Showing papers on "Dissipation published in 1973"

Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP)

Abstract: "Wave spectra were measured along a profile extending 160 kilometers into the North Sea westward from Sylt for a period often weeks in 1968 and 1969. During the main experiment in July 1969, thirteen wave stations were in operation, of which six stations continued measurements into the first two weeks of August. A smaller pilot experiment was carried out in September 1968. Currents, tides, air-sea temperature differences and turbulence in the atmospheric boundary layer were also measured. The goal of the experiment (described in Part 1) was to determine the structure of the source function governing the energy balance of the wave spectrum, with particular emphasis on wave growth under stationary offshore wind conditions (Part 2) and the attenuation of swell in water of finite depth (Part 3). The source functions of wave spectra generated by offshore winds exhibit a characteristic plus-minus signature associated with the shift of the sharp spectral peak towards lower frequencies. The two-lobed distribution of the source function can be explained quantitatively by the nonlinear transfer due to resonant wave-wave interactions (second order Bragg scattering). The evolution of a pronounced peak and its shift towards lower frequencies can also be understood as a selfstabilizing feature of this process. For small fetches, the principal energy balance is between the input by wind in the central region of the spectrum and the nonlinear transfer of energy away from this region to short waves, where it is dissipated, and to longer waves. Most of the wave growth on the forward face of the spectrum can be attributed to the nonlinear transfer to longer waves. For short fetches, approximately (80 ± 20) % of the momentum transferred across the air/sea interface enters the wave field, in agreement with Dobson's direct measurements of the work done on the waves by surface pressures. About 80-90 % of the wave-induced momentum flux passes into currents via the nonlinear transfer to short waves and subsequent dissipation; the rest remains in the wave field and is advected away. At larger fetches the interpretation of the energy balance becomes more ambiguous on account of the unknown dissipation in the low-frequency part of the spectrum. Zero dissipation in this frequency range yields a minimal atmospheric momentum flux into the wave field of the order of (10 to 40) % of the total momentum transfer across the air-sea interface -- but ratios up to 100 % are conceivable if dissipation is important. In general, the ratios (as inferred from the nonlinear energy transfer) lie within these limits over a wide (five-decade) range of fetches encompassing both wave-tank and the present field data, suggesting that the scales of the spectrum continually adjust such that the wave-wave interactions just balance the energy input from the wind. This may explain, among other features, the observed decrease of Phillips' "constant" with fetch. The decay rates determined for incoming swell varied considerably, but energy attenuation factors of two along the length of the profile were typical. This is in order of magnitude agreement with expected damping rates due to bottom friction. However, the strong tidal modulation predicted by theory for the case of a quadratic bottom friction law was not observed. Adverse winds did not affect the decay rate. Computations also rule out wave-wave interactions or dissipation due to turbulence outside the bottom boundary layer as effective mechanisms of swell attenuation. We conclude that either the generally accepted friction law needs to be significantly modified or that some other mechanism, such as scattering by bottom irregularities, is the cause of the attenuation. The dispersion characteristics of the swells indicated rather nearby origins, for which the classical (i event model was generally inapplicable. A strong Doppler modulation by tidal currents was also observed.

