Showing papers on "Dissipation published in 1995"

Finescale parameterizations of turbulent dissipation

Abstract: Fine- and microstructure data from a free fall profiler are analyzed to test models that relate the turbulent dissipation rate (e) to characteristics of the internal wave field. The data were obtained from several distinct been previously available. Observations from the ocean interior with negligible large-scale flow were examined to address the buoyancy scaling of e. These data exhibited a factor of 140 range in squared buoyancy frequency (N 2 ) with depth and uniform internal wave characteristics, consistent with the Garrett-Munk spectrum. The magnitude of e and its variation with N(∼N 2 ) was best described by the dynamical model of Henyey et al. A second dynamical model, by McComas and Muller, predicted an appropriate buoyancy scaling but overestimated the observed dissipation rates. Two kinematical dissipation parametrizations predicted buoyancy scalings of N 3/2 ; these are shown to be inconscient with the observations. Data from wave fields that depart from the canonical GM description are also examined an interpreted with reference to the dynamical models. The measurements came from a warm core ring dominated by strong near-inertial shears, a region of steep topography exhibiting high-frequency internal wave characteristics, and a midocean regime dominated at large wavelengths by an internal tide. Of the dissipation predictions examined, those of the Henyey et al. model in which eN − 2 scales as E 2 , where E is the nondimensional spectral shear level, were most consistent with observations. Nevertheless, the predictions for these cases exhibited departures from the observations by more than an order of magnitude. For the present data, these discrepancies appeared most sensitive to the distribution of internal wave frequency, inferred here from the ratio of shear spectral level to that for strain. Application of a frequency-based correction to the Henyey et al. model returned dissipation values consistent with observed estimates to within a factor of 2. These results indicate that the kinetic energy dissipation rate (and attendant turbulent mixing) is small for the background Garrett and Munk internal wave conditions (0.25eN −2 ∼ 0.7 × 10 − 5 m 2 s − 1). Dissipation and mixing become large when wave shear spectral levels are elevated, particularly by high-frequency waves. Thus, internal wave reflection/generation at steep topographic features appear promising candidates for achieving enhanced dissipation and strong diapycnal mixing in the deep ocean that appears required by box models and advection-diffusion balances

Quantized energy cascade and log-Poisson statistics in fully developed turbulence.

Abstract: It is proposed that the statistics of the inertial range of fully developed turbulence can be described by a quantized random multiplicative process. We then show that (i) the cascade process must be a log-infinitely divisible stochastic process (i.e., stationary independent log-increments); (ii) the inertial-range statistics of turbulent fluctuations, such as the coarse-grained energy dissipation, are log-Poisson; and (iii) a recently proposed scaling model [Z.-S. She and E. Leveque 72, 336 (1994)] of fully developed turbulence can be derived. A general theory using the Levy-Khinchine representation for infinitely divisible cascade processes is presented, which allows for a classification of scaling behaviors of various strongly nonlinear dissipative systems.

Non-linear dynamics of three-dimensional rods: Exact energy and momentum conserving algorithms

Abstract: The long-term dynamic response of non-linear geometrically exact rods under-going finite extension, shear and bending, accompanied by large overall motions, is addressed in detail. The central objective is the design of unconditionally stable time-stepping algorithms which exactly preserve fundamental constants of the motion such as the total linear momentum, the total angular momentum and, for the Hamiltonian case, the total energy. This objective is accomplished in two steps. First, a class of algorithms is introduced which conserves linear and angular momentum. This result holds independently of the definition of the algorithmic stress resultants. Second, an algorithmic counterpart of the elastic constitutive equations is developed such that the law of conservation of total energy is exactly preserved. Conventional schemes exhibiting no numerical dissipation, symplectic algorithms in particular, are shown to lead to unstable solutions when the high frequencies are not resolved. Compared to conventional schemes there is little, if any, additional computational cost involved in the proposed class of energy–momentum methods. The excellent performance of the new algorithm in comparison to other standard schemes is demonstrated in several numerical simulations.

