Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities

The interaction of a plane weak shock wave with a single discrete gaseous inhomogeneity is studied as a model of the mechanisms by which finite-amplitude waves in random media generate turbulence and intensify mixing. The experiments are treated as an example of the shock-induced Rayleigh-Taylor instability. or Richtmyer-Meshkov instability, with large initial distortions of the gas interfaces. The inhomogeneities are made by filling large soap bubbles and cylindrical refraction cells (5 cm diameter) whose walls are thin plastic membranes with gases both lighter and heavier than the ambient air in a square (8.9 cm side shock-tube text section. The wavefront geometry and the deformation of the gas volume are visualized by shadowgraph photography. Wave configurations predicted by geometrical acoustics, including the effects of refraction, reflection and diffraction, are compared to the observations. Departures from the predictions of acoustic theory are discussed in terms of gasdynamic nonlinearity. The pressure field on the axis of symmetry downstream of the inhomogeneity is measured by piezoelectric pressure transducers. In the case of a cylindrical or spherical volume filled with heavy low-sound-speed gas the wave which passes through the interior focuses just behind the cylinder. On the other hand, the wave which passes through the light high-sound-speed volume strongly diverges. Visualization of the wavefronts reflected from and diffracted around the inhomogeneities exhibit many features known in optical and acoustic scattering. Rayleigh-Taylor instability induced by shock acceleration deforms the initially circular cross-section of the volume. In the case of the high-sound-speed sphere, a strong vortex ring forms and separates from the main volume of gas. Measurements of the wave and gas-interface velocities are compared to values calculated for one-dimensional interactions and for a simple model of shock-induced Rayleigh-Taylor instability. The circulation and Reynolds number of the vortical structures are calculated from the measured velocities by modeling a piston vortex generator. The results of the flow visualization are also compared with contemporary numerical simulations

Shock wave focusing using geometrical shock dynamics

A finite-difference numerical method for geometrical shock dynamics has been developed based on the analogy between the nonlinear ray equations and the supersonic potential equation. The method has proven to be an efficient and inexpensive tool for approximately analyzing the focusing of weak shock waves, where complex nonlinear wave interactions occur over a large range of physical scales. The numerical results exhibit the qualitative behavior of strong, moderate, and weak shock focusing observed experimentally. The physical mechanisms that are influenced by aperture angle and shock strength are properly represented by geometrical shock dynamics. Comparison with experimental measurements of the location at which maximum shock pressure occurs shows good agreement, but the maximum pressure at focus is overestimated by about 60%. This error, though large, is acceptable when the speed and low cost of the method is taken into consideration. The error is primarily due to the under prediction of disturbance speed on weak shock fronts. Adequate resolution of the focal region proves to be particularly important to properly judge the validity of shock dynamics theory, under-resolution leading to overly optimistic conclusions

Rapid evaporation at the superheat limit

In an experimental investigation of the transient processes that occur when a single droplet of butane at the superheat limit vaporizes explosively, short-exposure photographs and fast-response pressure measurements have been used to construct a description of the complete explosion process. It is observed that only a single bubble forms within the drop during each explosion, and that the growth proceeds on a microsecond time scale. An interfacial instability driven by rapid evaporation has been observed on the surface of the bubbles. It is suggested that the Landau mechanism of instability, originally described in connection with the instability of laminar flames, also applies to rapid evaporation at the superheat limit. The photographic evidence and the pressure data are used to estimate the evaporative mass flux across the liquid-vapour interface after the onset of instability. The ;ate of evaporation is shown to be two orders of magnitude greater than would be predicted by conventional bubble-growth theories that do not account for the effects of instability. An estimate of the mean density within the bubbles during the evaporative stage indicates that it is more than one half of the critical density of butane. Additional interesting dynamical effects that are observed include a series of toroidal waves that form on the interface between the butane vapour and the external host liquid in the bubble column apparatus after the bubble has grown large enough to contact the outer edge of the drop, and violent oscillations of the bubble that occur on a millisecond time scale, after evaporation of the liquid butane is complete, that cause the disintegration of the bubble into a cloud of tiny bubbles by Rayleigh-Taylor instability

Shock dynamics in non-uniform media

The theory of shock dynamics in two dimensions is reformulated to treat shock propagation in a non-uniform medium. The analysis yields a system of hyperbolic equations with source terms representing the generation of disturbances on the shock wave as it propagates into the fluid non-uniformities. The theory is applied to problems involving the refraction of a plane shock wave at a free plane gaseous interface. The ‘slow–fast’ interface is investigated in detail, while the ‘fast–slow’ interface is treated only briefly. Intrinsic to the theory is a relationship analogous to Snell's law of refraction at an interface. The theory predicts both regular and irregular (Mach) refraction, and a criterion is developed for the transition from one to the other. Quantitative results for several different shock strengths, angles of incidence and sound-speed ratios are presented. An analogy between shock refraction and the motion of a force field in unsteady one-dimensional gasdynamics is pointed out. Also discussed is the limiting case for a shock front to be continuous at the interface. Comparison of results is made with existing experimental data, with transition calculations based on three-shock theory, and with the simple case of normal interaction