The weak friction approximation and tidal evolution in close binary systems

Abstract: The aim of this paper is to study the dynamical problem of tidal friction in a binary system consisting of deformable components, with the restriction that the angle of lag or advance of the tidal distortion with respect to the direction of the disturbing companion is small. The fractional distortion of the bodies due to rotation and tidal interaction is also treated as a first-order small quantity, and terms up to the fourth harmonic in the tidal potential are retained. In this linear approximation, the time-dependent tidal potential can be Fourier decomposed into a spectrum of simple harmonic terms, each of which is responsible for raising a ‘partial wave’ in the body; each such partial wave can then be treated independently of the others. This is the method first employed by Darwin. In Section 2, it is assumed that the phase lag in the response of the body (due to dissipation of kinetic energy of deformation) is proportional to the forcing frequency, which is justified for small amplitude oscillations of a viscous fluid or visco-elastic body. A simple expression is then obtained for the potential function for the distortion in terms of the disturbing potential and the structure of the body. In Section 3, the distortion potential function is employed in deriving the componentsR, S andW of the disturbing force which are then substituted in the Gaussian form of the equations for variation of the elements. In Section 4, the Eulerian equations for motion of deformable bodies are derived, using the so-called ‘mean axes’ of the body as the rotating axes of reference. In Section 5, it is shown that the dynamical effects of rotational distortion occur on a much shorter time scale than those arising from tidal friction, which allows one to consider the two phenomena as acting independently of one another. The collected set of Gaussian (orbital) and Eulerian (body) equations is re-written in terms of dimensionless variables for the tidal friction case, and the stability of the system is examined on the basis of these equations. In Section 6, the tidal friction equations are integrated numerically for the close binary system AG Persei and for the Earth-Moon system. In the former, the integrations were started from a highly elliptical orbit and the system was found to relax into a circular orbit, with synchronous rotation perpendicular to the orbit. In the latter, the integrations were performed backwards in time from the present day, and it was found that the lunar orbit rapidly becomes highly elliptical at the time of closest approach, thus indicating a probable capture of the Moon by the Earth. This result is in agreement with that obtained by other investigators; however, it is shown that the detailed behaviour of the system at the time of capture, in particular the inclination of the lunar orbit to the ecliptic, depends critically on the chosen rate of dissipation in the Moon's interior. A simple argument is presented which allows an estimation for the mean viscosity of a fluid body from the known age of the system: for the components of AG per, the result is 2×1011 g cm−1 s−1, indicating that the stars must have possessed turbulent convective outer regions during some part of their tidal evolution, while for the Earth, the result, is 1.4×1012 g cm−1 s−1. It is shown that the angle of tidal lag in nonsynchronous close binary systems in general is expected to be extremely small, and not observationally detectable.

Observations of a Stationary Mountain Wave and its Associated Momentum Flux and Energy Dissipation

Abstract: Analysis is presented of data obtained from instrumented aircraft flying in a mountain wave of moderate amplitude west of Denver, Colo., on 17 February 1970. Emphasis is placed on determination of the downward flux of westerly momentum generated by the wave, for which accurate measurements of vertical velocities on scales of order 50 km are essential. Three different methods are applied and compared: direct aircraft measurement, using vanes and an inertial platform; evaluation from the steady-state equation for conservation of potential temperature; and integration of the steady-state continuity equation. Each method produces errors, but by combining the results of the three methods a profile is obtained which agrees. fairly well with a steady-state theoretical prediction. An important side result is the discovery that gust-probe equipment is apparently not necessary for the direct aircraft measurement of wave momentum flux, but an inertial platform or similarly stable attitude reference level is...

The damping of surface gravity waves in a bounded liquid

Abstract: In deducing the viscous damping rate in surface waves confined by side walls, Ursell found in an example that two different calculations, one by energy dissipation within and the other by pressure working on the edge of the side-wall boundary layers, gave different answers. This discrepancy occurs in other examples also and is resolved here by examining the energy transfer in the neighbourhood of the free-surface meniscus. With due care near the meniscus a boundary-layer–Poincare method is employed to give an alternative derivation for the rate of attenuation and to obtain in addition the frequency (or wave-number) shift due to viscosity. Surface tension is not considered.

Energy and plane waves in linear viscoelastic media

Abstract: The mathematical framework for describing plane waves in elastic and linear anelastic media is presented. Theoretical results suggest that the nature of plane waves in anelastic materials is distinctly different from the nature of plane waves in elastic materials. In elastic media the only type of inhomogeneous plane wave (P or S) that can propagate is one for which planes of constant phase are perpendicular to planes of constant amplitude. However, in anelastic media this is the only type of inhomogeneous wave that cannot propagate. For an inhomogeneous P or S plane wave the particle motion is elliptical, the velocity is less than that of a corresponding homogeneous wave, the maximum attenuation is greater than that of a corresponding homogeneous wave, and the direction of maximum energy flow is not the direction of phase propagation. Expressions for the energy flux, energy densities, dissipated energy, stored energy, and Q−1 are derived from an explicit energy conservation relation, valid for an arbitrary steady state viscoelastic radiation field. Each energy expression is valid for homogeneous or inhomogeneous P or S plane waves in elastic or linear anelastic media.

