Spectral Distribution Of Kinetic Energy Research Articles

Entropy and Information causality in Entrepreneurship

Entrepreneurship begins with a conviction in an opportunity belief, formed by available information, and an elementary quantity of action put in to pursue that opportunity. The study of entrepreneurship involves the exploration of the process and motion driven by the spectral distribution of kinetic energy in an irreversible path. The distribution of energy, over the course of time, leads to irreversible actions with an increase of the total entropy into a stable distribution. Entrepreneurs are preoccupied with many activities. Some activities are distracting leading to wasted motion and heat while some are productive and purposeful activities. They must prioritize and distribute their kinetic energy towards purposeful endeavours seduced by the profits and benefits in the perceived opportunities. In the state of maximum entropy, with disorderliness and in state of disequilibrium, entrepreneurs need to guess the preferred pathway with the best probability of success to undertake.

Observing Mesospheric Turbulence With Specular Meteor Radars: A Novel Method for Estimating Second‐Order Statistics of Wind Velocity

There are few observational techniques for measuring the distribution of kinetic energy within the mesosphere with a wide range of spatial and temporal scales. This study describes a method for estimating the three‐dimensional mesospheric wind field correlation function from specular meteor trail echoes. Each radar echo provides a measurement of a one‐dimensional projection of the wind velocity vector at a randomly sampled point in space and time. The method relies on using pairs of such measurements to estimate the correlation function of the wind with different spatial and temporal lags. The method is demonstrated using a multistatic meteor radar data set that includes ≈105 meteor echoes observed during a 24‐hr time period. The new method is found to be in good agreement with the well‐established technique for estimating horizontal mean winds. High‐resolution correlation functions with temporal, horizontal, and vertical lags are also estimated from the data. The temporal correlation function is used to retrieve the kinetic energy spectrum, which includes the semidiurnal mode and a 3‐hr period wave. The horizontal and vertical correlation functions of the wind are then used to derive second‐order structure functions, which are found to be compatible with the Kolmogorov prediction for spectral distribution of kinetic energy in the turbulent inertial range. The presented method can be used to extend the capabilities of specular meteor radars. It is relatively flexible and has a multitude of applications beyond what has been shown in this study.

Investigation of spectrum characteristics of the vortex cascades in shear flow

The spectral distribution of kinetic energy of the vortex cascade in an unstable shear flow of an ideal compressible gas is presented. It has been proved that Kolmogorov's law −5/3 is satisfied for the developed turbulent flows.

On the spectral distribution of kinetic energy in large-scale atmospheric flow

Abstract. A one-dimensional form of the equation of motion with forcing and dissipation is formulated in the spectral domain and used to make long term integrations from which the spectral distribution of the kinetic energy is determined The forcing in the wave number domain is determined in advance and kept constant for the duration of the time integrations. The dissipation is proportional to the second derivative of the velocity. The applied equation is made non-dimensional by selecting a length scale from which the time scale and the velocity scale may be determined. The resulting equation contains no parameters apart from the forcing. The integrations use a large number of spectral components and no approximation is made with respect to the non-linear interaction among the spectral components. Starting from an initial state in which all the velocity components are set to zero the equation is integrated for a long time to see if it reaches a steady state. The spectral distribution of the kinetic energy is determined in the steady state, and it is found that the distribution, in agreement with observational studies, may be approximated by a power law of the form n-3 within certain wave number regions. The wave numbers for which the -3 power law applies is found between the region of maximum forcing and the dissipation range. The intensity of the maximum forcing is varied to see how the resulting steady state varies. In addition, the maximum number of spectral components is varied. However, the available computing power sets an upper limit to the number of components.

Spatial scales of surface wind observations and analysed wind fields over the North Atlantic Ocean

It is well known that spatial scales of oceanic eddies are smaller than scales of atmospheric eddies. Since the spectral distribution of kinetic energy of atmospheric eddies may influence the properties of wind driven oceanic eddies, an excellent resolution of small scale variability of wind fields used as input fields of coupled models of atmosphere and ocean is necessary. Analysis of spatial scales of atmospheric fields is done in terms of spectral energy densities. These are determined in two different ways: directly from objectively analysed fields or by using spatial correlation functions of direct observations averaged for 20 km × 20 km boxes. In the spectral range of wavelengths of less than 1000 km spectral energy densities of analysed fields have lost about 15 to 50% of the variance compared to direct observations. A considerable part of this loss of the variance depends on smoothing done by interpolation schemes themselves. Concerning problems of air-sea interaction care should be taken also to avoid that systematic errors of analysed wind fields lead to systematic errors in turbulent exchange. It is shown that high observed wind speeds are considerably underestimated in analysed fields of numerical models of weather prediction.

