We examine the inverse cascade of kinetic energy to large scales in rotating stratified turbulence as occurs in the oceans and in the atmosphere, while varying the relative frequency of gravity to inertial waves, N/f . Using direct numerical simulations with grid resolutions up to 1024^3 points, we find that the transfer of energy from three-dimensional to two-dimensional modes is most efficient in the range 1/2 ≤ N/f ≤ 2, in which resonances disappear. In this range, the cascade is faster than in the purely rotating case, and thus the interplay between rotation and stratification helps creating large scale structures. The ensuing inverse cascade follows a −5/3 spectral law with an approximately constant flux.The purely stratified case will also be examined in this context being limit of infinite N/f.
We report a new mechanism for creating vortices in a class of flows that are linearly stable and believed, by most researchers, to be also finite-amplitude stable. The vortices should form in stably-stratified Couette flows (both plane and circular), and in protoplanetary disks around forming protostars. Our study was motivated by the fact that protoplanetary disks must have flow instabilities that are capable of transporting angular momentum radially outward so that the protostars can accrete gas and grow into stars. The mechanism that we discovered allows small-amplitude perturbations (i.e., with small volumes and Rossby numbers) to form vortices that are large in volume and amplitude (with a Rossby number of order unity). The mechanism works by exciting neutrally stable baroclinic critical layers, which differ from the usual barotropic critical layers in uni-directional flows (responsible for the much-discussed but rarely-observed Kelvin’s cats-eye vortices). The singularities in the former layers are in their vertical velocities, while the latter are in their stream-wise velocities. The energy of the vortices becomes large, and it is supplied by the kinetic energy of the background shear flow. The vortices we found have an unusual property: a vortex that grows from a single, local perturbation triggers a new generation of vortices to grow at nearby locations. After the second generation of vortices grows large, it triggers a third generation. The triggering of subsequent generations continues ad infinitum so that a front dividing the vortex- dominated flow from the unperturbed flow advances until the entire domain fills with large vortices. The vortices do not advect across the region, the front of the vortex- populated fluid does. The region in protoplanetary disks where we have found this new mechanism is thought to be stable; thus, in the astrophysical literature this region is called the dead zone. Because the vortices we report here arise in the dead zone, grow large, and spawn new generations of vortices that march across the domain, we refer to them as zombie vortices. We consider the mechanism of the zombie vortices’ growth and advance in a proposed lab experiment: circular Couette flow with a vertically stably- stratified Boussinesq fluid (i.e., salt water) with a density that is linear with height. Because this flow is nearly homogenous, the first vortex formed by the initial instability self-replicates in an approximately spatially self-similar manner and fills the domain with a lattice of 3D vortices, which persists, despite the fact that the flow is turbulent.
First measurements of plasma temperature, density, and flow have been made on the Madison Plasma Dynamo Experiment (MPDX) that allow the particle and energy confinement as well as the plasma conductivity (η) and viscosity (ν) to be estimated. The MPDX is designed to create large flowing plasmas with high magnetic Reynolds number Rm = vL/η >> 1000, and an adjustable fluid Reynolds number 10 < Re = vL/ν < 1000, in the regime where the kinetic energy of the flow exceeds the magnetic energy (MA = v/vA >> 1). Simulations provide scenarios for generating large scale “slow” dynamos and small scale “fast” dynamos to be studied. Confinement is provided by alternating rings of 4 kG permanent magnets lining the vessel walls. Stirred is induced using anodes and thermally emissive Lanthanum hexaboride (LaB6) cathodes inserted in the confining magnetic multicusp edge of the plasma in a method first developed by the Plasma Couette Experiment (PCX) at UW Madison. An overview of plasma flows in PCX and MPDX will be presented as well as several experimental setups designed to achieve dynamo in MPDX. Resent results studying the vector turbulent EMF (the β effect) in the Madison Dynamo Experiment (MDE), a liquid sodium experiment at UW Madison will also be presented.
Turbulence is of tremendous importance in a wide range of astrophysical and geophysical flows. Unfortunately, the equations of motion are notoriously difficult to solve. I will introduce an approach to low-dimensional modeling of turbulent flows that focuses on the the large, coherent flow structures which often occur, such as convection rolls in the atmosphere or ocean currents. These structures and their dynamics can be described with relatively few variables using a model consisting of stochastic ordinary differential equations. As a model system to test this approach, we use Rayleigh-Benard convection experiments, in which a container is filled with water and heated from below. Buoyancy drives a flow which organizes into a roll-shaped circulation. This convection roll exhibits a wide range of dynamics including erratic meandering, spontaneous flow reversals, and several oscillation modes, all of which are reminiscent of phenomena observed in astro/geophysical flows. A simple model of stochastic motion in a potential quantitatively reproduces all of these observed flow dynamics. The potential term is a direct function of boundary geometry (i.e. topography), and is found to accurately predict the different flow dynamics observed in experiments with different boundary geometries. This approach may lead to more general and relatively easy to solve models for turbulent flows with potential applications to climate, weather, and even the turbulent dynamo that generates Earth’s magnetic field.