Damping of Water Waves Over Porous Bed

Abstract: Based on linearized Navier-Stokes equations and Darcy’s equations, the viscous damping of small amplitude surface waves over a permeable bed is reexamined. Boundary layer approximation is employed in order to solve the velocity field and pressure field. Demanding that the net dissipation per period must be balanced by the slow decay of wave energy, the damping rate is found. The shortcomings of previous works are examined and are improved. Theory agrees fairly well with the experimental results.

Deformation and striation of plasma clouds in the ionosphere: 2. Numerical simulation of a nonlinear two-dimensional model

Abstract: We present and solve numerically a coupled pair of nonlinear partial differential equations that describe the self-consistent evolution transverse to the magnetic field of plasma clouds artificially formed in the ionosphere. This model assumes that the height-integrated Pedersen conductivity of the cloud dominates the ionospheric contribution and that the cloud is sufficiently high so that κi = Ωi/νin ≫ 1. Several initial states are examined, and many features of field observations of recent barium releases are obtained: early time elongations in the E × B direction (due to convection and not diffusion), backside steepening, slower frontside motion, and striations or development of fingerlike sheets of plasma structure on the backside with a long-time tendency to fission into rods. The onset time for striations is a complicated function of the shape of the cloud, the intensity, the structure, and the location of the initial perturbation and the underlying dissipation.

Global stability of time-dependent flows: impulsively heated or cooled fluid layers

Abstract: The method of energy is used to discuss the stability of time-dependent diffusive temperature profiles in fluid layers subject to impulsive changes in surface temperature.Bounds for the ratio of disturbance energy production to dissipation are found to be parametric functions of time because the basic temperature develops through diffusion. This time dependence leads to the demarcation of regions of stability in a Rayleigh number-time plane and the interpretation of these regions is given. Numerical results are presented for the cases of impulsive heating and cooling of initialty isothermal fluid layers. New global stability results which give the Rayleigh number below which the diffusive solution to the Boussinesq equations is unique are reported for these cases.

Theoretical Analysis for a Damping Ratio of a Jointed Cantibeam

Abstract: The loss energy of a jointed cantibeam may be derived from a microscopic slip and a normal pressure on the interfaces. It is however very difficult to calculate theoretically the energy dissipation between the joint surfaces, because a characteristic of the micro-slip on the interfaces has not been fully clarified yet.In this study the mechanism of the energy dissipation and also the ways of theoretically calculating the damping ratio of the jointed cantibeam have been investigated by considering experimental results of the characteristic of static micro-slip between the jointed surfaces.From the results it is clarified that the damping ratio of the jointed cantibeam can be well calculated by using the equations proposed in this paper, and how the characteristic of micro-slip influences the behaviours of the damping ratio.

Stability of Hydromagnetic Thermoconvective Flow Through Porous Medium

Abstract: The stability of the onset of thermal convection of a conducting viscous fluid in a porous medium has been investigated using the linear (normal mode technique) and the non-linear (energy) stability theories. Both the theories show that the stability region is increased to the maximum extent when the usual viscous dissipation is also present in addition to the dissipation due to Darcy's resistance and Joule heating.

The Coupling of the Core to the Precession of the Earth

Abstract: The core follows the precession of the mantle by virtue of coupling to it. A simple model is presented which allows quantitative consideration of a superposition of both inertial and dissipative (electromagnetic) coupling torques. With the preferred value of the dissipative coupling coefficient, the dissipative mechanism accounts for only 2 or 3 per cent of the precessional coupling torque, but the dissipation amounts to about 3 times 10 Watts, which may suffice for a geomagnetic dynamo driven by precession. The dissipation itself is only weakly dependent upon the coupling coefficient and no assumption can lead to dissipation exceeding 10 W. This is much smaller than the loss of rotational energy by tidal friction; also it is hardly a significant contribution to the total core‐tomantle heat flux if we suppose that an adiabatic temperature gradient is maintained in the core, thus supporting the contention that the core contains potassium with a radioactive heat generation of order 10 W. Motion of the core is found to contribute to the semi‐annual terms of precession and nutation.

