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Jun 30, 2018
06/18

by
Aseel Farhat; Evelyn Lunasin; Edriss S. Titi

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In this paper we survey the various implementations of a new data assimilation (downscaling) algorithm based on spatial coarse mesh measurements. As a paradigm, we demonstrate the application of this algorithm to the 3D Leray-$\alpha$ subgrid scale turbulence model. Most importantly, we use this paradigm to show that it is not always necessary that one has to collect coarse mesh measurements of all the state variables, that are involved in the underlying evolutionary system, in order to recover...

Topics: Physics, Geophysics, Analysis of PDEs, Atmospheric and Oceanic Physics, Mathematics

Source: http://arxiv.org/abs/1702.01506

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Jun 30, 2018
06/18

by
Max Duarte; Ann Almgren; John Bell

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We introduce a low Mach number model for moist atmospheric flows that accurately incorporates reversible moist processes in flows whose features of interest occur on advective rather than acoustic time scales. Total water is used as a prognostic variable, so that water vapor and liquid water are diagnostically recovered as needed from an exact Clausius--Clapeyron formula for moist thermodynamics. Low Mach number models can be computationally more efficient than a fully compressible model, but...

Topics: Physics, Mathematics, Fluid Dynamics, Atmospheric and Oceanic Physics, Analysis of PDEs

Source: http://arxiv.org/abs/1409.2861

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Jun 27, 2018
06/18

by
Benjamin Krank; Wolfgang A. Wall

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A novel approach to wall modeling for the incompressible Navier-Stokes equations including flows of moderate and large Reynolds numbers is presented. The basic idea is that a problem-tailored function space allows prediction of turbulent boundary layer gradients with very coarse meshes. The proposed function space consists of a standard polynomial function space plus an enrichment, which is constructed using Spalding's law-of-the-wall. The enrichment function is not enforced but...

Topics: Atmospheric and Oceanic Physics, Computational Physics, Physics, Fluid Dynamics, Mathematics,...

Source: http://arxiv.org/abs/1505.05786

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Jun 28, 2018
06/18

by
Julian Mak; James R. Maddison; David P. Marshall

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Coarse resolution numerical ocean models must typically include a parameterisation for mesoscale turbulence. A common recipe for such parameterisations is to invoke down-gradient mixing, or diffusion, of some tracer quantity, such as potential vorticity or buoyancy. However, it is well known that eddy fluxes include large rotational components which necessarily do not lead to any mixing; eddy diffusivities diagnosed from unfiltered fluxes are thus contaminated by the presence of these...

Topics: Computational Physics, Atmospheric and Oceanic Physics, Mathematics, Fluid Dynamics, Optimization...

Source: http://arxiv.org/abs/1512.04045

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Jun 30, 2018
06/18

by
Gayaz Khakimzyanov; Nina Shokina; Denys Dutykh; Dimitrios Mitsotakis

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The practically important problem of the wave run-up is studied in this article in the framework of Nonlinear Shallow Water Equations (NSWE). The main novelty consists in the usage of high order local asymptotic analytical solutions in the vicinity of the shoreline. Namely, we use the analytical techniques introduced by S. Kovalevskaya and the analogy with the compressible gas dynamics (i.e. gas outflow problem into the vacuum). Our run-up algorithm covers all the possible cases of the wave...

Topics: Physics, Fluid Dynamics, Mathematics, Atmospheric and Oceanic Physics, Numerical Analysis, Analysis...

Source: http://arxiv.org/abs/1411.5514

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Jun 26, 2018
06/18

by
Mohammadreza Aminikashani; Murat Uysal; Mohsen Kavehrad

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In this paper, we propose a new probability distribution function which accurately describes turbulence-induced fading under a wide range of turbulence conditions. The proposed model, termed Double Generalized Gamma (Double GG), is based on a doubly stochastic theory of scintillation and developed via the product of two Generalized Gamma (GG) distributions. The proposed Double GG distribution generalizes many existing turbulence channel models and provides an excellent fit to the published...

Topics: Mathematics, Computing Research Repository, Information Theory, Atmospheric and Oceanic Physics,...

