The Generalized Energy Equation and Instability in the Two-layer Barotropic Vortex

The linear two-layer barotropic primitive equations in cylindrical coordinates are used to derive a gen- eralized energy equation, which is subsequently applied to explain the instability of the spiral wave in the model. In the two-layer model, there are not only the generalized barotropic instability and the super high- speed instability, but also some other new instabilities, which fall into the range of the Kelvin-Helmholtz instability and the generalized baroclinic instability, when the upper and lower basic flows are different. They are perhaps the mechanisms of the generation of spiral cloud bands in tropical cyclones as well.

ON THE ENERGY EQUATION FOR A SPATIALLY DEVELOPING INSTABILITY WAVE IN THE THEORY OF HYDRODYNAMIC STABILITY

In this article,it is shown that the energy equation for a spatially developing disturbance used in all the literatures dealing with the problem of hydrodynamic stability suffers from a small,but crucial error.

Estimation of Thermal Pollution Using Numerical Simulation of Energy Equation Coupled with Viscous Burgers’ Equation

In this paper, we implement energy equation coupled with viscous Burgers’ equation as a mathematical model for the estimation of thermal pollution of river water. The model is a nonlinear system of partial differential equations (PDEs) that read as an initial and boundary value problem (IBVP). For the numerical solution of the IBVP, we investigate an explicit second-order Lax- Wendroff type scheme for nonlinear parabolic PDEs. We present the numerical solutions graphically as a temperature profile, which shows good qualitative agreement with natural phenomena of heat transfer. We estimate the thermal pollution of water caused by industrialization on the bank of a river.

Tiêu Equation Experimentation of Understanding by Energy Transfer Quantum Mechanics

Background: The Tiêu equation has a ground roots approach to the process of Quantum Biology and goes deeper through the incorporation of Quantum Mechanics. The process can be measured in plant, animal, and human usage through a variety of experimental or testing forms. Animal studies were conducted for which, in the first day of the study all the animals consistently gained dramatic weight, even as a toxic substance was introduced as described in the introduction of the paper to harm animal subjects which induced weight loss through toxicity. Tests can be made by incorporating blood report results. Human patients were also observed to show improvement to their health as administration of the substance was introduced to the biological mechanism and plants were initially exposed to the substance to observe results. This is consistent with the Tiêu equation which provides that wave function is created as the introduction of the substance to the biological mechanism which supports Quantum Mechanics. The Tiêu equation demonstrates that Quantum Mechanics moves a particle by temperature producing energy thru the blood-brain barrier for example. Methods: The methods for the Tiêu equation incorporate animal studies to include the substance administered through laboratory standards using Good Laboratory Practices under Title 40 C.F.R. § 158. Human patients were treated with the substance by medical professionals who are experts in their field and have knowledge to the response of patients. Plant applications were acquired for observation and guidance of ongoing experiments of animals’ representative for the biologics mechanism. Results: The animal studies along with patient blood testing results have been an impressive line that has followed the Tiêu equation to consistently show improvement in the introduction of the innovation to biologic mechanisms. The mechanism responds to the substance by producing energy to the mechanism with efficient effect. For plant observations, plant organisms responded, and were seen as showing improvement thru visual observation.

The mechanical energy equation for total flow in open channels

The mechanical energy equation is a fundamental equation of a 1-D mathematical model in Hydraulics and Engineering Fluid Mechanics. This equation for the total flow used to be deduced by extending the Bernoulli＇s equation for the ideal fluid in the streamline to a stream tube, and then revised by considering the viscous effect and integrated on the cross section. This derivation is not rigorous and the effect of turbulence is not considered. In this paper, the energy equation for the total flow is derived by using the Navier-Stokes equations in Fluid Mechanics, the results are as follows：（1） A new energy equation for steady channel flows of incompressible homogeneous liquid is obtained, which includes the variation of the turbulent kinetic energy along the channel, the formula for the mechanical energy loss of the total flow can be determined directly in the deduction process.（2） The theoretical solution of the velocity field for laminar flows in a rectangular open channel is obtained and the mechanical energy loss in the energy equation is calculated. The variations of the coefficient of the mechanical energy loss against the Reynolds number and the width-depth ratio are obtained.（3） The turbulent flow in a rectangular open channel is simulated using 3-D Reynolds averaged equations closed by the Reynolds stress model（RSM）, and the variations of the coefficient of the mechanical energy loss against the Reynolds number and the width-depth ratio are discussed.