The Dissipation of Excess Heat from Water Systems

Abstract: A model for the prediction of excess temperature is shown to have the form of the classical diffusion equation. The excess temperature in this model is defined as the difference between the actual water temperature and the water temperature which would have occurred provided that a particular heat source, such as a power plant, had never existed. This definition of excess temperature is convenient because it directly represents the incremental effect that a heat source has on a water system and, provided that historical water temperature records are available, the excess temperature can be predicted without the use of solar or atmospheric radiation data. A prediction equation for the surface transfer coefficient for excess heat illustrates that this coefficient is primarily dependent upon the water temperature and wind speed, and that it is almost independent of the humidity and temperature of the air.

Coalescence in a weakly turbulent cloud

Abstract: In a recent paper on the effect of turbulence on droplet collisions in clouds, Woods, Drake and Goldsmith (1972) proposed that the principal factor was the strong spectral peak of shear near the Kolmogoroff micro-scale. This hypothesis led to an important simplification, namely that spatial and temporal fluctuations in the turbulent shear field could be ignored during an encounter between a pair of cloud droplets. However, the authors pointed out that their simple model of (isotropic, homogeneous) turbulence contained an assumption, namely that the shears are normally distributed, which would have to be re-examined if it turned out that droplet collision efficiency increased rapidly after a threshold value is exceeded. Subsequent measurements by Jonas and Goldsmith (1972) showed that this is indeed the case. In this paper we reconsider the efficiency of turbulent coalescence in the light of the new experimental data, and taking account of the intermittency of shear distribution. It is concluded that significant increases of collection efficiency will occur in clouds which are only weakly turbulent. For example, the collection efficiency for droplets of radii R = 20 μm and γ = 9 μm in a cloud with energy dissipation rate e = 55·5 cm2 s−3 will be approximately 14 per cent compared with 2 per cent for the same droplets falling though still air. The shear zone in the wind tunnel experiment designed by Woods et al. (1972) is a realistic approximation to the shear zones in cloud turbulence.

The Dynamic Response of Columns Under Short Duration Axial Loads

Abstract: Coupled nonlinear equations of motion in the axial and transverse directions are derived for a column under dynamic end load. Material dissipation is included by employing a Kelvin model for the material behavior. The dynamic response of the column in the presence of small transverse perturbations is investigated for short duration of axial loads. For certain geometric configurations, the inclusion of axial inertia permits parametric resonance of transverse modes due to the transient axial motion after the load is removed. The parametric effects are studied in detail. It is found that the usual simplified theory which neglects axial inertia adequately describes the column response provided the material dissipation is sufficiently large and/or the duration of loading is sufficiently long. For given dissipation parametric excitation becomes important as the load duration decreases. It becomes the dominant effect for very short duration loads.

Design of a high-performance 1024-B switched capacitor p-channel IGFET memory chip

Abstract: IGFET switched-capacitor memory cells are incorporated into a fully decoded dynamic, 1024-word by 1-b p-channel random-access memory. With 10-V drive circuitry, chip access time is measured to be 150 ns and cycle time is 300 ns. Measured on-chip power dissipation at a 300 ns cycle was less than 80 mW (80 /spl mu/W/b) and is correspondingly lower at lower speeds. Refresh power at 100/spl deg/C is less than 1 /spl mu/W/b.

Entropy changes for steady-state fluctuations

Abstract: The dissipative steady state far from equilibrium and subject to a slow modulation of external parameters is analyzed. It is shown that the time-integrated energy dissipation consists of three terms. The first of these is irreversible and consists of the time-integrated dissipation of the sequence of exact steady states defined by the externally controlled parameters traversed during the modulation. The second term is reversible and reflects the fact that the dissipation of the time-dependent modulated system, as calculated in a macroscopic way from ensemble averages, is not the same as the dissipation of a sequence of exact steady states. The third term is also reversible and relates to the ensemble dispersion in changes in stored energy during the modulation. If the system has a single degree of freedom and narrow fluctuations, then these fluctuations can be characterized by an effective temperature TN. The third term can then be shown to be equal toTN dS, whereS is the entropy calculated from the distribution function by the usual definition.

