Energy Of Mean Flow Research Articles

Energy Balance in a Turbulent Boundary Layer on a Rough Wall

Measurements of the mean flow and turbulence fields over a two-dimensional roughness reveal a shear stress distribution which is very different from that on a smooth wall. The usual mean flow energy equation fails to close indicating other terms may be important.

Modification of mean flow and turbulent energy by a change in surface roughness under conditions of neutral stability

AbstractA theory is developed which describes the adjustment of the flow of a hydrostatically neutral fluid in the lower portion of a fully‐turbulent boundary layer, after an abrupt change in surface roughness.The model is based on the hypothesis that the horizontal shear stress is proportional to the turbulent energy. The theory postulates that the flow is primarily governed by the dominant terms of the horizontal‐momentum, continuity, and turbulent‐energy equations. The model was solved by numerical techniques on a digital computer.Unlike previous models there are no a priori assumptions about the distribution of velocity or stress, the behaviour of the nondimensional wind shear, mixing length, or momentum‐exchange coefficient in the transition region.The theory, in contrast to earlier theories, suggests the distribution of turbulent energy, as well as velocity. An inflection point is predicted in the transition velocity‐profile. The nondimensional wind shear is found to differ significantly from unity in the transition region. These predictions agree with observation.

On the turbulent heat transfer by free convection from a vertical plate

Until now, the problem on the turbulent heat transfer by free convection has been solved by the profile method whose velocity and temperature profiles are given by experiments. In this paper, shear stress, heat flux, and eddy diffusivity distribution are assumed using the result of forced convection heat transfer, then the coupled partial differential equations for velocity and temperature which are reduced to simpler forms, can be easily solved by the trial and error method. The result can be applied for a wider range of Grashof and Prandtl numbers than that obtained from usual equations. On transition from laminar to turbulent, a certain dimensionless criterion is proposed, which gives the ratio of energy of mean flow and that dispersed near the wall. The same dimensionless value can be applied for both forced and free convection.

Reynolds Stress near a Flexible Surface Responding to Unsteady Airflow

The stability of boundary-layer flows that are formed on flexible surfaces is known to be affected by the surface response. A study of the manner in which energy is exchanged between the mean flow, the perturbation, and the vibrating surface has called for more knowledge of the way in which the Reynolds stress is influenced by wall vibration. The reason is that mean flow energy is transferred to the perturbation by the action of Reynolds stresses, so any change brought about in their level, as a result of surface motion, could influence the energy balance and consequently the stability of the system. An analysis of the Reynolds stresses near a vibrating surface is described and it is shown that they are increased by at least an order of magnitude whenever the surface is allowed to vibrate. [This research has been supported by the David Taylor Model Basin.]

Some Characteristic Features of l3arotropic Disturbances (II)

Kinetic energy exchange between a mean flow and a superposed disturbance in a two dimensional non-divergent fluid is investigated for a special example.It is found that, at initial moment, kinetic energy is transferred from the disturbance to the mean flow, if the mean flow has a scale which is smaller than the scale of the disdisturbance. Kinetic energy is transferred in the opposite direction if the opposite situation occurs.The mean flow kinetic energy reaches an extremum value after time Θ, which is a characteristic quantity, determined by the initial field of the fluid system. After then, the change of the mean flow energy occurs in opposite sense.Earth's rotation has a stabilizing effect in the sense that, it has a tendency to keep the state of the mean flow in the original one.

