Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics

This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of magnetized fluids. In order to be self-contained we first motivate the physical properties of a magnetic fluid and how it should behave under the laws of thermodynamics. Next, we introduce a mathematical model built from hyperbolic partial differential equations (PDEs) that translate physical laws into mathematical equations. After an overview of the continuous analysis, we thoroughly describe the derivation of a numerical approximation of the ideal MHD system that remains consistent to the continuous thermodynamic principles. The derivation of the method and the theorems contained within serve as the bulk of the review article. We demonstrate that the derived numerical approximation retains the correct entropic properties of the continuous model and show its applicability to a variety of standard numerical test cases for MHD schemes. We close with our conclusions and a brief discussion on future work in the area of entropy consistent numerical methods and the modeling of plasmas

An Aerial Study of Hawaiian Wave Patterns

Most of us who have had some experience at sea on small power or sailing boats have noted that the sea surface is crossed by usually more than a single train or set of waves. Each train can be identified by its direction, period, and height. Sometimes one train is so dominant that others may not be noticed. The Marshall Islanders of the nineteenth century and earlier, past masters in the art of handling small boats, used wave trains as a navigational aid with their famous stick charts . The dominant train of waves, produced by the trad e winds, was designated by long parallel sticks tied to a rigid frame. Trains of smaller waves, some produced by bending around islands-were shown by small sticks attached at angles to the long ones. A brief review of these maps and of pertinent literature was given by Emery, Tracey, and Ladd (1954:5)

Beachrock in the Hawaiian Islands

Volume: 10Start Page: 382End Page: 40

Microtopography of Five Small Areas of the Continental Shelf by Side-Scanning Sonar

The microtopography of the continental shelf in five areas between Nova Scotia and New York was investigated with side-scanning sonar. The results were checked against those previously obtained by conventional methods in all areas and against later visual observations of the bottom from a research submersible vessel in two areas. Side-scanning sonar proved to be an ideal device for learning the distribution and relationships of rock, boulder, and sand bottoms and for measuring the patterns and trends of several sizes of sand waves and of large ripple marks