Shear-free turbulent boundary layers. Part 1. Physical insights into near-wall turbulence

Abstract: Direct numerical simulation is used to examine the interaction of turbulence with a wall in the absence of mean shear. The influence of a solid wall on turbulence is analysed by first considering two ‘simpler’ types of boundaries. The first boundary is an idealized permeable wall. This boundary isolates and elucidates the viscous effects created by the wall. The second boundary is an idealized free surface. This boundary complements the first by allowing one to isolate and investigate the kinematic effects that occur near boundaries. The knowledge gained from these two simpler flows is then used to understand how turbulence is influenced by solid walls where both viscous and kinematic effects occur in combination.Examination of the instantaneous flow fields confirms the presence of previously hypothesized structures (splats), and reveals an additional class of structures (antisplats). Statistical analysis of the Reynolds stresses and Reynolds stress transport equations indicates the relative importance of dissipation, intercomponent energy transfer, and energy transport. It is found that it is not the structures themselves, but the imbalance between structures which leads to intercomponent energy transfer. Remarkably, this imbalance (and hence near-wall intercomponent energy transfer) is controlled by viscous processes such as dissipation and diffusion. The analysis presented herein is a departure from past notions of how boundaries influence turbulence. The efficacy of these qualitative physical concepts is demonstrated in Part 2 where improved near-wall turbulence models are derived based on these ideas.

Stability analysis of resistive wall kink modes in rotating plasmas.

Abstract: The stability analysis of external magnetohydrodynamic modes is carried out for a cylindrical plasma in the presence of a resistive wall, plasma flow, and coupling to the sound wave continuous spectrum. It is confirmed that the resonance of the mode with the sound continuum produces an effective dissipation. The combined effects of dissipation and plasma flow open up a window of stability to the external kinks. This theory can explain the numerical results of A. Bondeson and D. J. Ward [Phys. Rev. Lett. {bold 72}, 2709 (1994)].

Seabed stress determinations using the inertial dissipation method and the turbulent kinetic energy method

Abstract: Direct measurements of seabed stress are difficult, especially in field conditions. Several methods for estimating these stresses using current meter data are available. Two of these methods, the Inertial Dissipation Method and the Turbulent Kinetic Energy Method, are described below, and a Matlab program is used to analyse data from a wave-current environment.

Viscoelastic Dissipation in Wetting and Adhesion Phenomena

Abstract: When a liquid drop is placed on a smooth, rigid, solid substrate, it spreads until the final thermodgnamic equilibrium is attained. The kinetics of spreading of the drop are controlled by conversion of capillary potential energy into viscous dissipation within the liquid. However, if the solid is sufficiently soft, a local deformation, or »wetting ridge«, may form near the wetting front and the motion of the latter may lead to viscoelastic dissipation. We describe cases in which viscoelastic dissipation dominates and thus where spreading speed depends on bulk properties of the solid, rather than on liquid viscosity. This behavior in wetting can be considered to be analogous to dissipation phenomena in the adhesion of elastomers. Therefore, a comparison is made between wetting and adhesion dynamics. It appears clearly that a parallel can be drawn between the wetting of rubber and rubber adhesion to glass when both phenomena involve the same viscoelastic material. Kinetics of formation and breaking of corresponding interfaces is controlled by the damping properties of the soft solid substrate. In this paper, the viscoelastic properties of elastomers are described by two parameters, n and U o ; n is the usual speed power factor (n0.5-0.6) and U o a characteristic speed below which a fraction of the elastic strain energy in the wetting ridge is dissipated

Dissipative MHD solutions for resonant Alfven waves in 1-dimensional magnetic flux tubes

