Session GV: Geophysical Flows: Convection

Convective turbulence in rotating and non-rotating flat Cartesian cells

Frequently, the lateral extensions of a convection layer exceed the vertical one significantly, e.g., in atmospheric mesoscale systems. We study therefore turbulent Rayleigh-B\'{e}nard convection in a Cartesian slab with an aspect ratio of 8. The Rayleigh number is fixed to $10^7$ and the Prandtl number is 0.7. Free-slip boundary conditions are applied in the vertical direction. Three cases are considered: non- rotating, weakly rotating (Rossby number larger unity), and strongly rotating (Rossby number smaller unity) convection. The variation of the turbulent heat transport and the formation of lateral large-scale temperature patterns are discussed. The large-scale pattern formation, which is obseved for the non-rotating case only, is in line with detected clusters of thermal plumes. Extensions of this model to shallow moist convection are also discussed briefly.   

Double-Diffusive Convection in Low-Aspect Ratio Containers

Laboratory experiments and phenomenological modeling were undertaken to investigate the influence of container sidewalls on the evolution of diffusive layering in confined double-diffusive systems. Such flow configurations are common in engineering situations, including underground storage caverns of national strategic petroleum reserves. The laboratory flow configuration consisted of a linearly salt stratified fluid subjected to either heating from below or uniform heating from both the bottom and sidewalls. A number of different containers were used, allowing investigations over a range of governing parameters. The growth of the lowest mixed layer as well as multiple convecting layers aloft separated by diffusive interfaces were monitored using LIF, PIV and traversing temperature/conductivity probe techniques. The aspect ratio for side walls to become important was inferred by the bottom-layer growth measurements, which undergoes a transition of the growth law upon onset of side-wall effects. The combined side and bottom wall heating case was strikingly different from the bottom heating case, wherein layers of approximately equal heights are generated rather rapidly in the former as a result of convective plumes rising along the sidewalls and their arrest by the background stable density gradient. Theoretical arguments were advanced to explain and parameterize experimental observations.   

Dynamics of a thermally-driven mantle plume with Stereo PIV and Thermochromic Liquid Crystals

Although many have studied the chemistry and dynamics of mantle plumes, fundamental questions remain. These can be grouped into two general issues: a) Plume structure and dynamical interaction with the surrounding mantle, b) The degree of entrainment and mixing in mantle plumes of chemically distinct material from the deep mantle. Heat is used as the driving convective mechanism to form a single thermal plume. The experiments are conducted in a Plexiglas tank (inner dimensions of 26.5$\times $26.5$\times $26.5 cm). A small heater of 2.0 cm diameter and centered in the tank bottom is connected to programmable power supply. By varying voltage settings we can simulate varying heat fluxes in the deep mantle. Our experiments utilize Stereoscopic Particle Image Velocimetry (SPIV) and Thermochromic Liquid Crystals (TLC's) to reconstruct the 3D flow and temperature fields within the tank. Penetration height, plume head size, velocity and vorticity fields are determined using SPIV providing insight into the plume structure and the nature of the entrainment process.   

Three-dimensional simulations of double-diffusive salt-finger convection and layer formation

In double-diffusive convection, the buoyancy of the fluid is controlled by two components that diffuse at markedly different rates. In the so-called ``fingering'' case, the faster-diffusing component has a stabilizing gradient while the slower-diffusing component destabilizes the system through the formation of small-scale finger filaments. One important consequence of salt fingers is their ability to form persistent large-scale ``staircases'' of mixed layers separated by thin fingering interfaces. Although several theories have been put forward to explain the formation and subsequent merging of layers, there is considerable disagreement about the dominant physical processes involved. Until recently, three-dimensional direct numerical simulations of the process have been hampered by the vastly different length and time scales involved. Here, we present highly resolved two- and three-dimensional simulations of salt fingering and layer formation which allow to test existing theories on staircase formation. We observe markedly different structures in two and three dimensions, including large scale 3D wave-like instabilities that are absent in the two-dimensional case. These as well as other differences in physical behavior suggest that three-dimensional studies are essential for a complete picture of fingering systems.   

Abrupt transitions and hysteresis in thermohaline laboratory models

Steady ocean circulation models can change in three different ways as the forcing parameters are slowly altered: smooth evolution, abrupt transition without hysteresis, and abrupt transition with hysteresis. In the second, the transition point is independent upon whether the driving parameter is increased or decreased. In the third, the transition points differ depending upon whether the driving parameter approachs from one side or the other. The second and third ways are found in simplified numerical ocean circulation models that are driven either seasonally or with climate changes. Old and new laboratory experiments demonstrate both forms of abrupt transitions. A laboratory experiment that followed Stommel's box model for abrupt transitions had large abrupt transitions in temperature with salinity and clear and distinct hysteresis. Two experiments that allowed for more complex flows had a much smaller range of hysteresis but transitions were still distinct. A new experiment is reported here with virtually no hysteresis. It has a cavity immersed in a tank of fresh water at room temperature. The cavity is heated from below and salt water is steadily pumped in. The transition is abrupt, but the data have virtually no hysteresis.   