A Conservative Lagrangian Scheme for Solving Compressible Fluid Flows with Multiple Internal Energy Equations

Lagrangianmethods arewidely used inmany fields formulti-material compressible flow simulations such as in astrophysics and inertial confinement fusion(ICF),due to their distinguished advantage in capturing material interfaces automatically.In some of these applications,multiple internal energy equations such as those for electron,ion and radiation are involved.In the past decades,several staggeredgrid based Lagrangian schemes have been developed which are designed to solve the internal energy equation directly.These schemes can be easily extended to solve problems with multiple internal energy equations.However such schemes are typically not conservative for the total energy.Recently,significant progress has been made in developing cell-centered Lagrangian schemes which have several good properties such as conservation for all the conserved variables and easiness for remapping.However,these schemes are commonly designed to solve the Euler equations in the form of the total energy,therefore they cannot be directly applied to the solution of either the single internal energy equation or the multiple internal energy equations without significant modifications.Such modifications,if not designed carefully,may lead to the loss of some of the nice properties of the original schemes such as conservation of the total energy.In this paper,we establish an equivalency relationship between the cell-centered discretizations of the Euler equations in the forms of the total energy and of the internal energy.By a carefully designed modification in the implementation,the cell-centered Lagrangian scheme can be used to solve the compressible fluid flow with one or multiple internal energy equations and meanwhile it does not lose its total energy conservation property.An advantage of this approach is that it can be easily applied to many existing large application codes which are based on the framework of solving multiple internal energy equations.Several two dimensional numerical examples for both Euler equations and three-temperature hydrodynamic equations in cylindrical coordinates are presented to demonstrate the performance of the scheme in terms of symmetry preserving,accuracy and non-oscillatory performance.

ENERGY EQUATION AND SYMMETRIC INSTABILITY CRITERION

In this paper,by using generalized normal mode method the symmetric instability criterion which can be used not only in the constant parameters but also in the variable parameters was derived from the energy equation on the symmetric disturbance.If the thermal wind was in balance or quasi-balance,the criterion was consistent with that ob- tained by Emanuel with parcel method and Hoskins with normal mode method.It is shown that in the generating stage of disturbance,the symmetrically instable development of disturbance is associated with the energy transformation by which the energy of the basic field is transferred into the energy of the disturbance field.

Modelling Wave Transmission and Overtopping Based on Energy Balance Equation

Wave transmission and overtopping around nearshore breakwaters can have significant influence on the transmitted wave parameters,which affects wave conditions and sediment transportation and becomes the focus of design in engineering.The objective of this paper is to present a simplified model to estimate these important wave parameters.This paper describes the incorporation of wave transmission and overtopping module into a wave model for multi-directional random wave transformation based on energy balance equation with the consideration of wave shoaling,refraction,diffraction,reflection and breaking.Wen's frequency spectrum and non-linear dispersion relation are also included in this model.The influence of wave parameters of transmitted waves through a smooth submerged breakwater has been considered in this model with an improved description of the transmitted wave spectrum of van der Meer et al.(2000) by Carevic et al.(2013).This improved wave model has been validated through available laboratory experiments.Then the verified model is applied to investigate the effect of wave transmission and overtopping on wave heights behind low-crested breakwaters in a project for nearshore area.Numerical calculations are carried out with and without consideration of the wave transmission and overtopping,and comparison of them indicates that there is a considerable difference in wave height and thus it is important to include wave transmission and overtopping in modelling nearshore wave field with the presence of low-crested breakwaters.Therefore,this model can provide a general estimate of the desired wave field parameters,which is adequate for engineers at the preliminary design stage of low-crested breakwaters.

NEW PRINCIPLES OF WORK AND ENERGY AS WELLAS POWER AND ENERGY RATE FORCONTINUUM FIELD THEORIES

New principles of work and energy as well as power and energy rate with cross terms for polar and nonlocal polar continuum field theories were presented and from them all corresponding equations of motion and boundary conditions as well as complete equations of energy and energy rate with the help of generalized Piola's theorems were naturally derived in all and without any additional requirement. Finally, some new balance laws of energy and energy rate for generalized continuum mechanics were established. The new principles of work and energy as well as power and energy rate with cross terms presented in this paper are believed to be new and they have corrected the incompleteness of all existing corresponding principles and laws without cross terms in literatures of generalized continuum field theories.

Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method

The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.

