Session M19: Convection and Buoyancy-Driven Flows: Plumes and Gravity Waves/Currents

Stressed Horizontal Convection

We present experiments aimed at elucidating the interaction between wind-induced surface shear and the meridional overturning circulation. The effect of a shear stress on convection driven by a maintained dense source entering a homogeneous environment is explored. A saline plume enters a confined fresh-water environment at a boundary along with which a constant shear stress is being applied simultaneously. The system is driven to a statistically steady state, and the resulting density and velocity fields are obtained by Synthetic Schlieren and PIV techniques, respectively. The magnitude and direction of the shear stress is varied between experiments, as well as the density of the plume. Results indicate that there exists a competitive regime between the buoyancy and mechanical forcing, resulting in marked variations in flow features such as the interior stratification and boundary layer thickness, among others.   

Instabilities of plumes driven by localized heating in a stably stratified ambient

Plumes due to localized buoyancy sources are of wide interest due to their prevalence in many geophysical situations. This study investigates the transition from laminar to turbulent dynamics. Several experiments have reported that this transition is sensitive to external perturbations. As such, a well-controlled set-up has been chosen for our numerical study, consisting of a localized heat source at the bottom of an enclosed cylinder whose sidewall is maintained at a fixed temperature which varies linearly up the wall, and there is a localized heat source on the bottom. Restrincting the dynamics to the axisymmetric subspace, the first instability is to a puffing state. However, for smaller Grashof numbers, the plume becomes unstable to 3D perturbations and a swirling plume spontaneously appear. Further bifurcations observed in the rotating frame where the plume is stationary also exibits puffing, suggesting a connection between the unstable axisymmetric solution and the swirling plume. Further bifurcations result in quasiperiodic states with a very low frequency modulation, that eventually become turbulent.   

Plume emission statistics in turbulent Rayleigh-B\'enard convection

Rayleigh-Benard convection features ubiquitous coherent structures, which continue to survive in strong turbulence. The most prevalent are the thermal plumes and the large scale circulation (LSC). The thermal plumes and the LSC are intrinsically coupled, as thermal plumes cluster to form a LSC. We report statistics of the area, width and location of plumes extracted from high Rayleigh number (Ra $\leq 10^{12}$) direct numerical simulations in a cylindrical domain of aspect-ratio $0.33$. While the area of the plume is unimodally distributed close to the plates, far from the plates plume clustering results in a bimodal distribution. In addition, the analysis reveals that more plumes are emitted from areas with low shear as compared to areas with high shear.   

Impingement of a plume on a non-horizontal rigid boundary

Buoyancy driven flows created by density differences, plumes are a phenomenon observed in many situations in both nature and industry. Instances of plume impingement on a rigid boundary are also common. Whether this smoke from a candle impacting on a ceiling or, for a much larger scale example, plumes in the ocean descending onto the continental shelf, such as in dense water formation in the Weddell Sea. In both these cases, and many others, the boundary is rarely a horizontal plane and so motivates the study for a plume impacting on a non-horizontal geometry. After reviewing previous work of a plume impinging on a horizontal, we introduce the problem of a plume impinging on an incline by presenting experiments varying the angle of inclination and the distance between the boundary and plume source. In an attempt to understand dynamics of large scale plumes in ocean, we also present the same experiment in a rotating system.   

Three dimensional simulations of internal solitary waves

This study focuses on mass transport and mixing induced by mode-2 internal solitary waves (ISWs) propagating along a pycnocline between two continuously stratified fluid layers. A direct numerical simulation (DNS) model is developed for the incompressible three-dimensional Navier-Stokes equations in the Boussinesq limit. By using high order schemes in both space and time, the model is able to accurately capture the convection-dominated flow at high Reynolds and Schmidt numbers. Simulations both with and without background shear are conducted. The spatial frequency analysis of both density and vorticity fields reveals that no long range spanwise structures are present during the propagation of ISWs, which makes a relatively short spanwise depth sufficient to characterize the evolution of the flow. The growth of 3D structures during the propagation of ISWs is quantified using a spanwise roughness measure. The flow energy budget, dye transport, density mixing and vortex circulations are also analyzed.   