Source: http://arxiv.org/abs/1502.00348

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Jun 30, 2018
06/18

by
Didier Clamond; Denys Dutykh; Angel Duran

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The present study describes, first, an efficient algorithm for computing capillary-gravity solitary waves solutions of the irrotational Euler equations with a free surface and, second, provides numerical evidences of the existence of an infinite number of generalised solitary waves (solitary waves with undamped oscillatory wings). Using conformal mapping, the unknown fluid domain, which is to be determined, is mapped into a uniform strip of the complex plane. In the transformed domain, a...

Topics: Fluid Dynamics, Physics, Nonlinear Sciences, Mathematics, Atmospheric and Oceanic Physics, Pattern...

Source: http://arxiv.org/abs/1411.5519

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Jun 28, 2018
06/18

by
Philippe H. Trinh

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The standard analytical approach for studying gravity free-surface waves generated by a moving body often relies upon a linearization of the physical geometry, where the body is considered asymptotically small in one or several of its dimensions. In this paper, a methodology that avoids any such geometrical simplification is presented for the case of flows at low speeds. The approach is made possible through a reduction of the water-wave equations to a complex-valued integral equation that can...

Topics: Fluid Dynamics, Atmospheric and Oceanic Physics, Complex Variables, Mathematics, Physics

Source: http://arxiv.org/abs/1510.06647

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Jun 28, 2018
06/18

by
Jinkai Li; Edriss S. Titi

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In this paper, we consider a nonlinear interaction system between the barotropic mode and the first baroclinic mode of the tropical atmosphere with moisture; that was derived in [Frierson, D.M.W.; Majda, A.J.; Pauluis, O.M.: Dynamics of precipitation fronts in the tropical atmosphere: a novel relaxation limit, Commum. Math. Sci., 2 (2004), 591-626.] We establish the global existence and uniqueness of strong solutions to this system, with initial data in $H^1$, for each fixed convective...

Topics: Atmospheric and Oceanic Physics, Geophysics, Analysis of PDEs, Physics, Fluid Dynamics, Mathematics

Source: http://arxiv.org/abs/1507.05231

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Jun 29, 2018
06/18

by
Mark J. Ablowitz; Yi-Ping Ma; Igor Rumanov

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The appearance of a fundamental long-time asymptotic regime in the two space one time dimensional hyperbolic nonlinear Schr\"odinger (HNLS) equation is discussed. Based on analytical and extensive numerical simulations an approximate self-similar solution is found for a wide range of initial conditions -- essentially for initial lumps of small to moderate energy. Even relatively large initial amplitudes, which imply strong nonlinear effects, eventually lead to local structures resembling...

Topics: Nonlinear Sciences, Atmospheric and Oceanic Physics, Physics, Mathematics, Pattern Formation and...

Source: http://arxiv.org/abs/1606.02782

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Jun 29, 2018
06/18

by
Darren Engwirda; Maxwell Kelley

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A new, high-order slope-limiting procedure for the Piecewise Parabolic Method (PPM) and the Piecewise Quartic Method (PQM) is described. Following a Weighted Essentially Non-Oscillatory (WENO)-type paradigm, the proposed slope-limiter seeks to reconstruct smooth, non-oscillatory piecewise polynomial profiles as a non-linear combination of the natural and monotone-limited PPM and PQM interpolants. Compared to existing monotone slope-limiting techniques, this new strategy is designed to improve...

Topics: Fluid Dynamics, Atmospheric and Oceanic Physics, Computational Physics, Numerical Analysis,...

Source: http://arxiv.org/abs/1606.08188

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Jun 30, 2018
06/18

by
Didier Clamond; Denys Dutykh

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This paper describes an efficient algorithm for computing steady two-dimensional surface gravity wave in irrotational motion. The algorithm complexity is O(N log N), N being the number of Fourier modes. The algorithm allows the arbitrary precision computation of waves in arbitrary depth, i.e., it works efficiently for Stokes, cnoidal and solitary waves, even for quite large steepnesses. The method is based on conformal mapping, Babenko equation rewritten in a suitable way, pseudo-spectral...

