Showing papers on "Dissipation published in 1986"

Energy and action flow through the internal wave field: An eikonal approach

Abstract: The energy and action flow through the small-scale part of the oceanic internal wave field is modeled by use of the eikonal technique, which is not subject to a weak interaction assumption. Both Monte Carlo calculations and a simplified model are presented and found to agree. It is found that the action flows toward slightly higher frequency (and thus the waves gain energy), in striking contrast to weak interaction predictions of a strong frequency decrease. The energy dissipation scales with depth as N2 cosh−1 (N/f), in agreement with measurements. The overall level is, however, a factor of 4 smaller than measurements. Possible sources of this discrepancy are discussed. A comparison is made with previous theoretical approaches for the depth dependence of dissipation.

Dissipation in a fundamental model of quantum optical resonance

Abstract: The fully quantum-electrodynamical model of a two-level atom interacting with a single-cavity mode predicts an atomic evolution whose form is dictated by the discrete nature of the field energy and its statistical distribution. We demonstrate that the revivals of atomic excitation which are the signature of the quantum nature of the evolution are strongly affected by field dissipation even when the damping hardly affects the underlying Rabi oscillations.

Testing of a higher-order closure model for modeling airflow within and above plant canopies

Abstract: A higher-order closure model was developed to simulate airflow within and above vegetative environments. The model consists of equations for the mean wind, turbulent kinetic energy (TKE) components, tangential stress and simplified equations for the third-order transport terms that appear in the second-order equations. The model in general successfully simulated wind speed profiles within and above maize, been, soybeen, wheat, orange and spruce canopies. Profiles of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG1bGbauaadaahaaWcbeqaaiaaikdaaaaaaaaa!37EC!\[\overline {u'^2 } \] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG3bGbauaadaahaaWcbeqaaiaaikdaaaaaaaaa!37EE!\[\overline {w'^2 } \] for the maize canopy were overestimated near the top of the canopy where both shear and wake production of TKE are high. These errors are believed to be caused by incorrect parameterizations for either the dissipation rate of TKE and/or the pressure-velocity correlations in the budget equations for the second moments.

On long nonlinear internal waves over slope-shelf topography

Abstract: An experimental and theoretical study of the propagation and stability of long nonlinear internal waves over slope-shelf topography is presented. A generalised Korteweg-de Vries (KdV) equation, including the effects of nonlinearity, dispersion, dissipation and varying bottom topography, is formulated and solved numerically for single and rank-ordered pairs of solitary waves incident on the slope. The results of corresponding laboratory experiments in a salt-stratified system are reported. Very good agreement between theory and experiment is obtained for a range of stratifications, topography and incident-wave amplitudes. Significant disagreement is found in some cases if the effects of dissipation and higher-order (cubic) nonlinearity are not included in the theoretical model. Weak shearing and strong breaking (overturning) instabilities are observed and found to depend strongly on the incident-wave amplitude and the stratification on the shelf. In some cases the instability of the lowest-mode wave leads to the generation of a second-mode solitary wave. The application of these findings to the prediction and interpretation of field data is discussed.

Heating of the solar corona by the resonant absorption of Alfven waves

Abstract: An improved method for calculating the resonance absorption heating rate is discussed and the results are compared with observations in the solar corona. The primary conclusion to be drawn from these calculations is that to the level of the approximation adopted, the observations of the heating rate and nonthermal line broadening in the solar corona are consistent with heating by the resonance absorption mechanism.

On the Behavior of Hydromagnetic Surface Waves

Abstract: The behavior of velocity, magnetic field, and pressure perturbations about a continuously varying interface in pressure equilibrium is investigated in detail within ideal incompressible magnetohydrodynamics. A specific initial value problem is solved in quadrature for a thin interface and compared with the solution for a discontinuous interface. The unattenuated surface wave about a discontinuous interface is replaced at a thin interface by a collective surface disturbance which decays, with the associated energy density flowing into local oscillations within the interface. At long times the envelope of the local oscillations is concentrated within a small fraction of the thin interface (gradients within the envelope increase linearly with time, eventually resulting in a breakdown of the linearized ideal theory). Thus, the derived decay rate of the surface disturbance gives a mode-conversion rate rather than a heating rate. In applications to the propagation and dissipation of surface waves in the solar corona, this rate cannot in general be interpreted as a coronal heating rate.

Direct and inverse scattering in the time domain for a dissipative wave equation. II. Simultaneous reconstruction of dissipation and phase velocity profiles

Abstract: The one‐dimensional inverse scattering problem for inhomogeneous lossy media is considered. The model problem involves electromagnetic wave propagation in a medium of unknown thickness with spatially varying conductivity and permittivity. Two inversion algorithms are developed in the time domain using data obtained from normally incident plane waves. These algorithms utilize reflection data from both sides of the medium, and one of them also uses transmission data. These algorithms are implemented numerically on several examples, one of which includes the effects of noisy data. The possibility of using one‐sided reflection data and no transmission data is reviewed and analyzed.

