Estimation Of Dissipation Research Articles

Dynamic Event-Triggered State Estimation for Markov Jump Neural Networks With Partially Unknown Probabilities.

This article focuses on the investigation of finite-time dissipative state estimation for Markov jump neural networks. First, in view of the subsistent phenomenon that the state estimator cannot capture the system modes synchronously, the hidden Markov model with partly unknown probabilities is introduced in this article to describe such asynchronization constraint. For the upper limit of network bandwidth and computing resources, a novel dynamic event-triggered transmission mechanism, whose threshold parameter is constructed as an adjustable diagonal matrix, is set between the estimator and the original system to avoid data collision and save energy. Then, with the assistance of Lyapunov techniques, an event-based asynchronous state estimator is designed to ensure that the resulting system is finite-time bounded with a prescribed dissipation performance index. Ultimately, the effectiveness of the proposed estimator design approach combining with a dynamic event-triggered transmission mechanism is demonstrated by a numerical example.

Energy dissipation estimation of steel slit shear panel dampers with tapered links considering the effect of out-of-plane buckling

The steel slit shear panel (SSSP) with tapered links is one type of efficient energy-dissipating devices, with tapered shape of the links accommodating the bending moment demand when subjected to lateral shear deformation. To dissipate the maximum amount of seismic energy, full plasticity is expected to be developed. However, out-of-plane buckling, which is almost inevitable for thin plates, significantly reduces its energy dissipation capacity. This work aims to quantify the amount of energy dissipation of SSSPs with tapered links considering the effect of out-of-plane buckling. Quasi-static cyclic loading tests on five SSSP specimens with different design parameters are conducted, based on which the refined numerical model is built and validated. In estimating the energy dissipation, the effect of out-of-plane buckling needs to be considered. Otherwise, the estimated energy dissipation can be as much as over two times the tested value. To consider the effect of out-of-plane buckling, the index of average pinching parameter is adopted. A new method is derived for estimating the energy dissipation of SSSPs with considering the effect of out-of-plane buckling, feasibility of which is validated using the obtained test results.

Transfer function model-based Bayesian estimation of dissipation and sound speed in impedance tube measurements

The air dissipation, mainly due to the boundary effect at interior walls of impedance tubes, is noteworthy for normal incidence measurements of acoustic materials using the transfer function method. This work proposes a transfer function model-based Bayesian approach to estimate the dissipation factors. Other parameters, such as the sound speed and the microphone positions, are also critical, therefore, estimated as well, along with the dissipation. The measurement of the empty impedance tube with a rigid termination applies the two-microphone transfer function method. A hypothetical air layer assumed in front of the rigid backing enables the numerical comparison between the air layer’s theoretical and experimental transfer function values. Experimental results incorporating the estimated dissipation coefficient validate the accuracy of the proposed approach. Furthermore, the estimated parameters are incorporated into further evaluations of material properties using the transfer function method, which effectively reduces the residual absorption error of the impedance tube measurement.

Spectral/hp element methods' linear mechanism of (apparent) energy transfer in Fourier space: Insights into dispersion analysis for implicit LES

In recent years, different dispersion-diffusion (eigen)analyses have been developed and used to assess various spectral element methods (SEMs) with regards to accuracy and stability, both of which are very important aspects for under-resolved computations of transitional and turbulent flows. Not surprisingly, eigenanalysis has been used recurrently to probe the inner-workings of SEM-based implicit LES approaches, where numerical dissipation acts alone in lieu of a subgrid model. In this study we present and discuss an intriguing linear mechanism that causes energy transfer across Fourier modes as seen in the energy spectrum of SEM computations. Despite its linear nature, this mechanism has not been considered in eigenanalyses so far, possibly due to its connection to the often overlooked multiple eigencurves feature of periodic eigenanalysis. As we unveil the mechanism in the simplified context of linear advection, we point out how its effects might take place in actual turbulence simulations. In particular, we highlight how taking it into account in eigenanalysis can improve dissipation estimates in wavenumber space, potentially allowing for a superior correlation between dissipation estimates and energy spectra measured in SEM-based eddy-resolving turbulence computations.