Topics: Physics, Numerical Analysis, Analysis of PDEs, Atmospheric and Oceanic Physics, Classical Physics,...

Source: http://arxiv.org/abs/1702.04132

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Jun 30, 2018
06/18

by
Kyle T. Mandli; Clint N. Dawson

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An approach to utilizing adaptive mesh refinement algorithms for storm surge modeling is proposed. Currently numerical models exist that can resolve the details of coastal regions but are often too costly to be run in an ensemble forecasting framework without significant computing resources. The application of adaptive mesh refinement algorithms substantially lowers the computational cost of a storm surge model run while retaining much of the desired coastal resolution. The approach presented...

Topics: Physics, Mathematics, Numerical Analysis, Atmospheric and Oceanic Physics

Source: http://arxiv.org/abs/1401.5744

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Jun 30, 2018
06/18

by
Denys Dutykh; Didier Clamond; Dimitrios Mitsotakis

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This paper presents an extended version of the celebrated Serre-Green-Naghdi (SGN) system. This extension is based on the well-known Bona-Smith-Nwogu trick which aims to improve the linear dispersion properties. We show that in the fully nonlinear setting it results in modifying the vertical acceleration. Even if this technique is well-known, the effect of this modification on the nonlinear properties of the model is not clear. The first goal of this study is to shed some light on the...

Topics: Fluid Dynamics, Physics, Mathematics, Atmospheric and Oceanic Physics, Numerical Analysis, Analysis...

Source: http://arxiv.org/abs/1411.7754

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Jun 30, 2018
06/18

by
G. Haller; F. J. Beron-Vera

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In Haller and Beron-Vera (2013) we developed a variational principle for the detection of coherent Lagrangian vortex boundaries. The solutions of this variational principle turn out to be closed null-geodesics of the Lorentzian metric associated with a generalized Green-Lagrange strain tensor family. This metric interpretation implies a mathematical analogy between coherent Lagrangian vortex boundaries and photon spheres in general relativity. Here we give an improved discussion on this analogy.

Topics: Physics, Mathematics, Atmospheric and Oceanic Physics, General Relativity and Quantum Cosmology,...

Source: http://arxiv.org/abs/1406.1493

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Jun 30, 2018
06/18

by
Marsha Berger; Jonathan Goodman

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This paper examines the questions of whether smaller asteroids that burst in the air over water can generate tsunamis that could pose a threat to distant locations. Such air burst-generated tsunamis are qualitatively different than the more frequently studied earthquake-generated tsunamis, and differ as well from impact asteroids. Numerical simulations are presented using the shallow water equations in several settings, demonstrating very little tsunami threat from this scenario. A model...

Topics: Fluid Dynamics, Physics, Dynamical Systems, Atmospheric and Oceanic Physics, Mathematics

Source: http://arxiv.org/abs/1704.03552

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Jun 30, 2018
06/18

by
G. Tumolo; L. Bonaventura

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We present an accurate and efficient discretization approach for the adaptive discretization of typical model equations employed in numerical weather prediction. A semi-Lagrangian approach is combined with the TR-BDF2 semi-implicit time discretization method and with a spatial discretization based on adaptive discontinuous finite elements. The resulting method has full second order accuracy in time and can employ polynomial bases of arbitrarily high degree in space, is unconditionally stable...

Topics: Physics, Fluid Dynamics, Mathematics, Computing Research Repository, Atmospheric and Oceanic...

Source: http://arxiv.org/abs/1405.5245

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Jun 28, 2018
06/18

by
Gregory A. Barnett; Natasha Flyer; Louis J. Wicker

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Polyharmonic spline (PHS) radial basis functions (RBFs) are used together with polynomials to create local RBF-finite-difference (RBF-FD) weights on different node layouts for spatial discretization of the compressible Navier-Stokes equations at low Mach number, relevant to atmospheric flows. Test cases are taken from the numerical weather prediction community and solved on bounded domains. Thus, attention is given on how to handle boundaries with the RBF-FD method, as well as a novel...