Application of the Wigner–Ville Distribution to Temperature Gradient Microstructure: A New Technique to Study Small-Scale Variations

Abstract: The Wigner–Ville distribution, a new tool in the time–frequency analysis of signals, is applied to temperature gradient microstructure records. In particular, the Wigner–Ville distribution is used to compute the local instantaneous and maximum frequencies of the signal as a function of depth, and these frequencies are then related to the dissipation of turbulent kinetic energy. The method is applied to two temperature gradient microstructure records from the Wellington Reservoir. It is shown that a high resolution estimate of the dissipation is obtained that provides insight into the patchiness, the wavenumber content, and the Reynolds–Froude number variability of the integral scales of motion in a strongly stratified water column.

The dissipation of kinetic energy in a warm‐core ring

Abstract: Profiles of the rate of viscous dissipation of kinetic energy in a Gulf Stream warm-core ring show large rates in the thermocline and in the entrainment region near the edge of the ring. The thermostad has very low levels of dissipation except where that region is in contact with the Gulf Stream. Dissipation rates in the thermocline are independent of the large scale vertical shear and are consistent with the concept of near-inertial wave trapping by the ring's geostrophic shear. Near the edge, to depths of 1000 m, turbulence is associated with entrainment and interleaving. The e-fold decay scale for the dissipation of the ring's total energy is 2 to 3 years, but is only 140 days for the kinetic energy, so energy conversion from potential to kinetic must be occurring on time scales of 10 to 30 days. The vertical eddy diffusivity of the ring is 0.1 × 10−4 m2/s except in the thermostad where it is smaller by approximately a factor of 10. The eddy viscosity is more than 10 × 10−4 m2/s; hence tubulent diffusion is relaxing the velocity field faster than the thermal field.

An analysis of the role of drift waves in equatorial spread F

Abstract: An account is given of results of rocket measurements of the wave number spectrum of equatorial spread F irregularities, with emphasis on wavelengths less than 100 m. The measurements were made from two sounding rockets launched from Peru as part of Project Condor. The Condor density fluctuation spectra display a break at a wavelength near 100 m, identical to that found in the PLUMEX experiment (Kelley et al., 1982). The Condor data also confirm a subrange in which the density and the wave potential obey the Boltzmann relation - a strong indication of the presence of low-frequency electrostatic waves with finite wavelength parallel to the magnetic field, perhaps low-frequency drift waves as proposed by Kelley et al. The Condor data are also consistent with the previous conjecture that drift waves only exist above 300 km altitude. To investigate the difference in spectra observed over two altitude ranges, the data must be fitted to a form for the power spectrum taken from Keskinen and Ossakow (1981). The fitted spectrum, along with empirically determined growth and dissipation rates, is used to calculate the energy pumped into the spectrum at long wavelengths as well as the energy dissipated at shorter wavelengths. It is found that the energy is balanced by classical collisional effects in the low-altitude case, but energy balance in the high-altitude case requires an enhanced dissipation of about 500 times that due to classical diffusion. The model is consistent with, but does not uniquely imply, an inverse cascade of drift wave turbulence in equatorial spread F.

Statistical properties and correlation functions for drift waves

Abstract: The dissipative one-field drift wave equation is solved using the pseudospectral method to generate steady-state fluctuations. The fluctuations are analyzed in terms of space-time correlation functions and modal probability distributions. Nearly Gaussian statistics and exponential decay of the two-time correlation functions occur in the presence of electron dissipation, while in the absence of electron dissipation long-lived vortical structures occur. Formulas from renormalized, Markovianized statistical turbulence theory are given in a local approximation to interpret the dissipative turbulence.

Quantum tunneling, dissipation, and fluctuations.

Abstract: A theory of quantum tunneling with dissipation is constructed. The frequency-dependent transmission coefficient is calculated at zero and finite temperatures. A fluctuation-dissipation theorem for tunneling particles is derived.

