Woodbury, Town of and Woodbury Police Benevolent Association (Dispatchers)

In the Matter of TOWN OF WOODBURY, Orange County and WOODBURY POLICE BENEVOLENT ASSOCIATION (Dispatchers). FINDINGS OF FACT and RECOMMENDATIONS FOR RESOLUTION. Peter A. Korn, Fact Finder

Croton-Harmon Union Free School District and Croton-Harmon Clerical Unit, CSEA, Local 860

In the matter of the fact-finding between the Croton-Harmon Union Free School District, employer, and the Croton-Harmon Clerical Unit, CSEA, Local 860, union. PERB case no. 2010-213. Before: Peter A. Korn, fact finder

Town of Eastchester and Eastchester White & Blue Collar Unit, CSEA Local 1000. AFSCME, AFL-CIO, Westchester County Local 860

In the matter of the fact-finding between the Town of Eastchester, employer, and the Eastchester White & Blue Collar Unit, CSEA Local 1000. AFSCME, AFL-CIO, Westchester County Local 860, union. PERB case no. M2011-041. Before: Peter A. Korn, fact finder

Sleepy Hollow, Village of and Municipal Employee Unit, United Federation of Police Officers

In the matter of the fact-finding between the Village of Sleepy Hollow, employer, and the United Federation of Police Officers, Municipal Employee Unit, union. PERB case no. M2009-266. Before: Peter A. Korn, fact finder

Westchester Joint Water Works and Utility Workers Union of America, Local 1-2

In the matter of the fact-finding between the Westchester Joint Water Works, employer, and the Utility Workers Union of America, Local 1-2, union. PERB case no. M2017-137. Before: Peter A. Korn, fact finder.M2017_137.pdf: 26 downloads, before Oct. 1, 2020

Elementary dispersion analysis of some mimetic discretizations on triangular C-grids

Spurious modes supported by triangular C-grids limit their application for modeling large-scale atmospheric and oceanic flows. Their behavior can be modified within a mimetic approach that generalizes the scalar product underlying the triangular C-grid discretization. The mimetic approach provides a discrete continuity equation which operates on an averaged combination of normal edge velocities instead of normal edge velocities proper. An elementary analysis of the wave dispersion of the new discretization for Poincaré, Rossby and Kelvin waves shows that, although spurious Poincaré modes are preserved, their frequency tends to zero in the limit of small wavenumbers, which removes the divergence noise in this limit. However, the frequencies of spurious and physical modes become close on shorter scales indicating that spurious modes can be excited unless high-frequency short-scale motions are effectively filtered in numerical codes. We argue that filtering by viscous dissipation is more efficient in the mimetic approach than in the standard C-grid discretization. Lumping of mass matrices appearing with the velocity time derivative in the mimetic discretization only slightly reduces the accuracy of the wave dispersion and can be used in practice. Thus, the mimetic approach cures some difficulties of the traditional triangular C-grid discretization but may still need appropriately tuned viscosity to filter small scales and high frequencies in solutions of full primitive equations when these are excited by nonlinear dynamics

Global Well-Posedness of the Primitive Equations of Large-Scale Ocean Dynamics with the Gent-McWilliams-Redi Eddy Parametrization Model

We prove global well-posedness of the ocean primitive equations coupled to advection-diffusion equations of the oceanic tracers temperature and salinity that are supplemented by the eddy parametrization model due to Gent-McWilliams and Redi. This parametrization forms a milestone in global ocean modelling and constitutes a central part of any general ocean circulation model computation. The eddy parametrization adds a secondary transport velocity to the tracer equation and renders the original Laplacian operators in the advection-diffusion equations nonlinear, with a diffusion matrix that depends via the equation of state in a nonlinear fashion on both tracers simultaneously. The eddy parametrization of Gent-McWilliams-Redi augments the complexity of the mathematical analysis of the whole system which we present here. We show first that weak solutions exist globally in time, provided the parametrization uses a regularized density. Then we prove by a detailed analysis of the eddy operators the global well-posedness. Our results apply also to the ``small-slope approximation'' that is commonly used in global ocean simulations.Comment: 31 page