My research interests span astronomy, fluid mechanics and geophysics.  On this page I have put a few brief samples that represent things of interest to me.  If you would like more information about these topics or my research, please see  my (p)reprint page  or e-mail me at philip.yecko@montclair.edu.
 
Streamwise and Three-Dimensional Pattern Formation in Two-Fluid Flows:  At high relative velocity, the breakup of sheared immiscible fluids tends to occur as a result of very rapid nonlinear three-dimensional growth of small-scale structures (see also Atomization and Spray section below), as evident in this laboratory image

taken of a water jet surrounded by a co-flowing high speed jet of air.
The origin of these finger like structures is not yet completely understood.  The early onset of three-dimensionality is also not predicted by a linear stability analysis.  We have approached this problem from the perspective of turbulent transition, where streamwise oriented flow features are common.  In a recent study (see (p)reprint page) we have looked at the optimal transient energy growth in systems such as this and derived a predictive model for the number of ligaments expected to occur.  Computer simulations to examine this problem are underway.

Image: Ligament Mediated Drop Formation 
photograph by Ph. Marmottant
and E. Villermaux, LEGI, Grenoble
and IRPHE, Marseille, FRANCE

Instability in Rotating Shear and Boundary Layers (AKA: Transition to Turbulence in Pure Fluid Accretion Disks):  Rotation has been long known to have a stabilizing effect on three dimensional fluid motion.  Under very strong rotation, a quasi two-dimensional asymptotic limit known as geostrophy is approached.  Among other effects, turbulence in this setting takes on a very different character --and appearance--- compared to its three-dimensioanl counterpart.  One outcome of this is the ability of rotating flows to form large coherent vortices (see also below) and robust mean flows, both features that figure prominently in Earth's weather patterns.  Rotation is also important on smaller scales: in the turbomachinery industry, rotating surfaces (i.e. compressor blades) are the default and common flows, such as boundary layers, behave in uncommon ways.  Because the boundary layer is a well-studied, observed and measured prototype shear flow (and because boundary layers must be present somewhere in accretion disks, which, although studied are poorly observed and measured)  it makes sense to study the astrophysical problem in this context.

Shear Flows of Two Fluids, Atomization and Spray Formation:  A strong gust of wind over the surface of the sea can create phenomena that physics cannot describe very well: waves form and quickly steepen into thin sheets, finger-like protrusions grow out of these sheets and soon drops pinch off, forming sea spray.  Many industrial processes rely on exaggerations of this scenario to produce sprays with particular properties.  Combustion in liquid fuel rocket engines, for example, depends on a flow which can be quickly turned entirely to spray - or atomized.  Experiments show that many properties of the ultimate spray depend sensitively on the details of the initial wave-forming instability.

Using a Chebyshev collocation technique, we have explored the stability of shear flows described by the Navier-Stokes equations in the case where a liquid layer and a gas layer flow in parallel.  In addition to the traditional interface (or Kelvin-Helmholtz) mode, we have found that two viscous modes can compete for the title of most unstable, and for many realistic parameter values, one of these modes (concentrated in the liquid boundary layer) can overpower the interfacial mode.

Numerical simulations in two dimensions were peformed and the results verify these instabilities (and also serve as a check on the validity of the free surface tracking code (called SURFER) - a validity that cannot be a priori assumed).  A sample of these calculations is shown below for air (in blue, above) flowing over water (in red, below), each flowing with a Blasius profile, stress-matched at the interface; time increases to the right in equal intervals  Click and save on the first image to download the entire movie (MPEG format); further simulations by our group can be found on the   group webpage .
 

Theory and Modeling of Stellar Pulsation:  In certain phases of evolution, many stars are observed to undergo large amplitude radial pulsations which lead to periodic changes of the star's luminosity.  Physically, the star serves as a kind of acoustic cavity and the pulsations are sound waves - specifically the normal modes of that cavity.  The mechanism by which stars pulsate (so-called kappa mechanism) is an instability that is driven by the temperature and density dependence of the star's opacity.

Pulsating stars can be modeled effectively using one dimensional numerical codes for compressible fluid mechanics with radiative transfer.  Such models can be used to examine linear stability properties, to simulate fully nonlinear pulsation and to examine the stability of the nonlinear limit cycles.  Numerical models which do not include convection work well for stars which are weakly convective.  Convection induces changes which lead to the stablization of lower temperature stars, however, and is thought, because of its dissipative nature, to be the determining factor of the pulsation amplitude.  What is worse, stellar convection is typically characterized by astronomical Rayleigh numbers.

