Session S1: Geophysical Flows: General III

Large-eddy simulation of flow past a real-life stream restoration structure

We carry out high-resolution large-eddy simulation (LES) of flow around a rock vane, which is a widely used stream restoration structure. Mean velocities and turbulence statistics collected downstream of the rock vane installed in a laboratory flume are compared with the LES results. The comparisons demonstrate that the LES is able to accurately predict the measured mean velocities and turbulence statistics. The simulation shows that the rock vane effectively directs the oncoming flow away from the structure and creates a reduced velocity region in the downstream region. The computed results also reveal that the rock vane creates strong secondary helical flow that directs the near-bed flow toward the sidewall to which the rock vane is attached. This finding points to the conclusion that the downstream secondary flow can create deposition of sediments near the sidewall in a mobile bed condition, which can serve as an important mechanism for protecting near-bank scour in natural streams.   

Numerical Simulation of turbulent flow and sediment transport around real-life stream restoration structures

Local scour around three real-life in-stream restoration rock structures, including a rock-vane, a cross-vane, and a J-hook, is investigated numerically. To overcome the difficulties of generating high quality boundary-fitted meshes in natural mobile-bed channels with embedded rock structures, we employ the fluid-structure interaction Curvilinear Immersed Boundary (CURVIB) method adapted for morphodynamic simulations (Khosronejad et al., Adv. Water Res., 34(7) 2011). The mobile bed and the immersed structures are discretized with an unstructured triangular mesh and are treated as sharp-interface immersed boundaries embedded in a background curvilinear mesh used to discretize the fluid domain. The flow field is simulated by solving the unsteady RANS equations closed with the k-w turbulence model. The bed evolution is calculated by solving the Exner equation using an unstructured, finite-volume formulation. Comparisons with measurements show that the computed results capture both the spatial and temporal features of scour and deposition patterns with good accuracy.   

RANS Simulation of Passive Scalar Residence Times and Exchange Processes in Idealized and Natural Stream Systems

Natural stream systems contain a variety of dead zones characterized by flow separation, a mixing layer, and a recirculation zone. These dead zones play an important role in stream solute transport studies. Previous published work has focused on idealized storage zone geometries studied in laboratory flumes. Using RANS simulations, this study first examines these idealized geometries to determine the appropriate scaling relationships between idealized dead zone geometries and the residence times of a passive scalar. These scaling relationships are then applied to measurements from natural systems. The field-measured geometries are located in Oak and Soap creeks near Corvallis, Oregon. Field measurements for the natural systems included: (a) survey measurements to delineate storage zone morphologies; (b) Marsh-McBirney and acoustic Doppler velocimetry measurements for model boundary conditions and computation of turbulence parameters; and (c) continuous salt injections within storage zones and electrical conductivity measurements at point locations in the main channel and storage zones to quantify exchange rates and residence times.   

Shallow-water models for gravity currents/intrusions in double-continuous-stratification systems

High-Reynolds-number Boussinesq gravity currents and intrusions systems, in which both the ambient and the propagating ``current'' are linearly stratified, are considered. The main focus is on a current of fixed volume released from a lock; the height ratio of the fluids $H$, and the stratification parameter of the ambient $S$, are quite general. It is shown that a one-layer shallow-water model, in which the internal stratification enters as a new dimensionless parameter, $\sigma \in [0,1]$, provides insightful results. In general, the speed of propagation decreases when the internal stratification becomes more pronounced ($\sigma$ increases), and in some cases the current runs out of driving force. This model is a versatile and robust self-contained prediction tool, which can be applied to both rectangular and axisymmetric geometries, and to quite general continuously- stratified systems.   

Transitions of the propagation phases for non-Newtonian gravity currents

Transitions of the propagation phases for both two-dimensional and axisymmetric non-Newtonian gravity currents were investigated experimentally and theoretically. Fluid mud gravity currents, which exhibit power-law (shear thinning) rheological properties, were generated for constant-volume (in a flume) and constant-flux (in a flume and a three-dimensional tank) release configurations. Experimental observations indicated that, similar to their Newtonian counterparts (e.g. saline gravity currents), fluid mud gravity currents exhibit inertial and viscous propagation phases, preceded by either slumping (for the case of constant-volume release) or chaotic jet (for the case of constant-flux release) phase. When the currents make transitions from inertial to viscous phase, a thickening-thinning behavior was observed. Order-of-magnitude expressions for the transition time and position were derived and predictions of these expressions were compared to the experimental observations. A Moody-like diagram based upon a new friction factor and Reynolds number for power-law gravity currents is proposed to identify the transition from the inertial to viscous propagation phase.   

