Transverse Length Scale Research Articles

The effect of rotational Brownian motion on Witten–Sander aggregates

The effect of rotational diffusion on the growth of Witten–Sander aggregates is examined. Computer simulations of a model are analyzed where the growing aggregate rotates with a rotational diffusion constant Drot(R∥)∼1/[τrot(R∥/a)δ], while the irreversibly aggregating particles jump with a diffusivity a2/τ0(τ0,τrot are the time constants for translational and rotational jumps and a is the lattice spacing). In the simulations 0.0002<(τ0/τrot)<1600 is varied over seven orders of magnitude. In general the aggregates are anisotropic (despite the inherent symmetry of the model) with longitudinal and transverse length scales R∥ and R⊥. On scales r≪R⊥ the cluster remains fractal, but on scales R⊥≪r≪R∥ the cluster becomes linear. Estimates of the dependence of R∥ on N, (τ0/τrot), and δ are made and compared with the computer data. Both initial and asymptotic behavior are investigated, and several regimes of growth identified.

Steady flow past sudden expansions at large Reynolds number. Part I: Boundary layer solutions

In the steady laminar flow past a sudden channel expansion at large Reynolds number R, the longitudinal length scale of the separated eddy typically increases linearly with R whereas the transverse length scale is O(1). If these trends were to continue indefinitely, the equations of motion in the bulk flow would reduce to the boundary layer equations as R→∞. Previous investigators obtained steady finite difference solutions to the latter for all values of the expansion ratio when the inlet velocity profile was parabolic; however, when the inflow was uniform, numerical instabilities were encountered below a certain value of the expansion ratio. In the present work these instabilities are avoided through the use of a global Newton method, and uniform inflows to several sudden expansion geometries are considered. In each case steady solutions are found only above a critical value of the expansion ratio where the pressure gradient becomes singular near the reattachment point. These results suggest that for uniform inflows and smaller values of the expansion ratio, the eddy length will no longer increase linearly with R when the latter is sufficiently large.

TURBULENT NON-BUOYANT SURFACE JETS

This paper presents the results of an experimental study on the diffusion of plane and bluff turbulent surface jets. For plane surface jets, it has been found that its length scale grows at the same rate as a plane wall jet with its velocity scale being about 0.9 times the corresponding value for the plane free jet. For bluff surface jets, the vertical length scale increases at approximately the same rate as bluff wall jet whereas its transverse length scale grows at about half the rate of the corresponding bluff wall jets. The velocity scale decays inversely with the longitudinal distance, but the constant in the velocity scale relation is somewhat higher than that for the corresponding free circular jet.

A sufficient condition for stability of axisymmetric collisionless systems

A sufficient condition for the stability of an axisymmetric mirror machine is obtained using the guiding center plasma model. The criterion is particularly suited to configurations with comparable transverse and longitudinal length scales, so‐called short, fat equilibria. Under this ordering, the stabilizing effects of plasma compression is significant. These effects are included through the use of a positive definite lower bound on their contribution to an energy principle.

A potential overshoot of a magnetized plasma made by a disk probe

A potential overshoot is made in a current-carrying plasma with a longitudinal magnetic field by a floating disk probe which works as a disturber. The overshoot appears behind the disturber in the electron current. Its transverse and longitudinal scale lengths are measured and discussed.

Crossed beam correlation measurements and model predictions in a rocket exhaust plume

The crossed beam correlation technique in its schlieren mode has been used to measure the rms value of the density gradient fluctuation and a weighted rms value of the density fluctuation across the exhaust plume of a static, liquid bipropellant rocket engine at four different axial stations. A transverse integral length scale, a form of time and length scales in the flow direction, and convection velocity have also been measured. Some of these experimental results are compared with predictions from a computer model. Where direct comparisons are possible, agreement is satisfactory. Where it is not, expected trends are observed. The results bring into question the validity of a key modeling assumption, that turbulent density fluctuations are negligible.

A proposed method of measuring turbulence length scales using laser-Doppler anemometry and photon correlation

The established techniques of photon correlation laser-Doppler anemometry allow the measurement of the mean and variance of the instantaneous velocities in turbulent flow. A method is proposed by which the mean and variance of the instantaneous velocity differences between two probe volumes may be measured. It is shown that such measurements permit the longitudinal and transverse integral length scales and Taylor microscales to be calculated.

Three-Dimensional Wall Jet Originating from a Circular Orifice

SummaryAn incompressible three-dimensional turbulent wall jet originating from a circular orifice located adjacent to a plane wall is studied both theoretically and experimentally. An approximate similarity analysis predicts that the two transverse length scales,l0and L0, and the inverse of the mean velocity scale grow linearly with distance downstream x from the orifice. Experimental measurements of mean velocity and longitudinal turbulence intensity profiles were made both in air and water with hot-wire and hot-film anemometers respectively. The behaviour predicted by the similarity analysis was verified. It was found that the rate of growth of the length scale normal to the plane wall, dl0/dx, was somewhat less than that found for a two-dimensional wall jet, whereas the rate of growth of the length scale in the lateral direction, dL0/dx, was about seven times greater than dl0/dx.

Plane Turbulent Reattached Wall Jets

An experimental study of the diffusion of a plane turbulent jet issuing from a nozzle situated over an abrupt drop in the bed of a rectangular channel, under deep submergence, is presented. The characteristics of the reattached wall jet, after the reattachment line, have been investigated in detail regarding similarity of the transverse velocity distribution, velocity and length scales, and bed shear stress distribution. Some characteristics of the eddying region have also been studied.