Topics: Atmospheric and Oceanic Physics, Computational Physics, Physics, Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1509.02615

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Jun 28, 2018
06/18

by
Kaitlin Hill; Dorian S. Abbot; Mary Silber

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As Arctic sea ice extent decreases with increasing greenhouse gases, there is a growing interest in whether there could be a bifurcation associated with its loss, and whether there is significant hysteresis associated with that bifurcation. A challenge in answering this question is that the bifurcation behavior of certain Arctic energy balance models have been shown to be sensitive to how ice-albedo feedback is parameterized. We analyze an Arctic energy balance model in the limit as a smoothing...

Topics: Atmospheric and Oceanic Physics, Dynamical Systems, Mathematics, Physics

Source: http://arxiv.org/abs/1509.00059

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Jun 30, 2018
06/18

by
Daniel Karrasch; Mohammad Farazmand; George Haller

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Recent advances enable the simultaneous computation of both attracting and repelling families of Lagrangian Coherent Structures (LCS) at the same initial or final time of interest. Obtaining LCS positions at intermediate times, however, has been problematic, because either the repelling or the attracting family is unstable with respect to numerical advection in a given time direction. Here we develop a new approach to compute arbitrary positions of hyperbolic LCS in a numerically robust...

Topics: Physics, Nonlinear Sciences, Fluid Dynamics, Chaotic Dynamics, Mathematics, Atmospheric and Oceanic...

Source: http://arxiv.org/abs/1405.4727

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Jun 30, 2018
06/18

by
Daniel Karrasch; Florian Huhn; George Haller

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Coherent boundaries of Lagrangian vortices in fluid flows have recently been identified as closed orbits of line fields associated with the Cauchy-Green strain tensor. Here we develop a fully automated procedure for the detection of such closed orbits in large-scale velocity data sets. We illustrate the power of our method on ocean surface velocities derived from satellite altimetry.

Topics: Physics, Fluid Dynamics, Mathematics, Computing Research Repository, Atmospheric and Oceanic...

Source: http://arxiv.org/abs/1404.3109

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Jun 29, 2018
06/18

by
Alvaro Subias

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Finite elements has been proven to be an useful tool to discretize the vertical coordinate in the hydrostatic forecast models allowing to define model variables in full levels so that no staggering is needed. In the non-hydrostatic case a constraint in the vertical operators appears (called C1) that does not allow to reduce the set of semi-implicit linear equations to a single equation in one variable as in the analytic case. Recently vertical finite elements based in B-splines have been used...

Topics: Mathematics, Numerical Analysis, Atmospheric and Oceanic Physics, Physics

Source: http://arxiv.org/abs/1601.03446

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Jun 30, 2018
06/18

by
C. J. Cotter; A. T. T. McRae

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This article takes the form of a tutorial on the use of a particular class of mixed finite element methods, which can be thought of as the finite element extension of the C-grid staggered finite difference method. The class is often referred to as compatible finite elements, mimetic finite elements, discrete differential forms or finite element exterior calculus. We provide an elementary introduction in the case of the one-dimensional wave equation, before summarising recent results in...

Topics: Physics, Mathematics, Numerical Analysis, Atmospheric and Oceanic Physics

Source: http://arxiv.org/abs/1401.0616

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Jun 29, 2018
06/18

by
Andrea Natale; Jemma Shipton; Colin J. Cotter

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Compatible finite elements provide a framework for preserving important structures in equations of geophysical fluid dynamics, and are becoming important in their use for building atmosphere and ocean models. We survey the application of compatible finite element spaces to geophysical fluid dynamics, including the application to the nonlinear rotating shallow water equations, and the three-dimensional compressible Euler equations. We summarise analytic results about dispersion relations and...

Topics: Physics, Numerical Analysis, Atmospheric and Oceanic Physics, Mathematics

Source: http://arxiv.org/abs/1605.00551

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Jun 28, 2018
06/18

by
Cihan Bayindir

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In this paper an approach for decreasing the computational effort required for the spectral simulations of the water waves is introduced. Signals with majority of the components zero, are known as the sparse signals. Like majority of the signals in the nature it can be realized that water waves are sparse either in time or in the frequency domain. Using the sparsity property of the water waves in the time or in the frequency domain, the compressive sampling algorithm can be used as a tool for...

