where A represents the magnetic vector potential, is an integral of the hydromagnetic equations. This -integral made it possible to formulate a variational principle for the force-free magnetic fields. The integral expresses the fact that motions cannot transform a given field in an entirely arbitrary different field, if the conductivity of the medium isconsidered infinite. In this paper we shall show that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent. These integrals, as we shall presently verify, are I2 =fbHvdV, (2)

Proceedings of the National Academy of Sciences

1. Stochastic processes and random fields 2. Continuous semimartingales and stochastic integrals 3. Semimartingales with spatial parameter and stochastic integrals 4. Stochastic flows 5. Convergence of stochastic flows 6. Stochastic partial differential equations.

Stochastic flows and stochastic differential equations

A concise and factual abstract is required. The abstract should state briefly the purpose of the research, the principal results and major conclusions. An abstract is often presented separately from the article, so it must be able to stand alone. For this reason, References should be avoided, but if essential, then cite the author(s) and year(s). Also, non-standard or uncommon abbreviations should be avoided, but if essential they must be defined at their first mention in the abstract itself. Graphical abstract Although a graphical abstract is optional, its use is encouraged as it draws more attention to the online article. The graphical abstract should summarize the contents of the article in a concise, pictorial form designed to capture the attention of a wide readership. Graphical abstracts should be submitted as a separate file in the online submission system. Image size: Please provide an image with a minimum of 531 × 1328 pixels (h × w) or proportionally more. The image should be readable at a size of 5 × 13 cm using a regular screen resolution of 96 dpi. Preferred file types: TIFF, EPS, PDF or MS Office files. You can view Example Graphical Abstracts on our information site. Authors can make use of Elsevier's Illustration Services to ensure the best presentation of their images and in accordance with all technical requirements. Highlights Highlights are mandatory for this journal. They consist of a short collection of bullet points that convey the core findings of the article and should be submitted in a separate editable file in the online submission system. Please use 'Highlights' in the file name and include 3 to 5 bullet points (maximum 85 characters, including spaces, per bullet point). You can view example Highlights on our information site.

Deep-sea research. Part A, Oceanographic research papers

Comprehensive percussion studies at the university level are a relatively recent phenomenon when considering the long history of universities and conservatories in the Western musical tradition. The 1950’s and 60’s saw the beginning of what was to become the gradual inclusion, and ultimate expansion, of percussion studies programs in schools of music and conservatories in the United States. Like many programs around the country, the UWMadison percussion program began with graduate students (who were often pursuing degrees in music education or other related fields) teaching lessons and running the nascent studios. What follows is the story of the UW-Madison percussion program.

University of Wisconsin at Madison

The Journal of Engineering Mechanics covers activity and development in the field of applied mechanics as it relates to civil engineering. Research on bioengineering, computational mechanics, computer-aided engineering, dynamics of structures, elasticity, experimental analysis and instrumentation, fluid mechanics, flow of granular media, inelastic behavior of solids and structures, probabilistic methods, properties of materials, fracture mechanics, stability of structural elements and systems, and turbulence is reported. Typically, published papers describe the development and implementation of new analytical models, innovative numerical methods, and novel experimental methods and results.

Journal of Engineering Mechanics

We extend the Ito–Wentzell formula for the evolution of a time-dependent stochastic field along a semimartingale to k-form-valued stochastic processes. The result is the Kunita–Ito–Wentzell (KIW) formula for k-forms. We also establish a correspondence between the KIW formula for k-forms derived here and a certain class of stochastic fluid dynamics models which preserve the geometric structure of deterministic ideal fluid dynamics. This geometric structure includes Eulerian and Lagrangian variational principles, Lie–Poisson Hamiltonian formulations and natural analogues of the Kelvin circulation theorem, all derived in the stochastic setting.

/pdf/implications-of-kunita-ito-wentzell-formula-for-k-forms-in-m85ufzrfh2.pdf

Implications of Kunita–Itô–Wentzell Formula for k -Forms in Stochastic Fluid Dynamics

We extend the Ito-Wentzell formula for the evolution of a time-dependent stochastic field along a semimartingale to $k$-form-valued stochastic processes. The result is the Kunita-Ito-Wentzell (KIW) formula for $k$-forms. We also establish a correspondence between the KIW formula for $k$-forms derived here and a certain class of stochastic fluid dynamics models which preserve the geometric structure of deterministic ideal fluid dynamics. This geometric structure includes Eulerian and Lagrangian variational principles, Lie--Poisson Hamiltonian formulations and natural analogues of the Kelvin circulation theorem, all derived in the stochastic setting.