Turbulent Entrainment into Non-Newtonian Fluid Mud Gravity Currents

This study presents insights into turbulent entrainment of ambient water into fluid mud gravity currents. It is well established that fluid mud suspensions exhibit pseudo-plastic behavior. Gravity current laboratory experiments were conducted for constant-volume release configuration with different initial concentrations of fluid mud, representing different rheological properties (i.e. different Power-law model constants). A high quality data set of concentration and velocity profiles of fluid mud gravity currents was collected to calculate the entrainment velocity, $w_{e}$. The entrainment ratio ($E = w_{e}/U, U$ -- characteristic velocity) was calculated following the well-accepted Morton-Taylor-Turner entrainment hypothesis, which states that the inflow across the edge of a turbulent flow is proportional to some characteristic velocity. The entrainment ratio was further measured qualitatively using a light opaqueness technique. A semi-empirical parameterization for the entrainment ratio is proposed. The findings of this study are expected to be of significance for modeling various non-Newtonian gravity currents, in particular for modeling fluid mud gravity currents generated during dredge disposal operations in coastal waters.   

Non-Boussinesq internal bores: Bridging the gap between the single layer, and boussinesq cases

Internal bores, or hydraulic jumps, arise in many atmospheric and oceanographic phenomena. The classic single-layer hydraulic jump model accurately predicts a bore's behavior when the density difference between the expanding and contracting layer is large (i.e. water and air), but fails in the Boussinesq limit. A two-layer model, where mass is conserved separately in each layer and momentum is conserved globally, does a much better job but requires for closure an assumption about the loss of energy across a bore. Our previous study used 2D direct numerical simulations in order to directly examine the energy fluxes within a bore, and was able to provide us with an appropriate closure relation in the Boussinesq case. Now, we have extended our simulations to non-Boussinesq bores in order to generate an analytical model that bridges the gap between single, and two-layer models. We also perform 3D large eddy simulations to confirm that our model and results generalize to three dimensions, and higher Reynolds numbers.   

Radiative instability of a strong anticyclonic vortex in a rotating and stratified fluid

In strongly stratified fluids, an axisymmetric vertical columnar vortex with an angular velocity $\Omega$ is unstable because of a spontaneous radiation of internal waves. This radiative instability tends to be stabilized in the presence of a cyclonic background rotation $\Omega_{b}$ so that it is generally expected to not affect large-scale vortices in geophysical flows. In contrast, we show that an anticyclonic vortex with low negative Rossby number $Ro=\frac{\Omega}{\Omega_{b}}\geq-1$, which is centrifugally stable, can be also unstable due to radiative instability when the azimuthal wavenumber $m$ is sufficiently large: $\left|m\right|\geq3$. This new radiative instability has been investigated for several vortex profiles and we have found that it occurs if the potential vorticity of the vortex has a sufficiently steep radial profile. The properties of this instability and its mechanism will be explained by an asymptotic analysis for large azimuthal wavenumber. Moreover, its importance for geophysical anticyclonic vortices such as meddies will be discussed.   

Instabilities in sediment-laden systems

When a layer of particle-laden fresh water is placed above clear, saline water, both Rayleigh-Taylor and double-diffusive instabilities may arise. In the absence of salinity, the dominant parameter is the ratio of the particle settling velocity to the viscous velocity scale. As long as this ratio is small, particle settling has a negligible influence on the instability growth. However, when the particles settle more rapidly than the instability grows, the growth rate decreases inversely proportional to the settling velocity. In the presence of a stably stratified salinity field, this picture changes dramatically. An important new parameter is the ratio of the height of the nose region that contains both salt and particles to the thickness of the salinity interface. If this ratio is small (large) the dominant instability mechanism will be double-diffusive (Rayleigh-Taylor) dominant. In contrast to situations without salinity, particle settling can have a destabilizing effect and significantly increase the growth rate. Scaling laws obtained from the linear stability results are seen to be consistent with experimental observations and theoretical arguments put forward by other authors.