Topics: Computational Physics, Atmospheric and Oceanic Physics, Mathematics, Fluid Dynamics, Mathematical...

Source: http://arxiv.org/abs/1512.06286

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Jun 26, 2018
06/18

by
Hans Engler

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This note proposes rapidly convergent computational formulae for evaluating scattering kernels from radiative transfer theory. The approach used here does not rely on Legendre expansions, but rather uses exponentially convergent numerical integration rules. A closed form for the Henyey-Greenstein scattering kernel in terms of complete elliptic integrals is also derived.

Topics: Numerical Analysis, Physics, Mathematical Physics, Mathematics, Atmospheric and Oceanic Physics

Source: http://arxiv.org/abs/1501.02407

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Jun 28, 2018
06/18

by
Didier Clamond; Denys Dutykh; Dimitrios Mitsotakis

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For surface gravity waves propagating in shallow water, we propose a variant of the fully nonlinear Serre-Green-Naghdi equations involving a free parameter that can be chosen to improve the dispersion properties. The novelty here consists in the fact that the new model conserves the energy, contrary to other modified Serre's equations found in the literature. Numerical comparisons with the Euler equations show that the new model is substantially more accurate than the classical Serre equations,...

Topics: Atmospheric and Oceanic Physics, Mathematics, Classical Physics, Analysis of PDEs, Fluid Dynamics,...

Source: http://arxiv.org/abs/1511.07395

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Jun 30, 2018
06/18

by
Hakima Bessaih; Eric Olson; E. S. Titi

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We analyze the performance of a data-assimilation algorithm based on a linear feedback control when used with observational data that contains measurement errors. Our model problem consists of dynamics governed by the two-dimension incompressible Navier-Stokes equations, observational measurements given by finite volume elements or nodal points of the velocity field and measurement errors which are represented by stochastic noise. Under these assumptions, the data-assimilation algorithm...

Topics: Physics, Nonlinear Sciences, Fluid Dynamics, Chaotic Dynamics, Mathematics, Atmospheric and Oceanic...

Source: http://arxiv.org/abs/1406.1533

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Jun 28, 2018
06/18

by
Darin Comeau; Zhizhen Zhao; Dimitrios Giannakis; Andrew J. Majda

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The North Pacific exhibits patterns of low-frequency variability on the intra-annual to decadal time scales, which manifest themselves in both model data and the observational record, and prediction of such low-frequency modes of variability is of great interest to the community. While parametric models, such as stationary and non-stationary autoregressive models, possibly including external factors, may perform well in a data-fitting setting, they may perform poorly in a prediction setting....

Topics: Data Analysis, Statistics and Probability, Atmospheric and Oceanic Physics, Mathematics, Numerical...

Source: http://arxiv.org/abs/1509.05332

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Jun 29, 2018
06/18

by
Michael Bianco; Peter Gerstoft

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To provide constraints on their inversion, ocean sound speed profiles (SSPs) often are modeled using empirical orthogonal functions (EOFs). However, this regularization, which uses the leading order EOFs with a minimum-energy constraint on their coefficients, often yields low resolution SSP estimates. In this paper, it is shown that dictionary learning, a form of unsupervised machine learning, can improve SSP resolution by generating a dictionary of shape functions for sparse processing (e.g....

Topics: Atmospheric and Oceanic Physics, Data Analysis, Statistics and Probability, Physics, Mathematics,...

Source: http://arxiv.org/abs/1609.04840

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Jun 29, 2018
06/18

by
James Walsh

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M. Budyko and W. Sellers independently introduced seminal energy balance climate models in 1969, each with a goal of investigating the role played by positive ice albedo feedback in climate dynamics. In this paper we replace the relaxation to the mean horizontal heat transport mechanism used in the models of Budyko and Sellers with diffusive heat transport. We couple the resulting surface temperature equation with an equation for movement of the edge of the ice sheet (called the ice line),...