Dark energy from logarithmically modified gravity and deformed Coleman-Weinberg potential

Recent astrophysical measurements strongly suggest the existence of a missing energy component dubbed dark energy that is responsible for the current accelerated expansion of the universe.A new class of modified gravity theory is introduced which yields a universe accelerating in time and dominated by dark energy.The new modified gravity model constructed here concurrently includes a Gauss-Bonnet invariant term,barotropic fluid with a time-dependent equation of state parameter,a Coleman-Weinberg（CW） potential-like expression V（φ） =ξφm lnφn and a new Einstein-Hilbert term f（R,φ） =E（φ） R which depends on both the scalar curvature and the scalar fieldφthrough a generic logarithmic function E（φ） =lnφ.Here m and n take different values from the standard CW potential andξis a real parameter. It was shown that the presence of these terms provides many useful features which are discussed in some detail.

Nonlinear density wave and energy consumption investigation of traffic flow on a curved road

A new car-following model is proposed based on the full velocity difference model（FVDM） taking the influence of the friction coefficient and the road curvature into account. Through the control theory, the stability conditions are obtained,and by using nonlinear analysis, the time-dependent Ginzburg-Landau（TDGL） equation and the modified Korteweg-de Vries（mKdV） equation are derived. Furthermore, the connection between TDGL and mKdV equations is also given. The numerical simulation is consistent with the theoretical analysis. The evolution of a traffic jam and the corresponding energy consumption are explored. The numerical results show that the control scheme is effective not only to suppress the traffic jam but also to reduce the energy consumption.

A numerical study of coupled maps representing energy exchange processes between two environmental interfaces regarded as biophysical complex systems

The field of environmental sciences is abundant with various interfaces and is the right place for the application of new fundamental approaches leading towards a better understanding of environmental phenomena. Following the definition of environmental interface by Mihailovic and Bala? [1], such interface can be, for example, placed between: human or animal bodies and surrounding air, aquatic species and water and air around them, and natural or artificially built surfaces (vegetation, ice, snow, barren soil, water, urban communities) and the atmosphere, cells and surrounding environment, etc. Complex environmental interface systems are (i) open and hierarchically organised (ii) interactions between their constituent parts are nonlinear, and (iii) their interaction with the surrounding environment is noisy. These systems are therefore very sensitive to initial conditions, deterministic external perturbations and random fluctuations always present in nature. The study of noisy non-equilibrium processes is fundamental for modelling the dynamics of environmental interface regarded as biophysical complex system and for understanding the mechanisms of spatio-temporal pattern formation in contemporary environmental sciences. In this paper we will investigate an aspect of dynamics of energy flow based on the energy balance equation. The energy exchange between interacting environmen- tal interfaces regarded as biophysical complex systems can be represented by coupled maps. Therefore, we will numerically investigate coupled maps representing that exchange. In ana- lysis of behaviour of these maps we applied Lyapunov exponent and cross sample entropy.

NEW CONSERVATION LAWS OF ENERGY AND C-D INEQUALITIES IN CONTINUA WITHOUT MICROSTRUCTURE

Fundamental laws and balance equations as well as C-D inequalities in continuum mechanics are carefully restudied, incompleteness of existing balance laws of angular momentum and conservation laws of energy as well as C-D inequalities are pointed out, and finally new and more general conservation laws of energy and corresponding balance equations of energy as well as C-D inequalities in local and nonlocal asymmetric continua are presented.

Asking If the Existence of Vacuum Energy to Keep Computational “Bits” Present at Start of Cosmological Evolution, Even If Spatial Radius Goes to Zero, Not Planck Length, Is Possible

When initial radius Rinitial →0 if Stoica actually presents Einstein equations in a formalism which remove the big bang singularity pathology, then the reason for Planck length no longer holds. We present entanglement entropy in the early universe with a shrinking scale factor, due to Muller and Lousto, and show that there are consequences due to initial entangled SEntropy = 0.3r2h/a2 for a time dependent horizon radius rH = in cosmology, with (flat space conditions) for conformal time. Even if the 3 dimensional spatial length goes to zero, this construction preserves a minimum non-zero L vacuum energy, and in doing so keep the bits, for computational bits cosmological evolution even if Rinitial →0 . We state that the presence of computational bits is necessary for cosmological evolution to commence.

New Planck’s Law

In quantum mechanics, there are two very famous formulas. One is the energy formula of the bose particle, called Planck’s law. The other is the wavelength formula, which is called the de Broy wavelength. According to Einstein’s mass-energy equation, we have studied Planck’s law and De Bloy’s wavelength, and generalized it to the De Bloy’s wavelength formula from low speed to light speed. Then, on this basis, the smallest particle is defined as mass quantum. The new wavelength formula is obtained from the mass quantum and converted into the frequency formula. The generalized Planck’s law is obtained.