Our models have predicted a new kind of pulsational mode in Cepheids (the strange mode) which although difficult to observe, would serve as a useful probe of the stars interior.  We have also included a parameterized model of turbulent convective heat and momentum transport which has led to the first accurate theoretical prediction of the "red edge" (or low temperature boundary) of the instability strip, as well as the first accurate models of double-mode stellar pulsations.

                   Convective flux profile in a Cepheid
 
 
 

Acoustic potential well (Horn Function) of a Cepheid.
(for details see the paper: "Nature of strange modes in classical variable stars:" goto papers)
 
A large number of undergraduate Research Project have also resulted from the application of turbulent convective stellar
pulsation models to particular observational data and/or general problems.  Here is an example final project poster by
Columbia Applied Physics student A. Cosmas.

Angular Momentum Transport and Vortices in Astrophysical Disks:  Accretion disks are credited with many actions.  We have yet to observe one in great detail (but see, for example, Hubble observations reported in Sky & Telescope April 2003), although disks are found around massive compact objects (like black holes and neutron stars), in sprial glaxies, and as the precursors to solar systems.    From a fluid mechanical point of view, the disk is a shear flow forced by a gravitational potential.  Becasue of the very large Reynold's Numbers that characterize the flow in a disk, it has been argued that disks must be turbulent.  In the absence of detailed measurements and in the absence of a theory for turbulence, it is difficult even to parameterize this turbulence, or to describe it in a general way.  In Nature, wherever and whenever we have observed rotating turbulent flows, we have found vortices.  Vortices, if they are also found in astrophysical disks, may play an important role in accretion and, in the case of protoplanetary disks, in planet formation.

Numerical simulations of disks done in two dimensions and in Shallow Water have suggested that vortices, and Rossby-type waves, can exist in disks and do play a major role in accretion and in the dyanamics of the disk in general.  Some claims have been made that unmagnetized disks cannot be turbulent because there is no linear instability (in spite of the fact that the lack of a linear instability mechanism is not a sufficient condition for laminar flow).  Our simulations have not demonstarted an instability that leads to turbulence, but early laboratory experiments on Taylor-Couette flows (Taylor, 1936 ProcRoy.Soc.Lon.A) suggest that turbulence is found in such flows. 

Above: surface density in five time increments, each of ten outer disk orbit periods; spiral waves excited by the binary potential drive enhanced accretion and angular momentum transport (from P.Yecko, 1995, PhD thesis, Columbia University; simulations performed at the Pittsburgh Supercomputing Center.)

A two-dimensional spotted disk                                       A spotted disk in shallow water
 
 

Meddies and Stability in Buoyancy-Driven Rotating Flows:
First discovered by T. Rossby, oceanographers were at first surprised to find lens-shaped vortices of Mediterranean water in the Western Atlantic and Caribbean Sea.  These coherent structures (called Meddies) are now known to originate from the deep outflow of Mediterranean water from the Gibralter Strait.  This density-driven outflow forms, as a result of Coriolis force, a boundary current that follows the continental Iberian shelf northward.  At this stage, eddies are believed to break off from the primary current but the mechanism is certain.  With their high salt content and long coherence timescales and travel distances, meddies may be an immenseley important factor in determining the spatial variation of the ocean's density and therefore the large scale thermo-haline circulation.

To study such currents, we performed laboratory experiments.  The structure of boundary currents formed from intermediately dense water introduced into a rotating, stably stratified, two-layer environment wass investigated in a series of laboratory experiments, performed for Froude numbers ranging from 0.01 to 1. The thickness and streamwise velocity profiles in quasi-steady currents are measured using a pH activated tracer (thymol blue) and found to compare favorably to simplified analytic solutions and numerical models. Currents flowing along sloping boundaries in a stratified background exhibit robust stability at all experimental Froude numbers. Such stability is in sharp contrast to the unequivocal instability of such currents flowing against vertical boundaries, or of currents flowing along slopes in a uniform background. The presence of a variety of wave mechanisms in the ambient medium might account for the slower and wider observed structures and the stability of the currents, by effecting the damping of disturbances through wave radiation.

It is likely to be interactions with topographic features of lengthscale comparable to the current width which promotes the formation of meddies.   The figures below show a frame from a top-view laboratroy video (left), where the current and a meddy are made visible using flourescent dye; the tracks of floats released into meddies (center, courtesy Amy Bower); and a side-view schematic diagram of the experimental apparatus (right).

A Laboratory Meddy                                   Float tracks of Meddies                      Laboratory Apparatus