Topics: Physics, Dynamical Systems, Atmospheric and Oceanic Physics, Mathematics

Source: http://arxiv.org/abs/1607.07769

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Jun 30, 2018
06/18

by
Luigi Carlo Berselli; Matteo Cerminara; Traian Iliescu

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In this paper we study the motion of a fluid with several dispersed particles whose concentration is very small (smaller than $10^{-3}$), with possible applications to problems coming from geophysics, meteorology, and oceanography. We consider a very dilute suspension of heavy particles in a quasi-incompressible fluid (low Mach number). In our case the Stokes number is small and --as pointed out in the theory of multiphase turbulence-- we can use an Eulerian model instead of a Lagrangian one....

Topics: Physics, Fluid Dynamics, Mathematics, Atmospheric and Oceanic Physics, Analysis of PDEs,...

Source: http://arxiv.org/abs/1403.5448

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Jun 30, 2018
06/18

by
F. J. Beron-Vera; M. J. Olascoaga; G. Haller; M. Farazmand; J. Trinanes; Y. Wang

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Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here we show that inclusion of inertial effects (i.e., those produced...

Topics: Physics, Nonlinear Sciences, Fluid Dynamics, Chaotic Dynamics, Mathematics, Atmospheric and Oceanic...

Source: http://arxiv.org/abs/1408.6512

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Jun 27, 2018
06/18

by
Xueran Wu; Hendrik Elbern; Birgit Jacob

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The controllability of advection-diffusion systems, subject to uncertain initial values and emission rates, is estimated, given sparse and error affected observations of prognostic state variables. In predictive geophysical model systems, like atmospheric chemistry simulations, different parameter families influence the temporal evolution of the system.This renders initial-value-only optimisation by traditional data assimilation methods as insufficient. In this paper, a quantitative assessment...

Topics: Atmospheric and Oceanic Physics, Physics, Mathematics, Dynamical Systems

Source: http://arxiv.org/abs/1503.06585

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Jun 30, 2018
06/18

by
Andreas Dedner; Eike Hermann Müller; Robert Scheichl

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Many problems in fluid modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in "flat" domains. For example, in numerical weather- and climate-prediction an elliptic PDE for the pressure correction has to be solved at every time step in a thin spherical shell representing the global atmosphere. This elliptic solve can be one of the computationally most demanding components in semi-implicit semi-Lagrangian time stepping methods...

Topics: Distributed, Parallel, and Cluster Computing, Physics, Mathematics, Computing Research Repository,...

Source: http://arxiv.org/abs/1408.2981

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Jun 30, 2018
06/18

by
Xiaodong Luo; Ibrahim Hoteit

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This study considers the data assimilation problem in coupled systems, which consists of two components (sub-systems) interacting with each other through certain coupling terms. A straightforward way to tackle the assimilation problem in such systems is to concatenate the states of the sub-systems into one augmented state vector, so that a standard ensemble Kalman filter (EnKF) can be directly applied. In this work we present a divided state-space estimation strategy, in which data assimilation...

Topics: Physics, Nonlinear Sciences, Data Analysis, Statistics and Probability, Computation, Statistics,...

Source: http://arxiv.org/abs/1408.4236

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Jun 30, 2018
06/18

by
Xiaodong Luo; Ibrahim Hoteit

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The ensemble Kalman filter (EnKF) is an efficient algorithm for many data assimilation problems. In certain circumstances, however, divergence of the EnKF might be spotted. In previous studies, the authors proposed an observation-space-based strategy, called residual nudging, to improve the stability of the EnKF when dealing with linear observation operators. The main idea behind residual nudging is to monitor and, if necessary, adjust the distances (misfits) between the real observations and...

Topics: Physics, Nonlinear Sciences, Data Analysis, Statistics and Probability, Computation, Statistics,...

Source: http://arxiv.org/abs/1406.4307

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Jun 29, 2018
06/18

by
Sara Garbarino; Alberto Sorrentino; Anna Maria Massone; Alessia Sannino; Antonella Boselli; Xuan Wang; Nicola Spinelli; Michele Piana

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We consider the problem of retrieving the aerosol extinction coefficient from Raman lidar measurements. This is an ill--posed inverse problem that needs regularization, and we propose to use the Expectation--Maximization (EM) algorithm to provide stable solutions. Indeed, EM is an iterative algorithm that imposes a positivity constraint on the solution, and provides regularization if iterations are stopped early enough. We describe the algorithm and propose a stopping criterion inspired by a...