An Energy Assessment for Liquids in a Filled Precessing Spherical Cavity

Abstract: Experimental results and analytical approximations for energy dissipation due to liquids in a filled precessing spherical cavity are presented. The range of physical parameters include kinematic viscosities from 1 to 1000 centistokes, half coning angles from 5/8 to 10 deg, precession speeds from 0.15 to 200 rpm, and spin speeds (relative to the precessing frame) of from 7.5–900 rpm. These parameters and the associated energy dissipation rates, as low as 10−4 watts, place the results in the region of direct applicability to spinning satellite stability problems. A dimensionless parameter related to an Ekman number is used to correlate energy dissipation rates with laminar, intermediate, and fully turbulent flows. The reduced data are integrated with data from other sources and used to develop equations in dimensionless form for the experimental and analytical results. The results, while not defining details of fluid motion, place experimental bounds on the integrated shear stress at the cavity wall for analytical models.

Dissipation function of a viscoelastic material with temperature‐dependent properties

Abstract: An approximated energy equation is derived with the dissipation function expressed in terms of the loss modulus and the strain components The equation is suitable for the analysis of the thermomechanical behavior of a viscoelastic material subjected to cyclic loadings The material is assumed to be linear, homogeneous, and isotropic Its mechanical properties are temperature dependent and satisfy the time‐temperature equivalence

Measurement techniques for antennas in dissipative media

Abstract: Methods used to simulate dissipative media environments for antennas are reported and special techniques developed to determine the electrical properties of antennas in such media are discussed Tank systems for simulating infinite homogeneous isotropic media characterized by ratios of \alpha/\beta in the range 0 are described along with the apparatus for determining the constitutive parameters \sigma and \epsilon of the media A new device for measuring antenna input admittance is presented which permits a simple measurement of admittance over a broad frequency range where conventional methods are cumbersome in field use Apparatus for measuring antenna current and charge distributions is described together with a discussion of the associated probing errors Measured admittances and current and charge distributions are compared with current theories for thin wire linear and loop antennas in the dissipative media and are found to be in good agreement

On the Explosive Instabilities of Waves in Plasmas with Special Regard to Dissipation and Phase Effects

Abstract: The problem of explosive instability in plasma is studied with particular emphasis on the influence of dissipation and frequency indeterminacy on the dynamic phase-locking in a system of three waves.

Heat transfer in electronic systems with emphasis on asymmetric heating

Abstract: The trend in electronic circuit design is toward increasing power dissipation density. The performance and reliability of increasing number of electronic systems are now seriously threatened by thermal effects, so that it is necessary to reappraise the relevant thermal design procedures. This paper examines natural convection cooling and concerns the prediction of maximum temperatures of electronic cabinets containing arrays of vertically oriented circuit cards with unequal power dissipation levels. By means of a vertical channel model, the effects of channel spacing, channel height, and power dissipation level are assessed with emphasis on asymmetric powering of the channel walls. Methods are indicated for rapid evaluation of maximum temperatures and optimum channel spacing with asymmetric heating. The present results show that asymmetry reduces the thermal performance of the channel. Consequently, the power dissipation on the channel walls should be made nearly equal.

Nonlinear effects in steady supersonic dissipative gasdynamics. Part 2. Three-dimensional axisymmetric flow

Abstract: Steady, supersonic, dissipative, three-dimensional, axisymmetric flow is considered. A system of Burgers-type equations is shown to govern the flow field. In inviscid regions the Whitham theory gives the limiting form. Dissipative effects ultimately engulf the inviscid zone and at sufficiently large distances from the body the flow is governed by linear dissipative theory. The flow field is divided into zones based on the presence or absence of nonlinearity and dissipation. Estimates and criteria which describe the extent of these zones are given.

The Evolution of a Self-Sustained Oscillation in a Nonlinear Continuous System

Abstract: : A gas filled tube has a pressure sensitive heat source at the center, while energy is allowed to radiate from the ends. For a sufficiently large feedback coefficient the system is linearly unstable. Within the nonlinear theory, the self-excited oscillation initially grows until a shock forms. The shock acts as a dissipative mechanism so that a balance is achieved and ultimately a time periodic state is reached. The small amplitude disturbance in the pipe is represented as the superposition of two simple waves traveling in opposite directions, and without interaction. Based on this representation the problem reduces to solving a nonlinear difference equation. (Author)