Insights into the Mixing Efficiency of Submesoscale Centrifugal–Symmetric Instabilities

Abstract Submesoscale processes provide a pathway for energy to transfer from the balanced circulation to turbulent dissipation. One class of submesoscale phenomena that has been shown to be particularly effective at removing energy from the balanced flow is centrifugal–symmetric instabilities (CSIs), which grow via geostrophic shear production. CSIs have been observed to generate significant mixing in both the surface boundary layer and bottom boundary layer flows along bathymetry, where they have been implicated in the mixing and water mass transformation of Antarctic Bottom Water. However, the mixing efficiency (i.e., the fraction of the energy extracted from the flow used to irreversibly mix the fluid) of these instabilities remains uncertain, making estimates of mixing and energy dissipation due to CSI difficult. In this work we use large-eddy simulations to investigate the mixing efficiency of CSIs in the submesoscale range. We find that centrifugally dominated CSIs (i.e., CSI mostly driven by horizontal shear production) tend to have a higher mixing efficiency than symmetrically dominated ones (i.e., driven by vertical shear production). The mixing efficiency associated with CSIs can therefore alternately be significantly higher or significantly lower than the canonical value used by most studies. These results can be understood in light of recent work on stratified turbulence, whereby CSIs control the background state of the flow in which smaller-scale secondary overturning instabilities develop, thus actively modifying the characteristics of mixing by Kelvin–Helmholtz instabilities. Our results also suggest that it may be possible to predict the mixing efficiency with more readily measurable parameters (viz., the Richardson and Rossby numbers), which would allow for parameterization of this effect.

The Statistics of Oceanic Turbulence Measurements. Part II: Shear Spectra and a New Spectral Model

Abstract This manuscript provides (i) the statistical uncertainty of a shear spectrum and (ii) a new universal shear spectrum, and (iii) shows how these are combined to quantify the quality of a shear spectrum. The data from four collocated shear probes, described in Part I, are used to estimate the spectra of shear, Ψ(k), for wavenumbers k ≥ 2 cpm, from data lengths of 1.0 to 50.5 m, using Fourier transform (FT) segments of 0.5 m length. The differences of the logarithm of pairs of simultaneous shear spectra are stationary, distributed normally, independent of the rate of dissipation, and only weakly dependent on wavenumber. The variance of the logarithm of an individual spectrum, , equals one-half of the variance of these differences and is , where Nf is the number of FT segments used to estimate the spectrum. This term σlnΨ provides the statistical basis for constructing the confidence interval of the logarithm of a spectrum, and thus, the spectrum itself. A universal spectrum of turbulence shear is derived from the nondimensionalization of 14 600 spectra estimated from 5 m segments of data. This spectrum differs from the Nasmyth spectrum and from the spectrum of Panchev and Kesich by 8% near its peak, and is approximated to within 1% by a new analytic equation. The difference between the logarithms of a measured and a universal spectrum, together with the confidence interval of a spectrum, provides the statistical basis for quantifying the quality of a measured shear (and velocity) spectrum, and the quality of a dissipation estimate that is derived from the spectrum. Significance Statement The results reported here can be used to estimate the statistical uncertainty of a spectrum of turbulent shear or velocity that is derived from a finite number of discrete Fourier transform segments, and they can be used to quantify the quality of a spectrum.

The Statistics of Oceanic Turbulence Measurements. Part I: Shear Variance and Dissipation Rates

Abstract An empirically derived statistic is used to estimate the confidence interval of a dissipation estimate that uses a finite amount of shear data. Four collocated shear probes, mounted on a bottom anchored float, are used to measure the rate of dissipation of turbulence kinetic energy ϵ at a height of 15 m above the bottom in a 55 m deep tidal channel. One pair of probes measures ∂w/∂x while the other measures ∂υ/∂x, where w and υ are the vertical and lateral velocity. The shear-probe signals are converted into a regularly resampled space series to permit the rate of dissipation to be estimated directly from the variance of the shear using (and similarly for the υ component), for averaging lengths, L ranging from 1 to 104 Kolmogorov lengths. While the rate of dissipation fluctuates by more than a factor of 100, the fluctuations of the differences of between pairs of probes are stationary, zero mean, and distributed normally for averaging lengths of L = ∼30 to 104 Kolmogorov lengths. The variance of the differences, , scales as L−7/9, independent of stratification for buoyancy Reynolds numbers larger than ∼600, and for dissipation rates from ∼10−10 to ∼10−5 W kg−1. The variance decreases more slowly than L−1 because the averaging is done in linear space while the variance is evaluated in logarithmic space. This statistic provides the confidence interval of an ϵ estimate such as the 95% interval . This result also applies to the traditional ϵ estimates that are made by way of spectral integration, after L is adjusted for the truncation of the shear spectrum. Significance Statement The results reported here can be used to estimate the statistical uncertainty of a dissipation estimate that is derived from a finite length of turbulence shear data.

