Stephen W. Morris

Apparatus for the study of Rayleigh–Bénard convection in gases under pressure

We review the history of experimental work on Rayleigh–Benard convection in gases, and then describe a modern apparatus that has been used in our experiments on gas convection. This system allows for the study of patterns in a cell with an aspect ratio (cell radius/fluid layer depth) as large as 100, with the cell thickness uniform to a fraction of a μm, and with the pressure controlled at the level of one part in 105. This level of control can yield a stability of the critical temperature difference for the convective onset of better than one part in 104. The convection patterns are visualized and the temperature field can be inferred using the shadowgraph technique. We describe the flow visualization and image processing necessary for this. Some interesting results obtained with the system are briefly summarized.

The spatio-temporal structure of spiral-defect chaos

Abstract We present a study of the recently discovered spatially extended chaotic state known as spiral-defect chaos, which occurs in low-Prandtl number, large-aspect ratio Rayleigh-Benard convection. We employ the modulus squared of the space-time Fourier transform of time series of two-dimensional shadowgraph images to construct the structure factor S(k, ω). This analysis is used to characterize the average spatial and temporal scales of the chaotic state. We find that the correlation length and time can be described by power law dependences on the reduced Rayleigh number ϵ. These power laws have as yet no theoretical explanation.

ANNULAR ELECTROCONVECTION WITH SHEAR

We report experiments on convection driven by a radial electrical force in suspended annular smectic A liquid crystal films. In the absence of an externally imposed azimuthal shear, a stationary one-dimensional (1D) pattern consisting of symmetric vortex pairs is formed via a supercritical transition at the onset of convection. Shearing reduces the symmetries of the base state and produces a traveling 1D pattern whose basic periodic unit is a pair of asymmetric vortices. For a sufficiently large shear, the primary bifurcation changes from supercritical to subcritical. We describe measurements of the resulting hysteresis as a function of the shear at radius ratio

Natural versus forced convection in laminar starting plumes

\eta \sim 0.8

Nonlinear Geophysics: Why We Need It

. This simple pattern forming system has an unusual combination of symmetries and control parameters and should be amenable to quantitative theoretical analysis.

Electrically driven convection in a thin annular film undergoing circular Couette flow

A starting plume or jet has a well-defined, evolving head that is driven through the surrounding quiescent fluid by a localized flux of either buoyancy or momentum, or both. We studied the scaling and morphology of starting plumes produced by a constant flux of buoyant fluid from a small, submerged outlet. The plumes were laminar and spanned a wide range of plume Richardson numbers Ri. Ri is the dimensionless ratio of the buoyancy forces to inertial effects and thus our measurements crossed over the transition between buoyancy-driven plumes and momentum-driven jets. We found that the ascent velocity of the plume, nondimensionalized by Ri, exhibits a power law relationship with Re, the Reynolds number of the injected fluid in the outlet pipe. We also found that as the threshold between buoyancy-driven and momentum-driven flows was crossed, two distinct types of plume head morphologies exist: confined heads, produced in the Ri>1 regime, and dispersed heads, which are found in the Ri 1 regime, and dispersed heads, which are found in the Ri<1 regime. Head dispersal...

Patterns at the onset of electroconvection in freely suspended smectic films

Few geoscientists would deny that effects are often sensitively dependent on causes, or that their amplification is commonly so strong as to give rise to qualitatively new “emergent” properties, or that geostructures are typically embedded one within another in a hierarchy. Starting in the 1980s, a growing number felt the need to underline the absolute importance of such nonlinearity through workshops and conferences. Building on this, the European Geosciences Union (EGU) organized a nonlinear processes (NP) section in 1990; AGU established a nonlinear geophysics (NG) focus group in 1997; and both unions began collaborating on an academic journal, Nonlinear Processes in Geophysics, in 1994.

Aspect-Ratio Dependence of Charge Transport in Turbulent Electroconvection

We investigate the linear stability of a thin, suspended, annular film of conducting fluid with a voltage difference applied between its inner and outer edges. For a sufficiently large voltage, such a film is unstable to radially driven electroconvection due to charges which develop on its free surfaces. The film can also be subjected to a Couette shear by rotating its inner edge. This combination is experimentally realized using films of smectic A liquid crystals. In the absence of shear, the convective flow consists of a stationary, azimuthally one-dimensional (1D) pattern of symmetric, counter-rotating vortex pairs. When Couette flow is applied, an azimuthally traveling pattern results. When viewed in a co-rotating frame, the traveling pattern consists of pairs of asymmetric vortices. We calculate the neutral stability boundary for arbitrary radius ratio α and Reynolds number Re of the shear flow, and obtain the critical control parameter Rc(α,Re) and the critical azimuthal mode number mc(α,Re). The Co...

On the origin and evolution of icicle ripples

We report the results of experiments on electrically driven convection that occurs in a thin, freely suspended film of smectic A liquid crystal when an electric field is applied in the plane of the film. Convection in a vortex pattern is found above a well-defined critical voltage. The film behaves as a two-dimensional isotropic liquid: neither its thickness nor the director field are modified by the flow. We present measurements of the critical voltage at the onset of convection in two experimental configurations—one which allows the injection of charges into the film from the electrodes, and one which does not. When injection is present, the critical voltage for the onset of flow increases monotonically with increasing frequency of applied field. With no injection, there is no instability at DC and the critical voltage diverges there. The nature of the flow pattern observed at onset changes with frequency. Below a certain frequency the film flows in vortices that extend over the width of the film; above this frequency the flow is confined to two lines of smaller vortices localized along the electrodes. We present a simple discussion of the mechanisms which drive the convection.

Localized states in sheared electroconvection

We present measurements of the normalized charge transport or Nusselt number Nu as a function of the aspect ratio Gamma for turbulent convection in an electrically driven film. In analogy with turbulent Rayleigh-Bénard convection, we develop the relevant theoretical framework in which we discuss the local power-law scaling of Nu with a dimensionless electrical forcing parameter R. For these experiments where 10(4) less, similar R less, similar 2 x 10(5) we find that Nu approximately F(Gamma)Rgamma with either gamma=0.26 (+/-0.02) or gamma=0.20 (+/-0.03), in excellent agreement with the theoretical predictions of gamma=1/4 and 1/5. Our measurements of the aspect-ratio dependence of Nu for 0.3</=Gamma</=17 compares favorably with the function F(Gamma) from the scaling theory.