Abstract: The present paper extends the analysis by Sakurai, Goossens, and Hollweg (1991) on resonant Alfven waves in nonuniform magnetic flux tubes. It proves that the fundamental conservation law for resonant Alfven waves found in ideal MHD by Sakurai, Goossens, and Hollweg remains valid in dissipative MHD. This guarantees that the jump conditions of Sakurai, Goossens, and Hollweg, that connect the ideal MHD solutions forξr, andP′ across the dissipative layer, are correct. In addition, the present paper replaces the complicated dissipative MHD solutions obtained by Sakurai, Goossens, and Hollweg forξr, andP′ in terms of double integrals of Hankel functions of complex argument of order\(\frac{1}{3}\) with compact analytical solutions that allow a straightforward mathematical and physical interpretation. Finally, it presents an analytical dissipative MHD solution for the component of the Lagrangian displacement in the magnetic surfaces perpendicular to the magnetic field linesξ⊥ which enables us to determine the dominant dynamics of resonant Alfven waves in dissipative MHD.

Turbulent Mixing in Stably Stratified Shear Flows.

Abstract: Vertical mixing of momentum and heat is investigated in turbulent stratified shear flows. It is assumed that the flow has uniform shear and stratification with homogeneous turbulence and that an equilibrium is reached between kinetic and potential energy without gravity wave oscillations. A simple model is derived to estimate vertical diffusivities for Richardson numbers in between 0 and about 1. The model is based on the budgets of kinetic and potential energy and assumes a linear relationship between dissipation, shear, and vertical velocity variance for closure. Scalar fluctuations are related to shear or buoyancy frequency depending on the Richardson number. The turbulent Prandtl number and the growth rate of kinetic energy are specified as functions of this number. Model coefficients are determined mainly from laboratory measurements. Data from large-eddy simulations are used to determine the "stationary" Richardson number with balanced shear production, dissipation, and buoyancy terms. The ...

A novel circuit technology with surrounding gate transistors (SGT's) for ultra high density DRAM's

Abstract: This paper describes a novel circuit technology with Surrounding Gate Transistors (SGT's) For ultra high density DRAM's. In order to reduce the chip size drastically, an SGT is employed to all the transistors within a chip. SGT's connected in series and a common source SGT have been newly developed for the core circuit, such as a sense amplifier designed by a tight design rule. Furthermore, to reduce the inherent cell array noise caused by a relaxed open bit line (BL) architecture, a noise killer circuit placed in the word line (WL) shunt region and a twisted BL architecture within the sense amplifier region combined with a novel separation sensing scheme have been newly introduced. Using the novel circuit technology, a 32.9% smaller chip size can be successfully achieved for a 64-Mb DRAM and 34.4% for a 1-Gb DRAM compared with a DRAM composed of the planar transistor without sacrificing the access time, power dissipation, and V/sub cc/ margin. Furthermore,the effectiveness of this technology is verified by using the circuit simulation of the internal main nodes such as WL and BL. >

Resistive drift‐wave turbulence

Abstract: Two‐dimensional resistive drift‐wave turbulence is studied by high‐resolution numerical simulations in the limit of small viscosity. Density and potential fluctuations are cross‐coupled by resistive dissipation, proportional to the adiabaticity parameter, C, which determines the character of the system: adiabatic (C≫1) or hydrodynamic (C≪1). Various cases are computed for 0.1≤C≤5. Energy spectra exhibit a maximum at some wave number k0(C) and an inertial range behavior for k≳k0. The transfer of energy and vorticity is directly computed and confirms the persistence of local cascade dynamics in all regimes: the familiar dual cascade for the E×B flow eddies, and the direct cascade to small scales for the density as it is advected by the eddies. Inertial range spectral power laws agree surprisingly well with simple scaling predictions. No prominent large‐scale long‐lived coherent structures are observed, an absence that is consistent with the statistical properties, which are found to be perfectly Gaussian for k≲k0, but exhibit the non‐Gaussian behavior, typical for small‐scale intermittency, in the inertial range.