Turbulent Mixing Variability in an Energetic Standing Meander of the Southern Ocean

Abstract This study presents novel observational estimates of turbulent dissipation and mixing in a standing meander between the Southeast Indian Ridge and the Macquarie Ridge in the Southern Ocean. By applying a finescale parameterization on the temperature, salinity, and velocity profiles collected from Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats in the upper 1600 m, we estimated the intensity and spatial distribution of dissipation rate and diapycnal mixing along the float tracks and investigated the sources. The indirect estimates indicate strong spatial and temporal variability of turbulent mixing varying from O(10−6) to O(10−3) m2 s−1 in the upper 1600 m. Elevated turbulent mixing is mostly associated with the Subantarctic Front (SAF) and mesoscale eddies. In the upper 500 m, enhanced mixing is associated with downward-propagating wind-generated near-inertial waves as well as the interaction between cyclonic eddies and upward-propagating internal waves. In the study region, the local topography does not play a role in turbulent mixing in the upper part of the water column, which has similar values in profiles over rough and smooth topography. However, both remotely generated internal tides and lee waves could contribute to the upward-propagating energy. Our results point strongly to the generation of turbulent mixing through the interaction of internal waves and the intense mesoscale eddy field.

Improved estimation for energy dissipation in biochemical oscillations.

Biochemical oscillations, regulating the timing of life processes, need to consume energy to achieve good performance on crucial functions, such as high accuracy of the phase period and high sensitivity to external signals. However, it is a great challenge to precisely estimate the energy dissipation in such systems. Here, based on the stochastic normal form theory, we calculate the Pearson correlation coefficient between the oscillatory amplitude and phase, and a trade-off relation between transport efficiency and phase sensitivity can then be derived, which serves as a tighter form than the estimator resulting from the conventional thermodynamic uncertainty relation. Our findings demonstrate that a more precise energy dissipation estimation can be obtained by enhancing the sensitivity of the biochemical oscillations. Moreover, the internal noise and amplitude power effects have also been discovered.

On high-order numerical schemes for viscous relativistic hydrodynamics through the Kelvin–Helmholtz instability

ABSTRACT This work assesses the dissipative properties of high-order numerical methods for relativistic hydrodynamics. A causal theory of physical dissipation is included within a finite volume high-resolution shock-capturing framework based on the Israel–Stewart theory to study high-order WENO (weighted-essentially non-oscillatory) schemes for simulating the relativistic Kelvin–Helmholtz instability. We provide an estimation of the numerical dissipation of high-order schemes based on results obtained both with and without physically resolved dissipation and determine an empirical relationship between the numerical dissipation and the grid resolution. We consider the appearance of secondary flow features within the evolution of the Kelvin–Helmholtz instability and determine that they are numerical artifacts — this is partly based on arguments presented in terms of a frame-dependent form of the relativistic Reynolds number. There is a potential advantage of using high-order schemes in terms of their accuracy and computational cost on coarser grid resolutions when directly compared to low-order schemes on a fine grid in the presence of physical viscosity. It is possible to find reasonable agreement between numerical results that employ lower-order schemes using a finer grid resolution and results that employ higher order schemes at a coarser grid resolution when sufficient viscosity is present. Overall, the present analysis gives an insight into the numerical dissipation of high-order shock-wave capturing schemes which can be relevant to computational studies of astrophysical phenomena in the relativistic regime. The results presented herein are problem and scheme-dependent and serve to highlight the different roles of numerical and physical dissipation.

Enhanced dissipation and transition threshold for the 2-D plane Poiseuille flow via resolvent estimate

In this paper, we study the transition threshold problem for the 2-D Navier-Stokes equations around the Poiseuille flow (1−y2,0) in a finite channel with Navier-slip boundary condition. Based on the resolvent estimates for the linearized operator around the Poiseuille flow, we first establish the enhanced dissipation estimates for the linearized Navier-Stokes equations with a sharp decay rate e−cνt. As an application, we prove that if the initial perturbation of vorticity satisfies‖ω0‖L2≤c0ν34 for some small constant c0>0 independent of the viscosity ν, then the solution does not transition away from the Poiseuille flow for any time.

