the horizontal direction.
site is maintained by: Yakov Afanasyev.
Last updated: November, 2011.