Statistical Characteristics of the Atmospheric Disturbances

The periods of the atmospheric phenomena are supposed to differ from each other according to their scales, e. g., there may be a positive correlation between the magnitude of scales and length of periods in the atmosphere.The purpose of this paper is to investigate the statistical characteristics of the atmospheric disturbances of various scales and further to find out the mechanism of mutual transfer of vorticity and kinetic energy of mean flow and disturbances. If we succeed in this attempt, the results obtained from are expected to be useful also for such a forecasting problem as numerical prediction. In the present study the following characteristics of the atmospheric phenomena are dealt with, that is, (1) the so-called “width of perturbations ”, (2) the stationarity of variations, (3) the spectral distribution of pressure and (4) the kinetic energy spectra, employing the 36 term harmonic coefficients calculated from the values of 500 mb level along 50°N, 45°N and 30°N latitude circles in the Historical Weather Maps. The periods subjected to analysis are January (1946,1949), May, June and July (1951).The results obtained are as follows. First the component waves of disturbances can be classified into three (or four) parts. Then let n and F(n) denote wave number and spectral function respectively. The motion of waves of small wave number is non-isotropic, oscillatory and moreover F(n)=const. Meanwhile the motion of waves of great wave number is isotropic, progressive and F(n) ∝ n-7/3 as expected. Further it may be concluded that the mean flow and the component waves of n=1,2 belong to the former and component waves of n=≤6 belong to the latter region. Accordingly the components of n=3, 4, 5 are considered to constitute the region of middle wave number in our case.Next, the energy spectra indicate three sources of kinetic energy in the atmosphere, i. e., mean flow, component wave of n=3 and of n=6 or 7.

Momentum and energy diffusion in the turbulent wake of a cylinder

A detailed experimental investigation of the turbulent motion in the wake of a circular cylinder, 0.953 cm. diameter placed in a n air-stream of velocity 1280 cm.sec. -1 , has been carried out with particular reference to those quantities determining the transport of turbulent energy and mean stream momentum. At distances of 80, 120 and 160 diameters down-stream from the cylinder, direct measurements have been made of mean flow velocity, turbulent intensity , viscous dissipation, energy diffusion, scale, and form factors of the velocity components and their spatial derivatives.These observations show that, except close to the wake centre, the flow at a point fixed with respect to the cylinder is only intermittently turbulent, due to the passage of the point of observation through jets or billows of turbulent fluid emitted from the inner wholly turbulent core of the wake. Further consideration of the results indicates that the turbulent motion within the jets is solely responsible for the turbulent transfer of momentum , while diffusion of turbulent energy and of heat is carried out by the bulk movement of the jets. Most probably, the jets are initiated b y local fluctuations of pressure inside the turbulent core, and in the late r stages of their development that are slowed down by adverse pressure gradients. The existence of pressure-velocity correlations of sufficient magnitude is demonstrated by using the equation for the conservation of kinetic energy in the wake, all terms of which are know n excepting the one involving the pressure-velocity correlation, which is the n obtained by difference. While the conception of jets of turbulent fluid is more convenient for following the physical processes in the wake, the alternative but equivalent description that the turbulent motion consists of a motion of scale small compared with the mean flow superimposed on a slower turbulent motion whose scale is large compared with the mean flow may be used. A formal explanation of this two-stage turbulent structure in terms of the Fourier representation of the velocity field is suggested, which relates the structure to the presence of a quasi-constant source of energy of nearly fixed wave-number, and to the free boundary which allows an unlimited range of wave-numbers. It is expected that this type of motion will occur in all systems of turbulent shear flow with a free boundary, such as wakes, jets and boundary layers.

Turbulence and Energy Dissipation

Abstract This paper incorporates a study of the origin and dissipation of turbulence energy which makes possible a better understanding of the mechanics of energy losses that are introduced by various flow-disturbing devices such as expansions, bends, valves, etc. The important parameters which characterize turbulence are the root-mean-square values of the fluctuating velocity components, the length factor proportional to the size of the small eddies responsible for the dissipation of energy, and the length factor proportional to the average size of the eddies. The effect of variation of these parameters on the energy losses occurring in turbulent flow are discussed, and also the change in these parameters in the decaying turbulence beyond turbulence-producing devices is indicated. Data are presented showing the variation in the kinetic energy of mean flow and the turbulence energy in a 15-deg conical divergence. Visual studies of the start of turbulence at rounded entrances to smooth conduits seem to indicate that there is a regular vortex formation at the boundary, and the dispersion of these vortexes into the main fluid stream gradually establishes normal turbulent flow.