Baroclinic geostrophic adjustment in a rotating circular basin

Baroclinic geostrophic adjustment in a rotating circular basin is investigated in a laboratory study. The adjustment process consists of a linear phase before advective and dissipative effects dominate the response for longer time. This work describes in detail the hydrodynamics and energetics of the linear phase of the adjustment process of a two-layer fluid from an initial step height discontinuity in the density interface DeltaH to a final response consisting of both geostrophic and fluctuating components. For a forcing lengthscale r(f) equal to the basin radius R-0, the geostrophic component takes the form of a basin-scale double gyre while the fluctuating component is composed of baroclinic Kelvin and Poincare waves. The Burger number S=R/r(f) (R is the baroclinic Rossby radius of deformation) and the dimensionless forcing amplitude epsilon = DeltaH/H-1 (H-1 is the upper-layer depth) characterize the response of the adjustment process. In particular, comparisons between analytical solutions and laboratory measurements indicate that for time tau: 1 < tau < S-1 (tau is time scaled by the inertial period 2pi/f), the basin-scale double gyre is established, followed by a period where the double gyre is sustained, given by S-1 < tau < 2epsilon(-1) for a moderate forcing and S-1 < tau < tau(D) for a weak forcing (tau(D) is the dimensionless dissipation timescale due to Ekman damping). The analytical solution is used to calculate the energetics of the baroclinic geostrophic adjustment. The results are found to compare well with previous studies with partitioning of energy between the geostrophic and fluctuating components exhibiting a strong dependence on S. Finally, the outcomes of this study are considered in terms of their application to lakes influenced by the rotation of the Earth

Bubbles emerging from a submerged granular bed

This paper explores the phenomena associated with the emergence of gas bubbles from a submerged granular bed. While there are many natural and industrial applications, we focus on the particular circumstances and consequences associated with the emergence of methane bubbles from the beds of lakes and reservoirs since there are significant implications for the dynamics of lakes and reservoirs and for global warming. This paper describes an experimental study of the processes of bubble emergence from a granular bed. Two distinct emergence modes are identified, mode 1 being simply the percolation of small bubbles through the interstices of the bed, while mode 2 involves the cumulative growth of a larger bubble until its buoyancy overcomes the surface tension effects. We demonstrate the conditions dividing the two modes (primarily the grain size) and show that this accords with simple analytical evaluations. These observations are consistent with previous studies of the dynamics of bubbles within porous beds. The two emergence modes also induce quite different particle fluidization levels. The latter are measured and correlated with a diffusion model similar to that originally employed in river sedimentation models by Vanoni and others. Both the particle diffusivity and the particle flux at the surface of the granular bed are measured and compared with a simple analytical model. These mixing processes can be consider applicable not only to the grains themselves, but also to the nutrients and/or contaminants within the bed. In this respect they are shown to be much more powerful than other mixing processes (such as the turbulence in the benthic boundary layer) and could, therefore, play a dominant role in the dynamics of lakes and reservoirs

The wave-induced solute flux from submerged sediment

The issue of the transport of dissolved nutrients and contaminants between the sediment in the bottom of a lake or reservoir and the body of water above it is an important one for many reasons. In particular the biological and chemical condition of the body of water is intricately linked to these mass transport processes. As the review by Boudreau (Rev Geophys 38(3):389–416, 2000) clearly demonstrates those transport processes are very complex involving mechanisms as diverse as the wave-induced flux between the sediment and the overlying water and the effect of burrowing animals on the transport within the sediment as well as basic diffusion mechanisms. The present paper focuses on one facet of these transport processes; we re-examine the balance of diffusion and wave-induced advection and demonstrate that the wave-induced flux of a solute from submerged sediment is not necessarily purely diffusive as suggested by Harrison et al. (J Geophys Res 88:7617–7622, 1983) but can be dominated by a mean or time-averaged flux induced by the advective fluid motion into and out of the sediment caused by the fluctuating pressure waves associated with wave motion. Indeed along the subtidal shoreline where the fluctuating bottom pressures are greatest, wave-induced advection will dominate the mean, time-averaged transport of solute into or out of the sediment as suggested in the work of Riedl et al. (Mar Biol 13:210–221, 1972). However, the present calculations also indicate that this advective flux decreases rapidly with increasing depth so that further away from the shoreline the advective flux becomes negligible relative to the diffusive flux and therefore the latter dominates in deeper water

