# HPCCprojects:Double-diffusive instabilities in sediment-laden systems with applications to riverine outflows

# Double-diffusive instabilities in sediment-laden systems with applications to riverine outflows

## Project description

When a layer of particle-laden fresh water is placed above clear, saline water, both double-diffusive and Rayleigh-Taylor instabilities may arise. Such a configuration can arise from hypopycnal river outflows into the salty ocean. The presence of these two instabilities can increase the flux of sediment out of the plume beyond that predicted by Stokes settling of individual particles. In addition, the presence of settling particles modifies traditional double-diffusive fingering to create a distinctly different mode. With this motivation in mind, we study the modification of the double-diffusive instability in the presence of settling particles using the tools of linear stability (LS) and direct numerical simulation (DNS).

An important parameter that arises from LS results is the ratio of the unstable layer thickness to the diffusive interface thickness of the salinity profile. When this value is small, the instability eigenmodes primarily resemble double-diffusive modes, while at larger values the sediment and salinity interfaces become increasingly decoupled and the dominant instability mode becomes Rayleigh-Taylor like. Results from DNS show that this parameter quickly grows before plateauing at a constant value for the rest of the simulation. This value is determined solely by the balance between the advective settling flux of sediment into the rose region and the fingering flux out. The balance between the settling and fingering fluxes is characterized by the settling velocity, the salinity Schmidt number and the stability ratio. For settling-dominated situations, we show that the resulting instability mode becomes a phase-locked fingering mode. This mode has the same spectral content as the traditional fingering mode but the large scale convective overturning generated by the Rayleigh-Taylor mode creates a phase-locking that results in very thin, wisp-like plumes released from the base of the unstable layer. Across a large range of parameters, the interfacial sediment flux is seen to scale most appropriately with the pure double-diffusive flux. This is contrary to the traditional method of basing the flux on the Stokes settling velocity. In addition, a flux enhancement coefficient is calculated which corrects the double-diffusive flux in settling-dominated systems.

## Objectives

- To understand in a general way how the double-diffusive and Rayleigh-Taylor instability modes interact in a sediment-laden fluid.
- To understand the origin on the leaking mode, as opposed to the traditional fingering mode in double-diffusion, and how this mode modifies the flux out of the river plume. See Parsons et al (2001) for experimental evidence of the leaking mode.
- To predict the type of instability mode that will be present in a given system
*a priori*of its development.

## Time-line

- Start: Fall 2008

## Models in use

SISV, a **S**pectral, **I**mpliciti, **S**treamfunction-**V**orticity solver for the Navier-Stokes equations. This code has the following properties:

- 2d flow solver
- High accuracy. Spectral in horizontal and compact finite differences in vertical
- Runs in parallel with MPI-based communication
- Navier-Stokes equations to describe the fluid motion
- Transport equation to describe the particle (and/or salinity) motion
- Uses
*FFTW*and*LAPACK*for efficient calculations

## Results

List the results of your project

## Users

- Peter Burns
- Senthilkumaran Radhakrishnan
- Roman Fuchs
- Bartho Schulte

## Funding

This research was supported by NSF grants CBET-0854338, CBET-1067847 and OCE-1061300.

## Publications and presentations

- Burns, P. and Meiburg, E.
*Sediment-laden Fresh Water above Salt Water: Linear Stability analysis.*J. Fluid Mech. 691. pp 279. (2012) [1]

- Parsons, J., Bush, J. and Syvitski J.
*Hyperpycnal plume formation from riverine outflows with small sediment concentrations.*Sedimentology. 48. 465-478. (2001) [2]