A Note on Standing Internal Inertial Gravity Waves of Finite Amplitude

The effects of finite amplitude are examined in two-dimensional, standing, internal gravity waves in a rectangular container which rotates about a vertical axis at frequency f/ 2. Expressions are given for the velocity components, density fluctuations and isopycnal displacements to second order in the wave steepness in fluids with buoyancy frequency, N , of general form, and the effect of finite amplitude on wave frequency is given in an expansion to third order. The first order solutions, and the solutions to second order in the absence of rotation, are shown to conserve energy during a wave cycle. Analytical solutions are found to second order for the first two modes in a deep fluid with N proportional to sech( az ), where z is the upward vertical coordinate and a is scaling factor. In the absence of rotation, results for the first mode in the latter stratification are found to be consistent with those for interfacial waves. An analytical solution to fourth order in a fluid with constant N is given and used to examine the effects of rotation on the development of static instability or of conditions in which shear instability may occur. As in progressive internal waves, an effect of rotation is to enhance the possibility of shear instability for waves with frequencies close to f . The analysis points to a significant difference between the dynamics of standing waves in containers of limited size and progressive internal waves in an unlimited fluid; the effect of boundaries on standing waves may inhibit the onset of instability. A possible application of the analysis is to transverse oscillations in long, narrow, steep-sided lakes such as Loch Ness, Scotland.     

http://www.sciencedirect.com/science/article/pii/S1674987111000181

This study investigates the mechanism of formation of convection plumes of mushroom shape in sub-solidus mantle and their prediction.The seismic-tomographic images of columnar structures of several hundreds kilometers in diameter have been reported by several researchers,while the much cherished mushroom-shaped plume heads could only be found in computational geodynamics(CGD) models and simple small-scale laboratory analogue simulations.Our theory of transient instability shows that the formation of conv...     

Smithsonian Institution’s Global Volcanism Network

Information included in this summary is based on more detailed reports published in the Bulletin of the Global Volcanism Network, vol. 32, no. 6, June 2007 (on the Internet at ). Edited by scientists at the Smithsonian, this bulletin includes reports provided by a worldwide network of correspondents. The reports contain the names and contact information for all sources. Please note that these reports are preliminary and subject to change as events are studied in more detail. The Global Volcanism Program welcomes further reports of current volcanism, seismic unrest, monitoring data, and field observations.     

Smithsonian Institution’s Global Volcanism Network

Information included in this summary is based on more detailed reports published in the Bulletin of the Global Volcanism Network, vol. 32, no. 9, September 2007 (on the Internet at ). Edited by scientists at the Smithsonian, this bulletin includes reports provided by a worldwide network of correspondents. The reports contain the names and contact information for all sources. Please note that these reports are preliminary and subject to change as events are studied in more detail. The Global Volcanism Program welcomes further reports of current volcanism, seismic unrest, monitoring data, and field observations.     

Reports from the Smithsonian’s Global Volcanism Network,May 2008

Information included in this summary is based on more detailed reports published in the Bulletin of the Global Volcanism Network, vol. 33, no. 5, May 2008 (on the Internet at ). Edited by scientists at the Smithsonian, this bulletin includes reports provided by a worldwide network of correspondents. The reports contain the names and contact information for all sources. Please note that these reports are preliminary and subject to change as events are studied in more detail. The Global Volcanism Program welcomes further reports of current volcanism, seismic unrest, monitoring data, and field observations.     

Reports from the Smithsonian’s Global Volcanism Network,July 2008

Information included in this summary is based on more detailed reports published in the Bulletin of the Global Volcanism Network, vol. 33, no. 7, July 2008 (on the Internet at ). Edited by scientists at the Smithsonian, this bulletin includes reports provided by a worldwide network of correspondents. The reports contain the names and contact information for all sources. Please note that these reports are preliminary and subject to change as events are studied in more detail. The Global Volcanism Program welcomes further reports of current volcanism, seismic unrest, monitoring data, and field observations.     

Reports from the Smithsonian’s Global Volcanism Network,November 2008

Information included in this summary is based on more detailed reports published in the Bulletin of the Global Volcanism Network, vol. 33, no. 11, November 2008 (on the Internet at ). Edited by scientists at the Smithsonian, this bulletin includes reports provided by a worldwide network of correspondents. The reports contain the names and contact information for all sources. Please note that these reports are preliminary and subject to change as events are studied in more detail. The Global Volcanism Program welcomes further reports of current volcanism, seismic unrest, monitoring data, and field observations.     

Reports from the Smithsonian’s Global Volcanism Network,May 2009

Information included in this summary is based on more detailed reports published in the Bulletin of the Global Volcanism Network, vol. 34, no. 5, May 2009 (on the Internet at http://www.volcano.si.edu/). Edited by scientists at the Smithsonian, this bulletin includes reports provided by a worldwide network of correspondents. The reports contain the names and contact information for all sources. Please note that these reports are preliminary and subject to change as events are studied in more detail. The Global Volcanism Program welcomes further reports of current volcanism, seismic unrest, monitoring data, and field observations.     

Reports from the Smithsonian’s Global Volcanism Network,September 2008

Information included in this summary is based on more detailed reports published in the Bulletin of the Global Volcanism Network, vol. 33, no. 9, September 2008 (on the Internet at ). Edited by scientists at the Smithsonian, this bulletin includes reports provided by a worldwide network of correspondents. The reports contain the names and contact information for all sources. Please note that these reports are preliminary and subject to change as events are studied in more detail. The Global Volcanism Program welcomes further reports of current volcanism, seismic unrest, monitoring data, and field observations.