Responses to time-dependent forcing in horizontal convection

We examine the adjustment of a convective overturning circulation, forced by differential heating and cooling at the surface, to changing boundary conditions. The aim is to provide a deeper understanding of the dynamics of horizontal convection. In laboratory experiments with a long box forced by heat input over one half of the forcing boundary and cooling over the other half, a small step change in forcing leads to a shift from one equilibrium state to another, where each equilibrium state has zero net heat flux through the boundary. The approach to the new state is simply exponential if the change in boundary conditions produces a net destabilizing buoyancy flux, but can involve a change from full-depth to shallow circulation if there is a period of net stabilizing buoyancy flux. Flux and temperature boundary conditions give similar results and the adjustment times tend to be reduced by effects of rotation. Oscillatory forcing is examined for the case of a central region of stabilizing surface buoyancy flux between two regions of destabilizing flux (two plumes), the latter having imposed heat fluxes that are varied sinusoidally, so that the total heat input to the box is constant and the net heat input is zero. The interior temperature and stratification are explored as a function of oscillation period and amplitude.   

Characteristics of Geostrophically Balanced Convective Plumes from Simulations of Asymptotically Reduced Equations

Reduced equations for rotating convection in a Boussinesq fluid are derived via multiscale asymptotics in the limit of tall aspect ratio and low Rossby number. Simulations of these equations reveal the presence of long lived convective plumes that span the depth of the layer and which transport the majority of the heat flux across the layer. The characteristics of these convective plumes are examined with particular attention paid to both the structure of individual plumes and the integral properties of plume ensembles.   

Exploitation of combined visible hyperspectral and infrared imagery

Natural and anthropogenic surfactants accumulate at the air-sea interface, forming microlayer films, slicks, and foam patches. The resulting enhanced viscoelasticity of the interface alters the small-scale wave spectrum and near-surface turbulence. These changes alter the surface thermal boundary layer and ``skin'' temperature, making infrared thermal imagery ideal for detecting/mapping/studying ocean slicks. Slicks are found under a range of conditions and can result from physical straining of the sea surface (e.g. internal waves) as well as from local biological processes (e.g. plankton blooms). Airborne datasets that combine simultaneous airborne infrared and visible wavelength hyperspectral remote sensing data are now available and provide new opportunities to investigate the physical and biological processes that result in ocean slicks. In addition to the multiple sensors, these datasets are at spatial and time scales much smaller than possible with available satellite remote sensors. This enables the study of a much broader range of phenomena. In particular we investigate the relationship between surface accumulations of vegetative material, ocean slicks and surface temperature changes. We also investigate the relationship between the presence of slicks and water column chromophoric dissolved organic matter (CDOM).   

Budgets of Reynolds stress and turbulent kinetic energy in LES of Langmuir circulation in shallow water

We analyze budgets of Reynolds stress and turbulent kinetic energy (TKE) in large-eddy simulation (LES) of full-depth Langmuir circulation (LC) in a wind-driven shear current in shallow water. LES with near-wall resolution is performed, thereby resolving surface and bottom viscous boundary layers. The LES is driven by wind and wave forcing representative of conditions during field measurements of shallow water, full-depth LC and is able to capture the turbulent structure measured in the field. Analysis of the budgets reveals that LC impacts the energy transfer near the bottom. In traditional boundary layers, mean shear acts as the main source of downwind TKE (u'u') while pressure-strain correlation serves to re-distribute this energy to crosswind (v'v') and vertical (w'w') components. In the flow with LC, the Craik-Leibovich vortex force generating LC acts as a source of vertical TKE, while pressure-strain correlation re-distributes this energy to the crosswind component. LC also disrupts the usual log-layer balance between production and dissipation. Furthermore, LC disrupts the log-law, inducing a ``law of the wake-like'' behavior. These results have important implications on turbulence parameterizations for RANSS (Reynolds-averaged Navier-Stokes simulation) of the coastal ocean.   

Bubble convection within magma reservoirs

Volcanoes are gas-rich hence small bubbles slowly rise in magma reservoirs. Under certain condition of gas flux, bubble size and reservoir height, the bubble rise is no more homogeneous: the collective buoyancy of the bubbles produces instabilities and the bubble motion becomes driven by convection. If such a convection occurs, the residence time of bubbles in the reservoir is reduced and thus eruptive activity is modified. By analogy with thermal convection, we define Rayleigh ($Ra_{b}$) and Prandtl ($Pr_{b}$) numbers for bubble convection. However, the critical $Ra_{b}$ for bubble convection is hardly known from previous studies and its dependence to $Pr_{b}$ is ignored. Laboratory experiments are performed with small bubbles rising in a cylindrical tank filled with viscous oils in order to quantify bubble convection and apply it to real volcanoes. $Ra_{b}$ and $Pr_{b}$ are acurately determined from measurement, via two hydrophones, of bubble size and gas volume fraction. Bubble velocity is obtained by PIV. Experiments show two main regimes: a steady cellular regime at low Rab and a bubble plume regime when Rab is higher. The critical $Ra_{b}$ depends on the critical $Pr_{b}$ for the two transitions.