Effects of a radial electric field on tokamak edge turbulence

Abstract: Turbulence associated with sheared radial electric fields such as those arising in tokamak edge plasmas is investigated analytically Two driving mechanisms are considered: in the region of maximum vorticity (maximum electric field shear), the electric field is the dominant driving mechanism Away from the maximum, turbulence is driven by the density gradient In the latter case, previous work is extended to include the effects of the electric field on the spatial scales of density correlation in the frequency‐Doppler‐shifted, density‐gradient‐driven turbulence For radial‐electric‐field‐driven turbulence, the effects of magnetic shear on linear instability and on fully developed turbulence are examined In the case of weak magnetic shear, saturation occurs through an enstrophy cascade process which couples regions of driving and dissipation in wavenumber space For stronger magnetic shear, such that the width of the dissipation region resulting from parallel resistivity is comparable to the radial electric field scale length, saturation occurs through nonlinear broadening of the mode structure, which pushes enstrophy into the region of dissipation Estimates of mode widths, fluctuation levels, and scalings are obtained for both mechanisms Comparison is made with the results of fluctuation measurements in the TEXT tokamak [Phys Fluids 27, 2956 (1984)]

A Gaussian wave packet method for studying time dependent quantum mechanics in a curve crossing system: Low energy motion, tunneling, and thermal dissipation

Abstract: We explore numerically the behavior of a method of describing the time dependent quantum mechanics of a curve crossing system. The two nuclear wave functions corresponding to the two electronic states are each described by a Gaussian wave packet. The packet describing the incident state mimics the initial wave function, and the other packet is created by the time dependent Schrodinger equation. They are both propagated by using a variational method. The packets interact and we do not assume that they have a small width. Exploratory calculations are made for curve crossing dynamics at low kinetic energy above the barrier of the lowest adiabatic state, for tunneling, for multiple crossings, and for a curve crossing system which is strongly coupled to a harmonic bath whose motion is described by a mean trajectory classical Langevin method.

Anisotropy of the temperature dissipation in a turbulent wake

Abstract: Measurements by Freymuth & Uberoi (1971) of the terms in the transport equation for the temperature variance in a plane turbulent wake indicated approximate equality for the three components of the temperature dissipation, thus indicating isotropy for that quantity. This result was in sufficient disagreement with the results obtained in several other turbulent shear flows to warrant further measurements of the temperature dissipation in the wake. The present measurements indicate that the dissipation is larger than the isotropic value by about 50 % near the wake centreline and nearly 100 % near the region of maximum production. The magnitude of this ratio is similar to that obtained in other turbulent shear flows. The present measured ratio of total dissipation to isotropic dissipation leads to a satisfactory closure of the temperature variance budget for our experiments and also for the plane-wake measurements of Fabris (1974). It is concluded that the temperature dissipation is not isotropic.

On the simulation of thermo-mechanical forming processes

Abstract: A formulation for elastic-plastic constitutive equations is given based on principles of continuum thermo-mechanics and thermodynamics. Energy dissipation and phase changes are included in the mathematical model. It is shown that kinematic hardening can be described properly for large deformations, by a two-fractions model. A mixed Eulerian-Lagrangian finite element method has been developed by which nodal point locations may be adapted independently of the material displacement. Numerical problems, due to large distortions of elements, as may occur in the case of an Updated Lagrangian method, can be avoided, movement of (free) surfaces can be taken into account by adapting nodal surface point locations in a way that they remain on the moving surface. Local and weighed global smoothing are introduced in order to avoid numerical instabilities. Applications are shown by simulations of an upsetting process, a wire drawing process and a steel quenching process. The results of the simulation of the upsetting process show satisfactory agreement with the results of an experiment carried out.

The evolution of resonant water-wave oscillations

Abstract: This paper is concerned with the evolution of small-amplitude, long-wavelength, resonantly forced oscillations of a liquid in a tank of finite length. It is shown that the surface motion is governed by a forced Korteweg—de Vries equation. Numerical integration indicates that the motion does not evolve to a periodic steady state unless there is dissipation in the system. When there is no dissipation there are cycles of growth and decay reminiscent of Fermi–Pasta–Ulam recurrence. The experiments of Chester & Bones (1968) show that for certain frequencies more than one periodic solution is possible. We illustrate the evolution of two such solutions for the fundamental resonance frequency.

Tidal dissipation in a viscoelastic planet

Abstract: Tidal dissipation is examined using Maxwell standard liner solid (SLS), and Kelvin-Voigt models, and viscosity parameters are derived from the models that yield the amount of dissipation previously calculated for a moon model with QW = 100 in a hypothetical orbit closer to the earth The relevance of these models is then assessed for simulating planetary tidal responses Viscosities of 10 exp 14 and 10 ex 18 Pa s for the Kelvin-Voigt and Maxwell rheologies, respectively, are needed to match the dissipation rate calculated using the Q approach with a quality factor = 100 The SLS model requires a short time viscosity of 3 x 10 exp 17 Pa s to match the Q = 100 dissipation rate independent of the model's relaxation strength Since Q = 100 is considered a representative value for the interiors of terrestrial planets, it is proposed that derived viscosities should characterize planetary materials However, it is shown that neither the Kelvin-Voigt nor the SLS models simulate the behavior of real planetary materials on long time scales The Maxwell model, by contrast, behaves realistically on both long and short time scales The inferred Maxwell viscosity, corresponding to the time scale of days, is several times smaller than the longer time scale (greater than or equal to 10 exp 14 years) viscosity of the earth's mantle