The late-time development of the Richtmyer–Meshkov instability

Measurements have been made of the growth by the Richtmyer–Meshkov instability of nominally single-scale perturbations on an air/sulfur hexafluoride (SF6) interface in a large shock tube. An approximately sinusoidal shape is given to the interface by a wire mesh which supports a polymeric membrane separating the air from the SF6. A single shock wave incident on the interface induces motion by the baroclinic mechanism of vorticity generation. The visual thickness delta of the interface is measured from schlieren photographs obtained singly in each run and in high-speed motion pictures. Data are presented for delta at times considerably larger than previously reported, and they are tested for self-similarity including independence of initial conditions. Four different initial amplitude/wavelength combinations at one incident shock strength are used to determine the scaling of the data. It is found that the growth rate decreases rapidly with time, ddelta/dt[proportional]t–p (i.e., delta[proportional]t1–p), where 0.67<~p<~0.74 and that a small dependence on the initial wavelength lambda0 persists to large time. The larger value of the power law exponent agrees with the result of the late-time-decay similarity law of Huang and Leonard [Phys. Fluids 6, 3765–3775 (1994)]. The influence of the wire mesh and membrane on the mixing process is assessed

Dynamics of explosive degassing of magma: Observations of fragmenting two-phase flows

Liquid explosions, generated by rapid degassing of strongly supersaturated liquids, have been investigated in the laboratory with a view to understanding the basic physical processes operating during bubble nucleation and growth and the subsequent behavior of the expanding two-phase flow. Experiments are carried out in a shock tube and are monitored by high-speed photography and pressure transducers. Theoretical CO_2 supersaturations up to 455 times the ambient saturation concentration are generated by a chemical reaction; K_2CO_3 solution is suddenly injected into an excess of HCl solution in such a way as to mix the two solutions rapidly. Immediately after the injection event, a bubble nucleation delay of a few milliseconds is followed by rapid nucleation and explosive expansion of CO_2 bubbles forming a highly heterogeneous foam. Enhanced diffusion due to advection in the flow coupled with continuous mixing of the reactants, and hence on-going bubble nucleation after injection, generates an increasingly accelerating flow until the reactants become depleted at peak accelerations of around 150 g and velocities of about 15 m s^(−1). Stretching of the accelerating two-phase mixture enhances the mixing. Liberation of CO_2 vapor is spatially inhomogeneous leading to ductile fragmentation occurring throughout the flow in regions of greatest gas release as the consequence of the collision and stretching of fluid streams. The violence of the eruptions is controlled by using different concentrations of the HCl and K_2CO_3 solutions, which alters the CO_2 supersaturation and yield and also the efficiency of the mixing process. Peak acceleration is proportional to theoretical supersaturation. Pressure measurements at the base of the shock tube show an initial nucleation delay and a pressure pulse related to the onset of explosive bubble formation. These chemically induced explosions differ from liquid explosions created in other experiments. In explosions caused by sudden depressurization of CO_2-saturated water, the bubbles nucleate uniformly throughout the liquid in a single nucleation event. Subsequent bubble growth causes the two-phase mixture to be accelerated upward at nearly constant accelerations. Explosively boiling liquids, in which heterogeneous nucleation is suppressed, experience an evaporation wave which propagates down into the liquid column at constant average velocity. Fragmentation occurs at the sharply defined leading edge of the wavefront. The chemical flows effectively simulate highly explosive volcanic eruptions as they are comparable in terms of flow densities, velocities, accelerations, and in the large range of scales present. The large accelerations cause strong extensional strain and longitudinal deformation. Comparable deformation rates in volcanic systems could be sufficient to approach conditions for brittle fragmentation. Tube pumice is a major component of plinian deposits and ignimbrites and preserves evidence of accelerating flow conditions

Predicting Landscape-Scale CO 2 Flux at a Pasture and Rice Paddy with Long-Term Hyperspectral Canopy Reflectance Measurements

Measurements of hyperspectral canopy reflectance provide a detailed snapshot of information regarding canopy biochemistry, structure and physiology. In this study, we collected 5 years of repeated canopy hyperspectral reflectance measurements for a total of over 100 site visits within the flux footprints of two eddy covariance towers at a pasture and rice paddy in northern California. The vegetation at both sites exhibited dynamic phenology, with significant interannual variability in the timing of seasonal patterns that propagated into interannual variability in measured hyperspectral reflectance. We used partial least-squares regression (PLSR) modeling to leverage the information contained within the entire canopy reflectance spectra (400–900 nm) in order to investigate questions regarding the connection between measured hyperspectral reflectance and landscape-scale fluxes of net ecosystem exchange (NEE) and gross primary productivity (GPP) across multiple timescales, from instantaneous flux to monthly integrated flux