Dissipation in Internal Tides and Solitary Waves

Abstract: Solitons have been observed and studied on the Scotian Shelf using the vertical microstructure profiler EPSONDE. During one tidal cycle a packet of solitary waves has been sampled four times as it propagated onto the shelf to examine its evolution and decay. Enhanced turbulence and mixing were observed to occur in the strongest shear region of the wave packet as expected. About 20% of the energy lost as the solitary wave packet delayed can be attributed to turbulent dissipation. The effects of nonlinearity, dissipation, and dispersion are explored in terms of the Korteweg-de Vries-Burgers (KdVB) equation. The dispersive timescale is always much shorter than the dissipative timescale, and both decrease as the soliton moves onshelf. The mean dissipation timescale, of 12 h compared to the dispersion timescale of less than 1 h, suggests that the waves are consistent with the KdVB description. Calculated vertical diffusivities are in the range of 10−5–10−4 m2 s−1.

On passivity‐based output feedback global stabilization of euler‐lagrange systems

Abstract: It is well known that in systems described by Euler-Lagrange equations the stability of the equilibria is determined by the potential energy function. Further, these equilibria are asymptotically stable if suitable damping is present in the system. These properties motivated the development of a passivity-based controller design methodology which aims at modifying the potential energy of the closed loop and the addition of the required dissipation. To achieve the latter objective measurement of the generalized velocities is typically required. Our main contribution in this paper is the proof that damping injection without velocity measurement is possible via the inclusion of a dynamic extension provided the system satisfies a dissipation propggation condition. This allows us to determine a class of Euler-Lagrange systems that can be globally asymptotically stabilized with dynamic output feedback. We illustrate this result with the problem of set-point control of elastic joints robots. Our research contributes, if modestly, to the development of a theory for stabilization of nonlinear systems with physical structures which effectively exploits its energy dissipation properties.

A modeling investigation of the breaking wave roller with application to cross‐shore currents

Abstract: A mathematical model is developed for the creation and evolution of the aerated region, or “roller,” that appears as a wave breaks and passes through the surf zone. The model, which calculates the roller's cross-sectional area, is based on a short-wave averaged energy balance. The vertically integrated energy flux is split between the turbulent motion in the roller and the underlying organized wave motion, and the dissipation of energy is assumed to take place in the shear layer that exists at the interface between the two flow regimes. Calibration of the roller model is done by numerically solving equations for the cross-shore balances of mass and momentum, with roller contributions included, and then optimizing predictions of depth-averaged cross-shore currents. The laboratory data of Hansen and Svendsen [1984] for setup and cross-shore currents, driven by regular waves breaking on a planar beach, are used to set the roller model's fitting coefficient. The model is then validated utilizing five additional laboratory data sets found in the literature. Results indicate that employing stream function theory in calculating integral properties for the organized wave motion (wave celerity, and mass, momentum, and energy fluxes) significantly improves agreement as compared to results generated using linear wave theory. Using the roller model and stream function theory, root-mean-square error for the mean current is typically 19%. The bed stress is found to play a negligible role in the cross-shore mean momentum balance, relative to the radiation stress, setup, roller momentum flux, and convective acceleration of the current.

An efficient numerical tank for non-linear water waves, based on the multi-subdomain approach with BEM

Abstract: An efficient 2D non-linear numerical wave tank called LONGTANK has been developed based on a multi-subdomain (MSD) approach combined with the conventional boundary element method (BEM). The multi-subdomain approach aims at optimized matrix diagonalization, thus minimizing the computing time and reserved storage. The CPU per time step in LONGTANK simulation is found to increase only linearly with the number of surface nodes, which makes LONGTANK highly efficient especially when simulating long-time wave evolutions in space. Appropriate treatment of special points on the boundary ensures high resolution in LONGTANK simulation beyond initial deformation and breaking, which allows detailed study of breaking criterion, breaker morphology, breaking dissipation, vorticity generation, etc. Detailed numerical implementation has been given with demonstration of LONGTANK simulations.

