The Ocean Mesoscale Regime of the Reduced-Gravity Quasigeostrophic Model

2019 ◽  
Vol 49 (10) ◽  
pp. 2469-2498 ◽  
Author(s):  
R. M. Samelson ◽  
D. B. Chelton ◽  
M. G. Schlax
Keyword(s):  
Numerical Solutions ◽  
Signal Propagation ◽  
Model Parameters ◽  
Linear Wave ◽  
Mesoscale Variability ◽  
Reduced Gravity ◽  
Stochastic Field ◽  
Stochastic Forcing ◽  
Frequency Spectra ◽  
Quasigeostrophic Model

AbstractA statistical-equilibrium, geostrophic-turbulence regime of the stochastically forced, one-layer, reduced-gravity, quasigeostrophic model is identified in which the numerical solutions are representative of global mean, midlatitude, open-ocean mesoscale variability. Solutions are forced near the internal deformation wavenumber and damped linearly and by high-wavenumber enstrophy dissipation. The results partially rationalize a recent semiempirical stochastic field model of mesoscale variability motivated by a global eddy identification and tracking analysis of two decades of satellite altimeter sea surface height (SSH) observations. Comparisons of model results with observed SSH variance, autocorrelation, eddy, and spectral statistics place constraints on the model parameters. A nominal best fit is obtained for a dimensional SSH stochastic-forcing variance production rate of 1/4 cm2 day−1, an SSH damping rate of 1/62 week−1, and a stochastic forcing autocorrelation time scale near or greater than 1 week. This ocean mesoscale regime is nonlinear and appears to fall near the stochastic limit, at which wave-mean interaction is just strong enough to begin to reduce the local mesoscale variance production, but is still weak relative to the overall nonlinearity. Comparison of linearly inverted wavenumber–frequency spectra shows that a strong effect of nonlinearity, the removal of energy from the resonant linear wave field, is resolved by the gridded altimeter SSH data. These inversions further suggest a possible signature in the merged altimeter SSH dataset of signal propagation characteristics from the objective analysis procedure.

scholarly journals Sparse pursuit and dictionary learning for blind source separation in polyphonic music recordings

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sören Schulze ◽  
Emily J. King
Keyword(s):  
Single Channel ◽  
Spectral Characteristics ◽  
Musical Instruments ◽  
Model Parameters ◽  
Blind Separation ◽  
Audio Signals ◽  
Frequency Spectra ◽  
Acoustic Instruments ◽  
Invariant Properties ◽  
Music Recordings

AbstractWe propose an algorithm for the blind separation of single-channel audio signals. It is based on a parametric model that describes the spectral properties of the sounds of musical instruments independently of pitch. We develop a novel sparse pursuit algorithm that can match the discrete frequency spectra from the recorded signal with the continuous spectra delivered by the model. We first use this algorithm to convert an STFT spectrogram from the recording into a novel form of log-frequency spectrogram whose resolution exceeds that of the mel spectrogram. We then make use of the pitch-invariant properties of that representation in order to identify the sounds of the instruments via the same sparse pursuit method. As the model parameters which characterize the musical instruments are not known beforehand, we train a dictionary that contains them, using a modified version of Adam. Applying the algorithm on various audio samples, we find that it is capable of producing high-quality separation results when the model assumptions are satisfied and the instruments are clearly distinguishable, but combinations of instruments with similar spectral characteristics pose a conceptual difficulty. While a key feature of the model is that it explicitly models inharmonicity, its presence can also still impede performance of the sparse pursuit algorithm. In general, due to its pitch-invariance, our method is especially suitable for dealing with spectra from acoustic instruments, requiring only a minimal number of hyperparameters to be preset. Additionally, we demonstrate that the dictionary that is constructed for one recording can be applied to a different recording with similar instruments without additional training.