Topics: Physics, Numerical Analysis, Optics, Atmospheric and Oceanic Physics, Mathematics

Source: http://arxiv.org/abs/1608.07841

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Jun 27, 2018
06/18

by
Luca Bonaventura; Roberto Ferretti

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A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and convergence analysis are proposed. Numerical examples validate the proposed method and display its potential for consistent semi-Lagrangian discretization of advection--diffusion and nonlinear parabolic problems.

Topics: Atmospheric and Oceanic Physics, Computational Engineering, Finance, and Science, Physics,...

Source: http://arxiv.org/abs/1505.00940

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Jun 30, 2018
06/18

by
Francesco Fedele

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Recently, Banner et al. (2014) highlighted a new fundamental property of open ocean wave groups, the so-called crest slowdown. For linear narrowband waves, this is related to the geometric and dynamical phase velocities $U_d$ and $U_g$ associated with the parallel transport through the principal fiber bundle of the wave motion with $\mathit{U}(1)$ symmetry. The theoretical predictions are shown to be in fair agreement with ocean field observations, from which the average crest speed $c=U_d+U_g$...

Topics: Physics, Mathematics, Fluid Dynamics, Atmospheric and Oceanic Physics, Mathematical Physics

Source: http://arxiv.org/abs/1406.0051

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Jun 28, 2018
06/18

by
Shiv Priyam Raghuraman

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Using a recent conceptual model of the glacial-interglacial cycles we present more evidence of Milankovitch cycles being the trigger for retreat and forming of ice sheets in the cycles. This model is based on a finite approximation of an infinite dimensional model which has three components: Budyko's energy balance model describing the annual mean temperatures at latitudes, Widiasih's ODE which describes the behavior of the edge of the ice sheet, and Walsh et al. who introduced a snow line to...

Topics: Dynamical Systems, Atmospheric and Oceanic Physics, Mathematics, Physics

Source: http://arxiv.org/abs/1511.06008

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Jun 29, 2018
06/18

by
Bo You; Fang Li

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This paper is concerned with the long-time behavior of solutions for the three dimensional primitive equations of large-scale ocean and atmosphere dynamics in an unbounded domain. Since the Sobolev embedding is no longer compact in an unbounded domain, we cannot obtain the asymptotical compactness of the semigroup generated by problem (2.4)-(2.6) by the Sobolev compactness embedding theorem even if we obtain the existence of an absorbing set in more regular phase space. To overcome this...

Topics: Physics, Analysis of PDEs, Mathematical Physics, Atmospheric and Oceanic Physics, Mathematics

Source: http://arxiv.org/abs/1612.02679

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Jun 29, 2018
06/18

by
Sabine Hittmeir; Rupert Klein; Jinkai Li; Edriss S. Titi

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We study a moisture model for warm clouds that has been used by Klein and Majda as a basis for multiscale asymptotic expansions for deep convective phenomena. These moisture balance equations correspond to a bulk microphysics closure in the spirit of Kessler and of Grabowski and Smolarkiewicz, in which water is present in the gaseous state as water vapor and in the liquid phase as cloud water and rain water. It thereby contains closures for the phase changes condensation and evaporation, as...

Topics: Fluid Dynamics, Atmospheric and Oceanic Physics, Analysis of PDEs, Physics, Mathematics, Geophysics

Source: http://arxiv.org/abs/1610.00060

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Jun 27, 2018
06/18

by
Jinkai Li; Edriss S. Titi

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In this paper, we consider the Cauchy problem to the TROPIC CLIMATE MODEL derived by Frierson-Majda-Pauluis in [Comm. Math. Sci, Vol. 2 (2004)] which is a coupled system of the barotropic and the first baroclinic modes of the velocity and the typical midtropospheric temperature. The system considered in this paper has viscosities in the momentum equations, but no diffusivity in the temperature equation. We establish here the global well-posedness of strong solutions to this model. In proving...

