Scientific and Technical Aerospace Reports Volume 39 April 6, 2001

Newtonian fluids in the laboratory, a useful configuration involves a cylinder of liquid placed between two solid plates, which
are then stretched at an exponential rate. The quantitative results of these calculations will be presented in detail elsewhere, but
for example we will exhibit snapshots of the stretched bridges, and such quantities as the minimum radius, normalized force on
the plates, and Trout on ratio as a function of Hencky strain. These results resemble those found in experiment and simulation,
respectively.
Author (revised)
Molecular Dynamics; Fluid Flow; Field Theory (Physics); Newtonian Fluids; Equations of Motion
20010024923 California Univ., Physics Dept., Los Angeles, CA USA
Diffusing Light Photography of Containerless Ripple Turbulence
Wright, William, California Univ., USA; Putterman, Seth, California Univ., USA; Proceedings of the Fifth Microgravity Fluid
Physics and Transport Phenomena Conference; December 2000, pp. 800-819; In English; See also 20010024890; No Copyright;
Avail: CASI; A03, Hardcopy; A10, Microfiche
The high amplitude motion of the surface of a fluid displays a number of extraordinary phenomena ranging from localized
structures to turbulence. Among localized structures there can appear breather and kink solitons [sometimes called darkons] and
aspects of turbulence can be studied via the mutual scattering of ripples running along the surface of a fluid. As the height of the
surface of a fluid Zeta(r,t) as a function of position and time is the key parameter measurement of the above phenomena requires
a technique that can resolve large variations in Zeta(r,t). In our experiments the surface motion is made visible by suspending into
the water a .04% solution of polyballs. This concentration is sufficiently dense that light travelling through the water is so strongly
scattered that it diffuses. In this way the technique overcomes the problems presented by the appearance of caustics in attempts
to apply shadowgraphs to high amplitude fluid motion. The key criterion for the application of diffusing light principles to resolve
surface height is that the overall depth of the fluid must be greater than the transport mean free path which in turn must be comparable
to the maximum surface heights resolved. The concentration is sufficiently dilute that it does not affect the viscosity. Light
is then incident on the fluid from below and a charge coupled device (CCD) records the light to exit the fluid. Typically the image
of the surface is broken up into one million pixels [1024x1024] where each pixel is capable of recording a dynamic range of 65,000
gray scales [or 16 bits]. This image is converted into the surface height with the help of a calibration plot.This plot shows the
amount of light to exit the surface as a function of fluid depth. The deeper the fluid the smaller is the amount of light to make it
to the surface at that location. The dependence on surface slope is weak as demonstrated from photos of jello molds in the shape
of sine waves that are formed from these water polyball solutions. The maximum slopes of these molds corresponds to capillary
wave mach numbers of about 1/2, This imaging technique is useful for obtaining an instantaneous realization of the surface height
when the illumination is in the form of a short [microsecond] flash of light. The surface height as a function of time at a single
point in the fluid can be obtained by reading out the calibrated signal from a single pixel as a function of time. This technique has
been able to resolve, the hyperbolic secant profile of a breather soliton, the hyperbolic tangent profile of a darkon, the unusual
shear thinned states of non-Newtonian fluids, and the Kolmogorov spectrum of ripple turbulence. This last case constitutes the
core of a proposed experiment in microgravity and will be described further. The law for the spectrum in the inertial region can
be derived in parallel with Kolmogorov’s law of vortex turbulence. If E(sub k) denotes the ripple energy per unit area between
k and 2k then E(sub k) must be sufficiently large that nonlinear reversible processes dominate damping of mechanical energy due
to viscosity.. Furthermore the density of modes excited must be sufficiently large that their spacing in frequency space is less than
their broadening due to nonlinear interactions. In this limit one finds for the power spectrum of surface motion: Measurements
reveal reasonable agreement with both of theses formulas. The fact the the temporal spectrum agrees with the spatial spectrum
is another test of the imaging technique. A number of key assumptions underly the ’derivation’ of Kolmogorov’s law from the
theory of interacting propagating waves. They are 1) the random phase approximation and 2) a closure hypothesis. In its simplest
form the closure hypothesis says that the average of the product of action of two modes is the product of the averages [this can
be called a stosszahl ansatz]. The abiding question of turbulence is the extent to which these assumptions are violated. These issues
will be addressed in a microgravity environment where ripples will be studied on the surface of a positioned fluid sphere that is
about 12cm in diameter. The sphere will be held in place and excited by acoustic forces. Light will be brought in with an optical
fiber to the center of the sphere. From that point light will diffuse out to the surface where it will be imaged. On the surface of
a sphere the wavenumber k is replaced with l/R where l is an integer and R is the radius of the sphere. For a cascade starting at
1Hz [l about 8], the turbulent regime in k should extend over more than 1.5 decades. The advantages of microgravity are that the
forces of capillarity dominate the motion over a wider ranger of wave numbers than on the ground. This is desirable as the nonlinear
properties of capillary waves are much stronger than those of gravity waves. At these longer wavelengths capillary waves also
suffer less dissipation and so the effects of turbulent motion are more accessible. In low g it is possible to levitate a large drop of
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