Constitutive model and wave equations for linear, viscoelastic, anisotropic media

Abstract: Rocks are far from being isotropic and elastic. Such simplifications in modeling the seismic response of real geological structures may lead to misinterpretations, or even worse, to overlooking useful information. It is useless to develop highly accurate modeling algorithms or to naively use amplitude information in inversion processes if the stress-strain relations are based on simplified rheologies. Thus, an accurate description of wave propagation requires a rheology that accounts for the anisotropic and anelastic behavior of rocks. This work presents a new constitutive relation and the corresponding time-domain wave equation to model wave propagation in inhomogeneous anisotropic and dissipative media. The rheological equation includes the generalized Hooke’s law and Boltzmann’s superposition principle to account for anelasticity. The attenuation properties in different directions, associated with the principal axes of the medium, are controlled by four relaxation functions of viscoelastic type. A dissipation model that is consistent with rock properties is the general standard linear solid. This is based on a spectrum of relaxation mechanisms and is suitable for wavefield calculations in the time domain. One relaxation function describes the anelastic properties of the quasi-dilatational mode and the other three model the anelastic properties of the shear modes. The convolutional relations are avoided by introducing memory variables, six for each dissipation mechanism in the 3-D case, two for the generalized SH-wave equation, and three for the qP - qSVwave equation. Two-dimensional wave equations apply to monoclinic and higher symmetries. A plane analysis derives expressions for the phase velocity, slowness, attenuation factor, quality factor and energy velocity (wavefront) for homogeneous viscoelastic waves. The analysis shows that the directional properties of the attenuation strongly depend on the values of the elasticities. In addition, the displacement formulation of the 3-D wave equation is solved in the time domain by a spectral technique based on the Fourier method. The examples show simulations in a transversely-isotropic clayshale and phenolic (orthorhombic symmetry).

Transformation and synthesis of FSMs for low-power gated-clock implementation

Abstract: We present a technique that automatically synthesizes nite state machines with gated clocks to reduce the power dissipation of the nal implementation. We describe a new transformation for general incompletely speci ed Mealy-type machines that makes them suitable for gated clock implementation. The transformation is probabilistic-driven, and leads to the synthesis of an optimized combinational logic block that stops the clock with

Exponential Stability of Coupled Beams with Dissipative Joints: A Frequency Domain Approach

Abstract: Two examples of coupled Euler-Bernoulli beams with a dissipative joint are considered. The joint placements that lead to exponential stability for these systems are characterized. The technique used shows input-output stability of a related controlled, observed system, and then shows that in these examples, input-output stability implies exponential stability. In the first example, the energy dissipation arises from a discontinuity in the shear at the joint. In the second example, the energy dissipation arises from a discontinuity in the bending moment at the joint. The analysis of this system involves a complete spectrum analysis of the zero dynamics of the associated controlled, observed system.

Scaling and dissipation in the GOY shell model

Abstract: This is a paper about multifractal scaling and dissipation in a shell model of turbulence, called the Gledzer?Ohkitani?Yamada (GOY) model. This set of equations describes a one-dimensional cascade of energy towards higher wave vectors. When the model is chaotic, the high-wave-vector velocity is a product of roughly independent multipliers, one for each logarithmic momentum shell. The appropriate tool for studying the multifractal properties of this model is shown to be the energy flux on each shell rather than the velocity on each shell. Using this quantity, one can obtain better measurements of the deviations from Kolmogorov scaling (in the GOY dynamics) than were available up to now. These deviations are seen to depend upon the details of inertial-range structure of the model and hence are not universal. However, once the conserved quantities of the model are fixed to have the same scaling structure as energy and helicity, these deviations seem to depend only weakly upon the scale parameter of the model. The connection between multifractality in the velocity distribution and multifractality in the dissipation is analyzed. Arguments suggest that the connection is universal for models of this character, but the model has a different behavior from that of real turbulence. Also, the scaling behavior of time correlations of shell velocities, of the dissipation, and of Lyapunov indices are predicted. These scaling arguments can be carried over, with little change, to multifractal models of real turbulence.

Earthquake ground motion characteristics and seismic energy dissipation

Abstract: The sensitivity of seismic energy dissipation to ground motion and system characteristics is assessed. It is found that peak ground acceleration, peak ground velocity to acceleration (V/A), dominant period of ground excitation and effective response duration are closely correlated with the energy dissipated by a SDOF system. Ductility ratio and damping ratio have no significant influence on the energy dissipation. An energy dissipation index is proposed for measuring the damage potential of earthquake ground motion records which includes the effects of basic excitation and response characteristics contributing to the seismic energy dissipation. The proposed index is compared with several intensity measures for the set of 94 ground motion records considered in the study.