Implications of Using Dual Number Derivatives With a Numerical Solution

2013 ◽  
Author(s):  
Suryanarayana R. Pakalapati ◽  
Hayri Sezer ◽  
Ismail B. Celik
Keyword(s):  
Automatic Differentiation ◽  
Numerical Solutions ◽  
Computer Code ◽  
Model Parameters ◽  
Model Parameter ◽  
Systematic Assessment ◽  
Dual Number ◽  
Advection Diffusion Equation ◽  
Model Equations ◽  
Derivatives Of

Dual number arithmetic is a well-known strategy for automatic differentiation of computer codes which gives exact derivatives, to the machine accuracy, of the computed quantities with respect to any of the involved variables. A common application of this concept in Computational Fluid Dynamics, or numerical modeling in general, is to assess the sensitivity of mathematical models to the model parameters. However, dual number arithmetic, in theory, finds the derivatives of the actual mathematical expressions evaluated by the computer code. Thus the sensitivity to a model parameter found by dual number automatic differentiation is essentially that of the combination of the actual mathematical equations, the numerical scheme and the grid used to solve the equations not just that of the model equations alone as implied by some studies. This aspect of the sensitivity analysis of numerical simulations using dual number auto derivation is explored in the current study. A simple one-dimensional advection diffusion equation is discretized using different schemes of finite volume method and the resulting systems of equations are solved numerically. Derivatives of the numerical solutions with respect to parameters are evaluated automatically using dual number automatic differentiation. In addition the derivatives are also estimated using finite differencing for comparison. The analytical solution was also found for the original PDE and derivatives of this solution are also computed analytically. It is shown that a mathematical model could potentially show different sensitivity to a model parameter depending on the numerical method employed to solve the equations and the grid resolution used. This distinction is important since such inter-dependence needs to be carefully addressed to avoid confusion when reporting the sensitivity of predictions to a model parameter using a computer code. A systematic assessment of numerical uncertainty in the sensitivities computed using automatic differentiation is presented.

An Assessment of Prediction Methods for Waves Inside the Moonpool of a Vessel (Comparisons of Numerical Solutions With Experiments)

2015 ◽  
Author(s):  
Yusong Cao ◽  
Fuwei Zhang ◽  
Tae-Hwan Joung ◽  
Anders Ostman ◽  
Trygve Kristiansen
Keyword(s):  
Cfd Simulation ◽  
Numerical Solutions ◽  
Prediction Methods ◽  
Diffraction Radiation ◽  
Linear Wave ◽  
Water Tank ◽  
Linear Solution ◽  
Physical Test ◽  
Flow Solver ◽  
Radiation Theory

This paper presents a preliminary assessment of the computational accuracy and efficiency of three different prediction methods for the water motion inside the moonpool of a rectangular box with forced vertical motion in a water tank. The first method is a linear solution method based on the linear wave diffraction/radiation theory (WAMIT). The second one is a method based on a CFD simulation (STAR-CCM+), the third method is a hybrid method combining a potential flow solver and a viscous flow solver (PVC3D). The accuracy of each method is assessed by comparing the prediction with the physical test data. The computational efficiency (complexity of setting up the computation and the computation speed) of the methods is discussed.

scholarly journals Novel Time Method of Identification of Fractional Model Parameters of Supercapacitor

Energies ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 2877
Author(s):  
Miroslaw Lewandowski ◽  
Marek Orzylowski
Keyword(s):  
Energy Storage ◽  
Electric Vehicles ◽  
Dynamic Models ◽  
Storage Systems ◽  
Model Parameters ◽  
Correct Identification ◽  
Energy Storage Systems ◽  
Frequency Spectra ◽  
Test Drive ◽  
Fractional Model

Accurate dynamic models of supercapacitors (SCs) are a basis for the design, control and exploitation of the hybrid energy storage systems for electric vehicles. This paper concerns a fractional model of SC impedance, based on the Cole–Cole equation describing relaxation in electric double layer. This article provides a new method of identifying the parameters of fractional order model of SC impedance, performed without disconnecting the SC module from the energy storage system. The test drive for this purpose needs only the respect a few simple recommendations. The article presents the conditions of the mentioned test drive that will ensure the frequency spectra of the recorded signals lying in the bandwidth necessary for the correct identification of the model parameters. These parameters are determined by means of the Nelder–Mead simplex optimization method. The results of the identification described by the time method coincide with those obtained in the frequency domain. It has been shown in the last part of the article that the real energy losses in these systems significantly exceed the losses determined only on the basis of the nominal capacity and series equivalent resistance (ESR), to which the SC catalogue data are usually limited. This paper also provides an auxiliary frequency criterion for the selection of SCs intended for energy storage systems of electric vehicles.