On the effects of horizontal resolution and diffusion in a two-layer general circulation model with a zonally symmetric forcing

The general circulation of a two-layer spectral model with a simple symmetrical forcing is determined from long-term integrations. It is found that the zonal as well as the meridional mean flow is clearly influenced by the horizontal resolution of the model. Related to that, it is also found that the meridional eddy transport of momentum is increased significantly by an increase of the horizontal resolution. As a main result of the present study, it is demonstrated, that the response of the model to an increase of the horizontal resolution can also be obtained to a considerable extent by using a suitable, strongly scale-dependent, linear diffusion in the model. Considering especially the spectral distribution of kinetic energy, it is found that an increase of the horizontal resolution as well as the use of a selective horizontal diffusion on the smaller scales results in a significant increase of the eddy kinetic energy on the large scales connected with an enhancement of the baroclinicity of the zonal mean flow. As to be expected, the effect of increasing horizontal resolution or the scale selective diffusion is also to decrease the kinetic energy on the smaller scales, with the result that the energy spectrum is approaching a – 3-power law for a wider range of wavenumbers. DOI: 10.1034/j.1600-0870.1990.t01-4-00003.x

A numerical forecast of fluid motion in a rotating tank and a study of how finite-difference approximations affect non-linear interactions

Using observational data of the fluid motion in a laboratory experiment with a rotating tank numerical forecasts with three different models were made. The Ekman friction waa taken into account. The forecaats were verified statistically and the results for the different models were compared.
 An investigation of the effect of observational errors was made and it was found that errors in the initial field do not affect the prediction severely.
 The spectral distribution of kinetic energy in the forecast data and the verification data were compared. Systematic differences between observed and forecast distributions stimulated a study of the effect of finite differences on non-linear interactions. A theoretical discussion shows that when finite differences are applied to the nonlinear vorticity equation a leakage of energy from the long waves to the shortest ones occurs.
 To test this conclusion a numerical forecast was made with three different grid intervals, as well as a forecast of the Fourier components of the field of motion.
 Finally, it is discussed how the fictitious flow of energy may give rise to the special kind of computational instability that Phillips has investigated.

EQUATIONS GOVERNING THE ENERGETICS OF THE LARGER SCALES OF ATMOSPHERIC TURBULENCE IN THE DOMAIN OF WAVE NUMBER

Abstract By considering the Fourier analysis of the planetary field of motion in the atmosphere, it is possible to define “scales” of motion and to write equations which govern the behavior of these separate scales of motion. Specifically, equations for the rate of change of the kinetic and available potential energy of a disturbance of a given wave number are presented. Such equations, which include the effects of the generation and release of potential energy, friction, and the transfer of energy among the various scales of eddies and the mean flow, can serve as a basis for studying the day-to-day variations of the spectral distribution of kinetic energy and for computing the “steady-state” atmospheric energy cycle in the domain of wave number, with the use of daily hemispheric data.

On the Changes in the Spectral Distribution of Kinetic Energy for Twodimensional, Nondivergent Flow

On the Changes in the Spectral Distribution of Kinetic Energy for Twodimensional, Nondivergent Flow

On the Changes in the Spectral Distribution of Kinetic Energy for Twodimensional, Nondivergent Flow

Total kinetic energy as well as total vorticity squared are integral quantitics which cannot change in the course of time in a twodimensional flow of a homogeneous, nondivergent, and inviscid fluid when the fluid is isolated from the surroundings. The case is considered where the fluid is defined over the total region of thc surface of a sphere. The nature of the changes in time of the spectral distribution of kinetic energy is discussed on the basis of the two conservation requirements mentioned above. It is found that only fractions of the initial energy can flow into sniallcr scales and that a greater fraction simultaneously has to flow to components with larger scales. The upper limits to the flow of kinetic energy into components with scales less than a given one are found. The conservation theorems are also used to discuss the stability of a certain stationary flow for a twodimensional motion which is not necessarily spherical. It is shown how important it is for the proof of stability that not only the kinetic energy of the disturbance is supposed to be small but also its vorticities.In chapter II molecular viscosity is taken into account for the spherical flow. Finally some conclusive remarks are offered regarding the fundamental difference between twoand threedimentional flow.