/pdf/implications-of-kunita-it-o-wentzell-formula-for-k-forms-in-12g4ruywvq.pdf

Implications of Kunita-It\^o-Wentzell formula for $k$-forms in stochastic fluid dynamics

In analogy with similar effects in adiabatic compressible fluid dynamics, the effects of buoyancy gradients on incompressible stratified flows are said to be “thermal.” The thermal rotating shallow water (TRSW) model equations contain three small nondimensional parameters. These are the Rossby number, the Froude number, and the buoyancy parameter. Asymptotic expansion of the TRSW model equations in these three small parameters leads to the deterministic thermal versions of the Salmon's L1 (TL1) model and the thermal quasi-geostrophic (TQG) model, upon expanding in the neighborhood of thermal quasi-geostrophic balance among the flow velocity and the gradients of free surface elevation and buoyancy. The linear instability of TQG at high wavenumber tends to create circulation at small scales. Such a high-wavenumber instability could be unresolvable in many computational simulations, but its presence at small scales may contribute significantly to fluid transport at resolvable scales. Sometimes, such effects are modeled via “stochastic backscatter of kinetic energy.” Here, we try another approach. Namely, we model “stochastic transport” in the hierarchy of models TRSW/TL1/TQG. The models are derived via the approach of stochastic advection by Lie transport (SALT) as obtained from a recently introduced stochastic version of the Euler–Poincare variational principle. We also indicate the potential next steps for applying these models in uncertainty quantification and data assimilation of the rapid, high-wavenumber effects of buoyancy fronts at these three levels of description by using the data-driven stochastic parametrization algorithms derived previously using the SALT approach.

Stochastic mesoscale circulation dynamics in the thermal ocean

Holm (Proc R Soc A Math Phys Eng Sci 471(2176):20140963, 2015) introduced a variational framework for stochastically parametrising unresolved scales of hydrodynamic motion. This variational framework preserves fundamental features of fluid dynamics, such as Kelvin’s circulation theorem, while also allowing for dispersive nonlinear wave propagation, both within a stratified fluid and at its free surface. The present paper combines asymptotic expansions and vertical averaging with the stochastic variational framework to formulate a new approach for developing stochastic parametrisation schemes for nonlinear waves in fluid dynamics. The approach is applied to two sequences of shallow water models which descend from Euler’s three-dimensional fluid equations with rotation and stratification under approximation by asymptotic expansions and vertical averaging. In the entire family of nonlinear stochastic wave–current interaction equations derived here using this approach, Kelvin’s circulation theorem reveals a barotropic mechanism for wave generation of horizontal circulation or convection (cyclogenesis) which is activated whenever the gradients of wave elevation and/or topography are not aligned with the gradient of the vertically averaged buoyancy.

/pdf/stochastic-wave-current-interaction-in-thermal-shallow-water-31bcdqyzg1.pdf

Stochastic Wave–Current Interaction in Thermal Shallow Water Dynamics

Holm (Proc. Roy. Soc 2015) introduced a variational framework for stochastically parametrising unresolved scales of hydrodynamic motion. This variational framework preserves fundamental features of fluid dynamics, such as Kelvin's circulation theorem, while also allowing for dispersive nonlinear wave propagation within a stratified fluid, as well as at its free surface. The present paper combines asymptotic expansions and vertical averaging with the stochastic variational framework to formulate a new approach for developing stochastic parametrisation schemes. This formulation is illustrated for wave dynamics in stratified shallow water flows. In the nonlinear wave-current interaction theory derived here, Kelvin's circulation theorem reveals a barotropic mechanism for wave generation of horizontal circulation (cyclogenesis) which is activated whenever the gradients of wave elevation and/or topography are not aligned with the gradient of the vertically averaged buoyancy.

Erwin Luesink

Papers

Implications of Kunita–Itô–Wentzell Formula for k -Forms in Stochastic Fluid Dynamics

Implications of Kunita-It\^o-Wentzell formula for $k$-forms in stochastic fluid dynamics

Stochastic mesoscale circulation dynamics in the thermal ocean

Stochastic Wave–Current Interaction in Thermal Shallow Water Dynamics

Stochastic wave-current interaction in stratified shallow water dynamics