scholarly journals The influence of vertical density and velocity distributions on snow avalanche runout

2010 ◽  
Vol 51 (54) ◽  
pp. 200-206 ◽  
Author(s):  
Ashok K. Keshari ◽  
Deba P. Satapathy ◽  
Amod Kumar
Keyword(s):  
Flux Distribution ◽  
Numerical Solutions ◽  
Model Parameters ◽  
Dynamics Model ◽  
Turbulent Friction ◽  
One Dimensional ◽  
Variation Diminishing ◽  
Flow Features ◽  
Vertical Density ◽  
Two Fluid

AbstractA one-dimensional avalanche dynamics model accounting for vertical density and velocity distributions is presented. Mass and momentum flux distribution factors are derived to incorporate the effect of density and velocity variations within the framework of depth-integrated models. Using experiments of avalanche flows on an inclined snow chute at Dhundhi, Manali, India, we conceptualize snow flow rheology as a Voellmy fluid where the distribution of internal shearing is given by a Newtonian fluid (NF) or Criminale–Ericksen–Filbey fluid (CEFF). Then the generalized mass and momentum distribution factors are computed for these two fluid models for different density stratifications. Numerical solutions are obtained using a total variation diminishing Lax–Friedrichs (TVDLF) finite-difference method. The model is validated with the experimental results. We find that the flow features of the chute experiments are simulated well by the model. The velocities and runout distances are obtained for the Voellmy model with both NF and CEFF extensions for various input volumes, and the optimum values of the model parameters, namely, coefficients of dynamic and turbulent friction, are determined.

Time Domain Simulation of Combustion Instabilities in Annular Combustors

2003 ◽  
Vol 125 (3) ◽  
pp. 677-685 ◽  
Author(s):  
C. Pankiewitz ◽  
T. Sattelmayer
Keyword(s):  
Heat Release ◽  
Time Domain ◽  
Time Lag ◽  
Initial Perturbation ◽  
Limit Cycle Oscillation ◽  
Model Parameters ◽  
Linear Wave ◽  
Computational Domain ◽  
Combustion Instabilities ◽  
Mean Flow

A novel method for the simulation of combustion instabilities in annular combustors is presented. It is based on the idea to solve the equations governing the acoustics in the time domain and couple them to a model for the heat release in the flames. The linear wave equation describing the temporal and spatial evolution of the pressure fluctuations is implemented in a finite element code. Providing high flexibility, this code in principle allows both the computational domain to be of arbitrary shape and the mean flow to be included. This yields applicability to realistic technical combustors. The fluctuating heat release acting as a volume source appears as a source term in the equation to be solved. Employing a time-lag model, the heat release rate at each individual burner is related to the velocity in the corresponding burner at an earlier time. As saturation also is considered, a nonlinearity is introduced into the system. Starting the simulation from a random initial perturbation with suitable values for the parameters of the heat release model, a self-excited instability is induced, leading to a finite-amplitude limit cycle oscillation. The feasibility of the approach is demonstrated with three-dimensional simulations of a simple model annular combustor. The effect of the model parameters and of axial mean flow on the stability and the shape of the excited modes is shown.

Diffusion-driven instability in oscillating environments

1995 ◽  
Vol 6 (4) ◽  
pp. 355-372 ◽  
Author(s):  
Jonathan A. Sherratt
Keyword(s):  
Diffusion Coefficients ◽  
Numerical Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Model Parameters ◽  
Seasonal Fluctuations ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Ecological Applications ◽  
Parameter Values

Diffusion-driven instability in systems of reaction-diffusion equations is a commonly used model for pattern formation in both embryology and ecology. In ecological applications, model parameters tend to oscillate in time, because of either daily or seasonal fluctuations in the environment. I investigate the effects of such fluctuations on diffusion-driven instability by considering analytically the possibility of Turing bifurcations when the parameter values (diffusion coefficients and kinetic parameters) oscillate in time between two sets of constant values, with a period that is either very short or very long compared to the time scale of the growth and predation kinetics. I show that oscillations in the kinetics can have quite different effects from oscillations in the dispersal terms. I also discuss the comparison between the solution forms predicted by linear theory and the numerical solutions of a simple nonlinear predator-prey model.