Analysis on the Interaction between Turbulence and Secondary Circulation of the Surface Layer at Jinta Oasis in Summer

The kinetic energy variations of mean flow and turbulence at three levels in the surface layer were calculated by using eddy covariance data from observations at Jinta oasis in 2005 summer. It is found that when the mean horizontal flow was stronger, the turbulent kinetic energy was increased at all levels, as well as the downward mean wind at the middle level. Since the mean vertical flow on the top and bottom were both negligible at that time, there was a secondary circulation with convergence in the upper half and divergence in the lower half of the column. After consideration of energy conversion, it was found that the interaction between turbulence and the secondary circulation caused the intensification of each other. The interaction reflected positive feedback between turbulence and the vertical shear of the mean flow. Turbulent sensible and latent heat flux anomaly were also analyzed. The results show that in both daytime and at night, when the surface layer turbulence was intensified as a result of strengthened mean flow, the sensible heat flux was decreased while the latent heat flux was increased. Both anomalous fluxes contributed to the cold island effect and the moisture island effect of the oasis.

Energy and entropy equations in coupled nonequilibrium thermal mechanical diffusive chemical heterogeneous system

In this paper we give an appropriate energy equation considering the diffusion and the energy production contributions of species for a complex coupled system with chemical reaction. It is shown that the contribution of the mass diffusion on the internal energy is the same whether it is introduced by the mass flow through the outer boundary or by the inner chemical reaction. In addition, the diffusion is a purely irreversible process and does not produce reversible entropy or entropy flow. Based on this theory a new entropy production rate equation is derived for the coupled thermal diffusive chemical heterogeneous system. The evolution equations of the heat conduction and the mass diffusion derived from this theory are fully consistent with the Fourier and Fick＇s laws.

Density enhancement mechanism of upwind schemes for low Mach number flows

Many all-speed Roe schemes have been proposed to improve performance in terms of low speeds. Among them, the F-Roe and T-D-Roe schemes have been found to get incorrect density fluctuation in low Mach flows, which is expected to be with the square of Mach number. Asymptotic analysis presents the mechanism of how the density fluctuation problem relates to the incorrect order of terms in the energy equation paU△U. It is known that changing the upwind scheme coefficients of the pressure-difference dissipation term DP and the velocity-difference dissipation term in the momentum equation DPU to the order of O （c- 1） and O（c0） can improve the level of pressure and velocity accuracy at low speeds. This paper shows that corresponding changes in energy equation can also improve the density accuracy in low speeds. We apply this modification to a recently proposed scheme, TV-MAS, to get a new scheme, TV-MAS2. Unsteady Gresho vortex flow, double shear-layer flow, low Mach number flows over the inviscid cylinder, and NACA0012 airfoil show that energy equation modification in these schemes can obtain the expected square Ma scaling of density fluctuations, which is in good agreement with corresponding asymptotic analysis. Therefore, this density correction is expected to be widely implemented into allspeed compressible flow solvers.

Simulation of Non-Isothermal Turbulent Flows Through Circular Rings of Steel

This article is intended to examine the fluid flow patterns and heat transfer in a rectangular channel embedded with three semi-circular cylinders comprised of steel at the boundaries.Such an organization is used to generate the heat exchangers with tube and shell because of the production of more turbulence due to zigzag path which is in favor of rapid heat transformation.Because of little maintenance,the heat exchanger of such type is extensively used.Here,we generate simulation of flow and heat transfer using nonisothermal flow interface in the Comsol multiphysics 5.4 which executes the Reynolds averaged Navier stokes equation(RANS)model of the turbulent flow together with heat equation.Simulation is tested with Prandtl number(Pr=0.7)with inlet velocity magnitude in the range from 1 to 2 m/sec which generates the Reynolds number in the range of 2.2×10^(5) to 4.4×10^(5) with turbulence kinetic energy and the dissipation rate in ranges(3.75×10^(−3) to 1.5×10^(−2))and(3.73×10^(−3)−3×10^(−2))respectively.Two correlations available in the literature are used in order to check validity.The results are displayed through streamlines,surface plots,contour plots,isothermal lines,and graphs.It is concluded that by retaining such an arrangement a quick distribution of the temperature over the domain can be seen and also the velocity magnitude is increasing from 333.15%to a maximum of 514%.The temperature at the middle shows the consistency in value but declines immediately at the end.This process becomes faster with the decrease in inlet velocity magnitude.