A phase separation model for binary fluids with hereditary viscosity

We consider a diffuse interface model for an incompressible binary viscoelastic fluid flow. The model consists of the Navier–Stokes–Voigt equations where the instantaneous kinematic viscosity has been replaced by a memory term incorporating hereditary effects coupled with the Cahn–Hilliard equation with Flory–Huggins potential. The resulting system is subject to no‐slip condition for the (volume averaged) fluid velocity and to no‐flux boundary conditions for the order parameter and the chemical potential . We first establish the well‐posedness of the initial and boundary value problem. Then, taking advantage of an Ekman‐type damping, we obtain a dissipative estimate. Thus, we can define a dissipative dynamical system on a suitable phase space. Also, we show that any weak solution is such that regularizes in finite time, and in dimension two, it stays uniformly away from pure phases; that is, the instantaneous strict separation property holds. Finally, we prove the existence of the global attractor, and exploiting the strict separation property, we demonstrate that an exponential attractor exists in dimension two.

Global quasi-neutral limit for a two-fluid Euler-Poisson system in one space dimension

The quasi-neutral limit of one-fluid Euler-Poisson systems leads to incompressible Euler equations. It was widely studied in previous works. In this paper, we deal with the quasi-neutral limit in a two-fluid Euler-Poisson system. This limit presents a different feature since it leads to compressible Euler equations. We justify this limit for global smooth solutions near constant equilibrium states in one space dimension. Specifically, we prove a global existence of smooth solutions by establishing uniform energy estimates with respect to the Debye length and the time. This allows to pass to the limit in the system for all time. Moreover, we establish global error estimates between the solution of the two-fluid Euler-Poisson system and that of the compressible Euler equations. The proof is based on classical uniform energy estimates together with various dissipation estimates. In order to control the quasi-neutrality of the velocities of two-fluids, similar conditions on the initial data are needed.

A new method for parameterization of wave dissipation by sea ice

We present a method for predicting wave dissipation by sea ice that is based on the dimensional analysis of data with a scaling defined by ice thickness. Applying the method to an extensive dataset from the measurements during the “Polynyas, Ice Production, and seasonal Evolution in the Ross Sea” (PIPERS) cruise in 2017, we derive a new model of wave dissipation which describes a nonlinear dependence on ice thickness, and reveals the interrelation between the dependences on ice thickness and on wave frequency. This nonlinear dependence on ice thickness can have important implications on predicting low-frequency waves. The root-mean-square error of the prediction is significantly reduced using the new model, compared with other existing parametric models that are also calibrated for the PIPERS dataset. The new model also explicitly describes a condition of similarity between large- and small-scale observations, which is shown to exist when various laboratory datasets collapse onto the prediction. Thus, the new model improves the estimate of wave dissipation by ice across multiple scales.

Global strong solutions and large‐time behavior of 2D tropical climate model with zero thermal diffusion

In this article, we study the global well‐posedness and large‐time behaviors of solutions to the two‐dimensional tropical climate system with zero thermal diffusion for small initial data in the whole space. The main approaches include high‐ and low‐frequency decomposition method and exploiting the structure of system (1) to obtain the estimates of thermal dissipation. We utilize the time decay properties of the kernels to a linear differential equation to obtain the decay rates of solutions of the low‐frequency part and the decay property of exponential operator for the high‐frequency part. The key ingredient here is the explicit large‐time decay rate of solutions.

Pressure–Strain Interaction as the Energy Dissipation Estimate in Collisionless Plasma

The dissipative mechanism in weakly collisional plasma is a topic that pervades decades of studies without a consensus solution. We compare several energy dissipation estimates based on energy transfer processes in plasma turbulence and provide justification for the pressure–strain interaction as a direct estimate of the energy dissipation rate. The global and scale-by-scale energy balances are examined in 2.5D and 3D kinetic simulations. We show that the global internal energy increase and the temperature enhancement of each species are directly tracked by the pressure–strain interaction. The incompressive part of the pressure–strain interaction dominates over its compressive part in all simulations considered. The scale-by-scale energy balance is quantified by scale filtered Vlasov–Maxwell equations, a kinetic plasma approach, and the lag dependent von Kármán–Howarth equation, an approach based on fluid models. We find that the energy balance is exactly satisfied across all scales, but the lack of a well-defined inertial range influences the distribution of the energy budget among different terms in the inertial range. Therefore, the widespread use of the Yaglom relation in estimating the dissipation rate is questionable in some cases, especially when the scale separation in the system is not clearly defined. In contrast, the pressure–strain interaction balances exactly the dissipation rate at kinetic scales regardless of the scale separation.