The hydrodynamics of rotating superfluids. II. Finite temperature, dissipative theory

Abstract: The hydrodynamics of rotating superfluids at finite temperature is formulated, accounting for the elastic properties of the vortex lattice. This theory, which is a generalization of previous work at zero temperature, includes normal fluid motions and dissipation and is used here to investigate the transverse and longitudinal normal modes of the system. Mutual friction, arising microscopically from collisions between the vortex lines and the excitations comprising the normal fluid, leads to a profound change in the nature of the two transverse modes allowed at finite temperatures. One such mode, similar to the Tkachenko mode in zero-temperature theory, is associated with the motion of the total mass current and is damped by first viscosity but unaffected by mutual friction. The other mode, associated with the relative motion of the normal and superfluid-vortex components, is highly damped by mutual friction and cannot propagate at angles greater than a critical angle ϑ c measured from the rotation axis.

Energy dissipation mechanism of the optically excited molecules in solvents: A trajectory study for a photoisomerization process of the π‐conjugated molecule in Ar and water

Abstract: The energy dissipation mechanism of an optically excited molecule in solution is studied by using a classical molecular dynamics (MD) calculation. We chose ethylene in Ar or water as a model system and perform the MD calculation to analyze the solvent response to the optically excited ethylene motions that are large in magnitude and high in frequency. It is found that the energy dissipation is very fast; it is in the order of a picosecond in water and of a few to a few tens of picoseconds in Ar. The energy decay rate strongly depends on each ethylene mode and on the nature of solvent–solvent interaction. Due to the characteristic form of water–water interaction, that is strong and sensitive to the mutual geometrical changes, a large water kinetic fluctuation occurs. The ethylene motions couple to this water fluctuation efficiently transferring the ethylene energy to the water libration energy, that is immediately distributed into the various inter‐ and intrawater modes. A multistep collision process leading the energy flow from the ethylene internal vibration→the ethylene rotation→the solvent molecule motion, not accounted for in the gas‐like models such as isolated binary collision model, is a pathway for the fast energy dissipation in Ar and water. We also employ a simple model of an oscillator in Ar to make a detail analysis of the energy decay mechanism, especially of its dependence on the oscillator amplitude, the solvent–solvent interaction, and the solvent density.

Wave energy dissipation in arbitrarily shaped harbours of variable depth

Abstract: A finite element model for combined refraction-diffraction problems of linear water waves has been extended to include the effect of various dissipative mechanisms on wave excitation response in harbours of arbitrary shape and variable depth. Especially, the effects of bottom friction, partial absorption along the harbour, contours, and transmission through permeable breakwaters have been considered. Although, within the mild slope approximation, the model is valid for arbitrary wave lengths, in this paper its effectiveness for harbour design applications is demonstrated for long wave induced resonance phenomena. For this purpose a realistic harbour geometry has been selected. A hydraulic scale-model of this harbour enabled experimental verification of the computational results.

Escape over a potential barrier: The activation rate in bistable systems

Abstract: The classical noise activated equilibration process for a particle moving in a metastable potential well is considered as an eigenproblem. The smallest nonzero real eigenvalue of Kramers' Fokker-Planck model is evaluated analytically by means of Rayleigh's quotient. The treatment allows both for asymmetry in the bistable potential and for arbitrary frictional dissipation. For weak damping the reaction rate tends to zero and depends on both initial and final states.

Second-order modeling of near-wall turbulence

Abstract: A new model form of the wall‐proximity effect on the pressure‐strain correlation term is carefully derived based on realizability. All other models used in this paper also satisfy realizability. As a test flow for a complete set of second‐order realizable models, the turbulent boundary layer with zero‐pressure gradient was calculated. Numerical solutions of the mean velocity, component energies, shear stress, and dissipation of the turbulence energy are obtained, which are in excellent agreement with experiment.

Spacecraft nutational instability prediction by energy-dissipation measurements

Abstract: Nutational divergence of a spinning spacecraft was studied experimentally and later compard with flight data. Laboratory measurements of liquid energy dissipation in model tanks, with and without propellant management devices, were performed during forced precession of the tanks. Results were used to predict divergence time constants via the energy sink approach and were compared to time constants obtained from flight data. Agreement within 21% was obtained, considered very good since the energy sink approach was used for an exceptionally high liquid-fraction spacecaft. By contrast, analytical estimates were in error by one to three orders of magnitude. Time constants were also compared to drop tests with excellent agreement. Data encompass three designs of propellant management devices and several parameter variations for each design.