scholarly journals Spatio-temporal modeling of COVID-19 epidemic

2021 ◽  
pp. 23-37
Author(s):  
V.L. Sokolovsky ◽  
◽  
G.B. Furman ◽  
D.A. Polyanskaya ◽  
E.G. Furman ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
Mass Vaccination ◽  
Reaction Diffusion Equations ◽  
Disease Spread ◽  
Correct Prediction ◽  
Model Parameters ◽  
Population Mobility ◽  
Personal Protection Equipment ◽  
Infected People ◽  
Spatio Temporal

In autumn and winter 2020–2021 there was a growth in morbidity with COVID-19. Since there are no efficient medications and mass vaccination has only just begun, quarantine, limitations on travels and contacts between people as well as use of personal protection equipment (masks) still remain priority measures aimed at preventing the disease from spreading. In this work we have analyzed how the epidemic developed and what impacts quarantine measures exerted on the disease spread; to do that we applied various mathematical models. It was shown that simple models belonging to SIR-type (S means susceptible; I, infected; and R, recovered or removed from the infected group) allowed estimating certain model parameters such as morbidity and recovery coefficients that could be used in more complicated models. We examined spatio-temporal epidemiologic models based on finding solutions to non-stationary two-dimensional reaction-diffusion equations. Such models allow taking into account uneven distribution of population, changes in population mobility, and changes in frequency of contacts between susceptible and infected people due to quarantine. We applied obtained analytical and numerical solutions to analyze different stages in the epidemic as well as its wave-like development influenced by imposing and canceling quarantine limitations. To take into account ultimate rate at which the disease spreads and its incubation period (when an infected person is not a source of contagion), we suggest using equations similar to the Cattaneo-Vernotte one. The suggested model allows predicting where the front of morbidity spread is going to occur, that is, a moving frontier between areas where there are infected people and areas where they are absent. Use of such models provides an opportunity to introduce differential quarantine measures basing on more objective grounds. At the end of 2020 mass vaccination started in some countries. We estimated a necessary number of people that had to be vaccinated so that new waves of COVID-19 epidemic would be prevented; in our estimates, not less than 80% of the country population should be vaccinated. Correct prediction of epidemic development is becoming more and more vital at the moment due to new and more contagious COVID-19 virus strains occurring in England, South Africa, and some other countries. Our research results can be used for predicting spread of COVID-19 and other communicable diseases; they can make for taking the most efficient measures for successful control over epidemics.

scholarly journals Combined Influence of Nutrient Supply Level and Tissue Mechanical Properties on Benign Tumor Growth as Revealed by Mathematical Modeling

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2213
Author(s):  
Maxim Kuznetsov
Keyword(s):  
Hydraulic Conductivity ◽  
Tumor Growth ◽  
Normal Tissue ◽  
Numerical Solutions ◽  
Stress Gradient ◽  
Growth Curves ◽  
Nutrient Supply ◽  
Benign Tumors ◽  
Model Parameters ◽  
Supply Level

A continuous mathematical model of non-invasive avascular tumor growth in tissue is presented. The model considers tissue as a biphasic material, comprised of a solid matrix and interstitial fluid. The convective motion of tissue elements happens due to the gradients of stress, which change as a result of tumor cells proliferation and death. The model accounts for glucose as the crucial nutrient, supplied from the normal tissue, and can reproduce both diffusion-limited and stress-limited tumor growth. Approximate tumor growth curves are obtained semi-analytically in the limit of infinite tissue hydraulic conductivity, which implies instantaneous equalization of arising stress gradients. These growth curves correspond well to the numerical solutions and represent classical sigmoidal curves with a short initial exponential phase, subsequent almost linear growth phase and a phase with growth deceleration, in which tumor tends to reach its maximum volume. The influence of two model parameters on tumor growth curves is investigated: tissue hydraulic conductivity, which links the values of stress gradient and convective velocity of tissue phases, and tumor nutrient supply level, which corresponds to different permeability and surface area density of capillaries in the normal tissue that surrounds the tumor. In particular, it is demonstrated, that sufficiently low tissue hydraulic conductivity (intrinsic, e.g., to tumors arising from connective tissue) and sufficiently high nutrient supply can lead to formation of giant benign tumors, reaching tens of centimeters in diameter, which are indeed observed clinically.

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