Local stability of axisymmetric plumes

A linear stability analysis of a forced plume with non-zero momentum at the inlet is performed for $Pr = 1$, $Re = 100$ and $Ri$ near 1. The steady base flow is obtained as a laminar solution of the steady Navier Stokes equations. The base flow asymptotes to a self-similar solution as it evolves downstream. In the non-self-similar regime close to the inlet, both axisymmetric mode ($m = 0$) and the helical mode ($m = 1$) are convectively unstable at sufficiently low Richardson number. In the self-similar regime, only the helical mode is absolutely unstable and the axisymmetric mode is stable. Higher helical modes ($m \ge 2$) are seen to be convectively unstable very close to the inlet and become stable as the flow evolves downstream. The transition from convective to absolute instability makes the flow a good candidate for observing steep nonlinear global modes associated with buoyancy.   

Experimental study of lock-exchange gravity currents: Coupling between particle distributions and flow structures

This work presents detailed experimental investigations of the interactions between the particles and flows of the lock-exchange particle-laden gravity currents. A phase Doppler particle analyzer provided non-intrusive and synchronous measurements of the velocities and grain sizes of the particles. High-speed particle image velocimetry was used to measure the flow fields. The measurements showed that the particle behavior and the currents were intricately coupled. Particle distributions at different parts of the current are given, showing that the particles' behaviors are highly related to the flow fields. The influences of the grain size to the flow fields are also investigated by comparing flow fields of currents carrying different particles to each other, as well as the un-laden currents. The presence of particles seems to postpone the evolving of the flow structures, it weakens the vorticity of the shear layer in the head but strengthens the voriticty in the body or tail of the currents. The influences to the flow fields increases with the grain size.   

Experimental study of lock-exchange gravity currents: Flow structures and instabilities

This work describes experimental investigations of lock-exchange gravity currents. High-speed particle image velocimetry and laser-induced fluorescence were used to study the spatial and temporal evolving of various flow structures and instabilities. Gravity currents develop a head-body-tail structure with different characteristics. The flow details inside the head are investigated. Kelvin-Helmholtz and gravitational instabilities are the two dominant instability modes here. These instabilities and their interactions strongly affect the head shape and the formation of the vertical structures in the currents. Two sets of inclined vertical structures are observed far behind the head. One set locates at the upper shear layer, tilting opposite to the flow direction. This set of structures evolves form the broken down K-H billows resulting from the interaction of the Kelvin-Helmholtz instability and gravitational instability in the current head. The other set locates at the bottom of the flow, tilting along the flow direction. This set is the result of the gravitational instability at the bottom.   

Bent-over plume models for large-area highly-buoyant turbulent plumes

The problem of large-area turbulent plumes driven laterally by wind has numerous applications in environmental fluid mechanics. For example, one of the primary mechanisms of wildfire spread is through the creation of spot fires that result from embers being lofted into the atmosphere by a fire plume and then transported ahead of the fire by wind. We review existing entrainment models for bent over plumes and investigate the modeling approach most appropriate for large-area highly-buoyant plumes. We present analytic solutions for the far-field behavior of a bent-over plume in the presence of both a uniform and power-law velocity profile. The plume trajectory in a power-law velocity profile is flatter and the volume and momentum fluxes are larger compared to a plume in a uniform velocity field. Comparison with experimental measurements shows that modeling the boundary layer velocity profile is important to accurate prediction of plume trajectory. The results of a sensitivity analysis show that the choice of entrainment model has little influence on plumes with flatter trajectories but has a large effect on more vertical trajectories that are typical of large-area highly-buoyant plumes under low wind conditions. Further, the choice of boundary layer velocity profile function influences the trajectory of more vertical plumes. However, model predictions are insensitive to any eccentricity in the plume cross-section.   

Simulations of Convective Excitation of Internal Waves in Water

We will present a series of simulations of convective excitation of internal gravity waves (IGWs) in water. We mimic the experimental set-up of Perrard et al. (2013), where water is cooled to zero degrees at the bottom of a tank, and keep at approximately room temperature at the top of a tank. The density maximum of water at 4 degrees renders the fluid convectively unstable between zero and four degrees, and stably stratified above four degrees. Our 2D simulations of the experiment show qualitatively similar IGW excitation spectrum. We then investigate two commonly discussed excitation mechanisms: interface forcing, and deep excitation. We run simplified simulations testing these two excitation mechanisms using the data from the full simulation, and compare the wave fields. We find that the interface forcing simulations overestimate the excitation of high frequency waves because high frequency interface motions are associated with nonlinear convection and not linear IGWs. On the other hand, the deep excitation of IGWs by Reynolds stresses accurately reproduces excitation spectrum. The correlation between the full simulation wave field and the deep excitation wave field is ~0.95. This suggests that deep excitation is the dominant excitation mechanism for this system.