A split‐characteristic based finite element model for the shallow water equations

Abstract: A new algorithm for the solution of the shallow water equations is introduced. The formulation is founded on a suitable operator-splitting procedure for which a characteristic-based rational form of including balancing dissipation terms is achieved. In the semi-explicit form the method circumvents the requirement of a critical time step given in terms of the wave celerity, which is restrictive for the analysis of long-wave propagation in shallow waters. In this work the robustness of the algorithm is illustrated for transient shallow water problems and for some supercritical flows, where the choice of an algorithm with optimal diffusion properties is manifest

Nonlinear resonant absorption of Alfvén waves in three dimensions, scaling laws, and coronal heating

Abstract: The nonlinear evolution of the resonant absorption of standing and propagating Alfven waves in an inhomogeneous plasma is studied via solution of the time-dependent, three-dimensional, low-β, resistive MHD equations over a wide parameter range. When the nonlinear effects become important, the velocities at the dissipation layer were found to be lower than the linear scaling of S1/3 would predict, where S is the Lundquist number. Highly sheared velocities that are subject to the Kelvin-Helmholtz-like instability were found at the narrow dissipation layers. Three-dimensional Kelvin-Helmholtz-like vortices appear at and near the dissipation layers and propagate along the slab of plasma when traveling Alfven wave solution are considered. The narrow resonant heating layers are deformed by the self-consistent shear flow. In the solar active regions where the resonant absorption of Alfven waves is believed to occur, the instability may lead to turbulent enhancement of the dissipation parameters and account for the observed turbulent velocities inferred from the nonthermal broadening of x- ray and EUV emission lines. The self consistent J×B force changes significantly the density structure of the loop that leads to a shift in the global mode frequency response of the loop and a subsequent drop in the heating rate. In the solar corona the density evolution of the loop is likely to be dominated by evaporation of material from the transition region.

Exact dynamics of a quantum dissipative system in a constant external field.

Abstract: We study the quantum dynamics of the simplest dissipative system, a particle moving in a constant external field and interacting with a bath of harmonic oscillators with Ohmic spectral density. Applying the main idea and methods developed in our recent work [L. H. Yu and C. P. Sun, Phys. Rev. A 49, 592 (1994)] to this system, we obtain the simple and exact solutions for the coordinate operator of the system in the Heisenberg picture and the wave function of the composite system of the system and the bath in the Schr\"odinger picture. An effective Hamiltonian for the dissipative system is explicitly derived from these solutions. The meaning of the wave function described by this effective Hamiltonian is clarified by analyzing the effect of the Brownian motion. In particular, the general effective Hamiltonian for an arbitrary potential is directly derived with this method for the case when the Brownian motion can be ignored. Using this effective Hamiltonian, we show an interesting result that the dissipation suppresses the wave-packet spreading.

Numerical simulation of bump‐on‐tail instability with source and sink

Abstract: A numerical procedure has been developed for the self‐consistent simulation of the nonlinear interaction of energetic particles with discrete collective modes in the presence of a particle source and dissipation. A bump‐on‐tail instability model is chosen for these simulations. The model presents a kinetic nonlinear treatment of the wave–particle interaction within a Hamiltonian formalism. A mapping technique has been used in this model in order to assess the long time behavior of the system. Depending on the parameter range, the model shows either a steady‐state mode saturation or quasiperiodic nonlinear bursts of the wave energy. It is demonstrated that the mode saturation level as well as the burst parameters scale with the drive in accordance with the analytical predictions. The threshold for the resonance overlap condition and particle global diffusion in the phase space are quantified. For the pulsating regime, it is shown that when γL≳0.16 ΔΩ, where γL is the linear growth rate for the unperturbed ...