Table of contents

A numerical study of the stratified flow past a bell-shaped hill is presented. The three-dimensional unsteady Navier-Stokes equations under the Boussinesq approximation are solved by a finite difference method in a generalized coordinate system. The characteristic phenomena of the stratified flow with various Froude numbers are successfully simulated. The results are compared with theoretical and experimental data and good agreement is obtained.

A pseudo-spectral code is used to simulate unsteady three-dimensional Bénard convection in a fluid of moderate Prandtl number, Pr = 10. Periodic, quasi-periodic and chaotic regimes are identified for Rayleigh numbers R in the range 40R_c ⩽ R ⩽ 75R_c. Attention is focussed on calculating experimentally measurable properties of the temperature field; the Nusselt number, and the phase shift impressed on light shone through the fluid, due to temperature-induced variations in the refractive index of the fluid. Statistical properties of these quantities are discussed for the three flow regimes. The horizontally averaged Nusselt number can show qualitatively different behaviour from pointwise measurements of the phase-shift; in particular it is insensitive to the presence of travelling wave instabilities. Insufficient spatial resolution of the flow appears to suppress chaotic temporal behaviour.

Using data obtained with an array of eight X-probes, the most likely arrangements of organized motion have been identified in the near-field of a turbulent circular jet. An approximation to the large scale vorticity is used to detect the organization, while a time-delay probability method is used to search for dominant arrangements or modes. At the end of the potential core (x/d = 4), the opposing or symmetrical mode is more dominant than the alternating or antisymmetrical mode. However, the alternating mode becomes increasingly dominant throughout the interaction region of the jet. The streamwise spacing of the organized motion grows linearly with distance from the nozzle in proportion to the jet half-radius.

An earlier proof of the superconvergence of Multhopp's discretization for the flow past a two-dimensional flat plate showed the potentiality of an optimal discretization scheme for vortex-lattice methods. The study of the superconvergence of Multhopp's discretization is extended to the more complicated flow past a thin airfoil, with camber line represented by a polynomial of degree 4. The approach is based on an error analysis. We show that the numerical solution for the vorticity density on the camber line is complete agreement with the extract solution when a Multhopp discretization is used;the lift and pitching moment are also exact. To obtain this kind of high accuracy, the only limitation is that the number of the elements used is greater than 2.

It is shown that the Weierstrass-Mandelbrot function simulates the irregularity in a turbulent velocity record and yields correct forms for the energy and dissipation spectra. In particular, the universal properties of a corresponding multi-fractal function are demonstrated by showing its ability to reproduce and explain turbulent flow spectra measured near the walls of straight and curved channels and in the obstructed space between a pair of disks corotating in an axisymmetric enclosure. The simulation capabilities of the multi-fractal function strongly suggest that turbulence is fractal in the frequency range of the turbulent energy spectrum where the slope of the logarithm of the spectrum, G, is -3 < G < -1. The scale-independent frequency range of the energy spectrum correctly represented by the multi-fractal function includes the isotropic dissipation subrange (-3 < G < -5/3), the inertial subrange (G = -5/3), and the "inner" portion of the anisotropic large-scale subrange (-5/3 < G < -1).

Surface slicks at sea are characterized by the occurence of capillary-wave damping materials at the air-water interface. Physical mechanisms causing such slicks are believed to include internal waves, Langmuir circulations, and other phenomena involving vertical or horizontal transport and compression of surfactants We report the rates of transport and deposition of four naturally occurring surface-active organic materials to the seawater-air interface by an ascending current field. Our results indicate that the susceptibility of these materials to transport by current follows the same relative order as their susceptibility by bubbles (although the latter rate is dramatically greater). The current transport results obtained can be explained by standard surface adsorption kinetics. Our data also indicate that subtle variations in the chemical structure and polarity of different materials may be major determining factors influencing their transport to the sea surface by currents.

The force field around a circular cylinder (D = 5.1 cm) towed at U = 0.15 m/s was explored by measuring the lift F_ℓ and drag F_d of a small (cylindrical) probe inserted at various locations near the cylinder. By taking the Fourier transform of the lift F_ℓ the force component a(f₀) that fluctuates in the transverse direction at the circular cylinder's vortex frequency f₀ was isolated. This signature of vortex shedding could be detected in a "forefield" that stretches cylinder diameter upstream and to the side of the main cylinder. At all points in the forefield the oscillating force component opposite to the lift F_L(t) of the main cylinder. In downstream direction the phase difference between a(f₀) and F_L grows steadily, implying a phase velocity of v ≈ 0.8U.

The oblique shock reflection over a multi-guttered model wedge is investigated at constant Mach number. The experimental parameters were the reflecting wedge angle and the depth of the gutter. It is found that, unlike the case of a smooth surface, the wave structure is not self-similar but similar with respect to the coordinate system made dimensionless by the depth when the wedges are geometrically similar (regardless of Reynolds number based on the depth). Again, unlike the smooth surface, the wave structure is essentially unsteady, and the entire body of waves reflected from the bottom of the gutters play a key role in the configuration of a precursory reflected wave as well as in the behavior of the triple point. The slope of the triple point trajectory suggests that it approaches asymptotically that for a smooth surface.

Flow characteristics of the time-dependent non-Newtonian fluid obeying Casson's stress-strain relation have been investigated in the annular space between two coaxial rotating cylinders. The problem is considered when the inner cylinder is at rest and the outer cylinder rotating with a constant velocity. For the steady flow condition, the velocity distribution, pressure coefficient, stresses and shear rates have been obtained for various values of aspect ratio. Also the extent of core formation and critical values of Casson number have been determined. The analysis is useful for viscometric studies of blood in rheogoniometers and also for getting insight into blood flow anomalies.