Technical note: Turbulence measurements from a light autonomous underwater vehicle

Abstract. A self-contained turbulence instrument from Rockland Scientific was installed on a light autonomous underwater vehicle (AUV) from OceanScan Marine Systems and Technology Lda. We report on the data quality and discuss limitations of dissipation estimated from two shear probes during a deployment in the Barents Sea in February 2021. The AUV mission lasted for 5 h, operating at a typical horizontal speed of 1.1 m s−1. The AUV was programmed to find and cross the maximum along-path thermal gradient at 10, 20 and 30 m depths along 4 km transects. Although the AUV vibrations contaminate the shear probe records, the noise is mitigated by removing vibration-induced components from shear spectra using the accelerometer signal measured in multiple directions. Dissipation rate estimates in the observed transects varied in the range 1×10-8 and 6×10-6 W kg−1, with the values from the two orthogonal probes typically in agreement to within a factor of 2. Dissipation estimates from the AUV show good agreement with nearby vertical microstructure profiles obtained from the ship during the transects, indicating that the turbulence measurements from the AUV are reliable for this relatively turbulent environment. However, the lowest reliable dissipation rates are limited to 5×10-8 W kg−1, making this setup unfit for use in quiescent environments.

Gene expression programming for computing energy dissipation over type-B piano key weir

Computation of energy dissipation over weir (or spillway) structures is vital to solving numerous engineering problems, notably during floods. Therefore, an accurate estimation of the energy dissipation at the base of the spillway is essential. The spillways must be designed to spill large amounts of water at high efficiency with high structural performances without causing any damage to the structure or its surroundings. Energy dissipation over weir structures is difficult to predict using conventional formulas based on empirical methods. Consequently, new and accurate techniques are still highly demanded. In this study, Gene Expression Programs (GEP) were used to estimate the relative energy dissipation at the base of type-B Piano Key Weirs (PKWs) by taking three non-dimensional parameters into account: headwater ratio, magnification ratio, and the number of cycles. The performances of the GEP model were compared with empirical equations based on statistical factors coefficient of determination (R2), and root mean square error (RMSE). The computed values of the relative residual energy using the proposed models are within ±5% of the observed ones. Results indicate that the proposed GEP model predicted the relative residual energy satisfactorily with the coefficient of determination (R2 = 0.9979 for training, 0.9980 for testing) and root mean square error (RMSE) of 0.0099, 0.0092 for training and testing datasets, respectively.

The Cauchy problem for an inviscid Oldroyd-B model in three dimensions: global well posedness and optimal decay rates

In this paper, we consider the Cauchy problem for an inviscid compressible Oldroyd-B model in three dimensions. The global well posedness of strong solutions and the associated time-decay estimates in Sobolev spaces are established near an equilibrium state. The vanishing of viscosity is the main challenge compared with [47] where the viscosity coefficients are included and the decay rates for the highest-order derivatives of the solutions seem not optimal. One of the main objectives of this paper is to develop some new dissipative estimates such that the smallness of the initial data and decay rates are independent of the viscosity. Moreover, we prove that the decay rates for the highest-order derivatives of the solutions are optimal, which is of independent interest. Our proof relies on Fourier theory and delicate energy method.

Submesoscale Coherent Vortices in the South Atlantic Ocean: A Pathway for Energy Dissipation

AbstractMesoscale eddies propagate westward across the South Atlantic basin. As they reach the westernmost part of the basin, at approximately 20°S, they interact with a quasi‐zonal seamount chain, the Vitória‐Trindade Ridge (VTR). The interactions with the local topography lead to submesoscales instabilities, which ignite the formation of submesoscale coherent vortices (SCVs) such as those described in the present study for the first time in the VTR region. Here, using high‐resolution hydrographic and microstructure measurements, we describe the dynamics of two adjacent SCVs wandering through the ridge. We find that the anticyclonic SCVs are characterized by a low potential vorticity and angular momentum signature, and are therefore prone to both centrifugal and symmetric instabilities. This dynamic regime suggests small‐scale turbulence is actively cascading energy down to dissipation, diagnosed from turbulent kinetic energy dissipation estimates within one of the SCVs through microstructure measurements. The energy dissipation levels observed within the SCV are two orders of magnitude larger than in surrounding waters. The thermohaline signatures of each SCV reveal homogenized waters in their cores but with small thermohaline anomalies when compared to surrounding waters, suggesting a remote generation site. Here, we argue that such vortices are essential agents for energy dissipation in the ocean. We speculate that the observed SCVs were formed due to mesoscale eddy‐topography interaction along the VTR and advected by the meandering South Equatorial Current to the location of field observations.