Topics: Fluid Dynamics, Atmospheric and Oceanic Physics, Analysis of PDEs, Mathematics, Geophysics, Physics

Source: http://arxiv.org/abs/1504.05285

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Jun 30, 2018
06/18

by
Chongsheng Cao; Jinkai Li; Edriss S. Titi

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In this paper, we consider the initial-boundary value problem of the 3D primitive equations for oceanic and atmospheric dynamics with only horizontal diffusion in the temperature equation. Global well-posedness of strong solutions are established with $H^2$ initial data.

Topics: Physics, Fluid Dynamics, Mathematics, Atmospheric and Oceanic Physics, Analysis of PDEs, Geophysics

Source: http://arxiv.org/abs/1401.1234

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Jun 30, 2018
06/18

by
Chongsheng Cao; Jinkai Li; Edriss S. Titi

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In this paper, we consider the 3D primitive equations of oceanic and atmospheric dynamics with only horizontal eddy viscosities in the horizontal momentum equations and only vertical diffusivity in the temperature equation. Global well-posedness of strong solutions is established for any initial data such that the initial horizontal velocity $v_0\in H^2(\Omega)$ and the initial temperature $T_0\in H^1(\Omega)\cap L^\infty(\Omega)$ with $\nabla_HT_0\in L^q(\Omega)$, for some $q\in(2,\infty)$....

Topics: Physics, Geophysics, Fluid Dynamics, Analysis of PDEs, Atmospheric and Oceanic Physics, Mathematics

Source: http://arxiv.org/abs/1703.02512

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Jun 28, 2018
06/18

by
Richard Blender; Gualtiero Badin

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A geometric approach to derive the Nambu brackets for ideal two-dimensional (2D) hydrodynamics is suggested. The derivation is based on two-forms with vanishing integrals in a periodic domain, and with resulting dynamics constrained by an orthogonality condition. As a result, 2D hydrodynamics with vorticity as dynamic variable emerges as a generic model, with conservation laws which can be interpreted as enstrophy and energy functionals. Generalized forms like surface quasi-geostrophy and...

Topics: Fluid Dynamics, Mathematics, Atmospheric and Oceanic Physics, Mathematical Physics, Physics

Source: http://arxiv.org/abs/1510.04832

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Jun 30, 2018
06/18

by
François Genoud; David Henry

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In this paper we use the short-wavelength instability approach to derive an instability threshold for exact trapped equatorial waves propagating eastwards in the presence of an underlying current.

Topics: Fluid Dynamics, Physics, Mathematics, Atmospheric and Oceanic Physics, Analysis of PDEs,...

Source: http://arxiv.org/abs/1403.1880

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Jun 27, 2018
06/18

by
Xiaodong Luo; Andreas S. Stordal; Rolf J. Lorentzen; Geir Nævdal

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The focus of this work is on an alternative implementation of the iterative ensemble smoother (iES). We show that iteration formulae similar to those used in \cite{chen2013-levenberg,emerick2012ensemble} can be derived by adopting a regularized Levenberg-Marquardt (RLM) algorithm \cite{jin2010regularized} to approximately solve a minimum-average-cost (MAC) problem. This not only leads to an alternative theoretical tool in understanding and analyzing the behaviour of the aforementioned iES, but...

Topics: Atmospheric and Oceanic Physics, Data Analysis, Statistics and Probability, Physics, Statistics,...

Source: http://arxiv.org/abs/1505.01135

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Jun 30, 2018
06/18

by
Colin J. Cotter; Robert C. Kirby

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We study mixed finite element methods for the linearized rotating shallow water equations with linear drag and forcing terms. By means of a strong energy estimate for an equivalent second-order formulation for the linearized momentum, we prove long-time stability of the system without energy accumulation -- the geotryptic state. A priori error estimates for the linearized momentum and free surface elevation are given in $L^2$ as well as for the time derivative and divergence of the linearized...

Topics: Physics, Mathematics, Numerical Analysis, Atmospheric and Oceanic Physics

Source: http://arxiv.org/abs/1410.0045