Inclined gravity currents filling basins: The influence of Reynolds number on entrainment into gravity currents

In many important natural and industrial systems, gravity currents of dense fluid feed basins. Examples include lakes fed by dense rivers and auditoria supplied with cooled air by ventilation systems. As we will show, the entrainment into such buoyancy driven currents can be influenced by viscous forces. Little work, however, has examined this viscous influence and how entrainment varies with the Reynolds number, Re. Using the idea of an entrainment coefficient, E, we derive a mathematical expression for the rise of the front at the top of the dense fluid ponding in a basin, where the horizontal cross-sectional area of the basin varies linearly with depth. We compare this expression to experiments on gravity currents with source Reynolds numbers, Res , covering the broad range 100 < Res < 1500. The form of the observed frontal rises was well approximated by our theory. By fitting the observed frontal rises to the theoretical form with E as the free parameter, we find a linear trend for E(Res ) over the range 350 < Res < 1100, which is in the transition to turbulent flow. In the experiments, the entrainment coefficient, E, varied from 4 × 10−5 to 7 × 10−2. These observations show that viscous damping can be a dominant influence on gravity current entrainment in the laboratory and in geophysical flows in this transitional regime

The role of intratidal oscillations in sediment resuspension in a diurnal, partially mixed estuary

Using detailed observations of the mean and turbulent properties of flow, salinity and turbidity that spanned 2001/02, we examined the physical mechanisms underpinning sediment resuspension in the low-energy Swan River estuary, Western Australia. In this diurnal tidally-dominated estuary, the presence of intratidal oscillations, a tidal inequality lasting 2 to 3 hours on the flood tide, generated by interactions of the four main diurnal and semidiurnal astronomical constituents, K₁, O₁, M₂, and S₂, played a major role in modifying vertical stratification and mixing. These intratidal oscillations are controlled by phase differences between the tropic and synodic months rather than being temporally-fixed by bed friction, as occurs in semidiurnal estuaries. Intratidal oscillations are largest, at around 0.1 m, near to the Austral solstice when the lunar and solar declination are in-phase. Despite the seemingly small change in water level, shear-induced interfacial mixing caused destratification of the water column with the top-to-bottom salinity (ΔS) difference of 3.5 present early in the flood tide eroded to less than 0.3 by the end of the intratidal oscillation. High turbidity peaks, of 250 nephelometric turbidity units, coincided with these intratidal oscillations and could not be explained by bed friction since shear stress from mean flow did not exceed threshold criteria. High Reynolds stresses of ∼1 Nm⁻² did, however, exceed τcr and together with negative Reynolds fluxes indicate a net downward transport of material. Destratification of the water column induced by shear instabilities resulted in large overturns capable of moving in situ material towards the bed during intratidal oscillations and these turbidities were ∼10 times greater than those from bed-generated resuspension observed later during the flood tide

Experimental investigation of the initial regime in fingering electrodeposition: dispersion relation and velocity measurements

Recently a fingering morphology, resembling the hydrodynamic Saffman-Taylor instability, was identified in the quasi-two-dimensional electrodeposition of copper. We present here measurements of the dispersion relation of the growing front. The instability is accompanied by gravity-driven convection rolls at the electrodes, which are examined using particle image velocimetry. While at the anode the theory presented by Chazalviel et al. describes the convection roll, the flow field at the cathode is more complicated because of the growing deposit. In particular, the analysis of the orientation of the velocity vectors reveals some lag of the development of the convection roll compared to the finger envelope.Comment: 11 pages, 15 figures, REVTEX 4; reference adde