Production Rate Of Kinetic Energy Research Articles

On Destruction of a Thermally Stable Layer by Compositional Convection in the Earth's Outer Core

We discuss destruction of a thermally stable layer in the upper part of the Earth's outer core by compositional convection excited at the inner core boundary. We propose to use the radial distribution of power induced by thermal and compositional buoyancy (rate of kinetic energy production) as a measure of occurrence of thermal and compositional convection. The power consists of the terms proportional to convective entropy flux and convective compositional flux. In the region with positive power, convection is active because kinetic energy can be produced by buoyancy force, and a stably stratified layer could not be formed there. On the other hand, in the region with negative power, convection is suppressed and a stably stratified layer may be produced. Considering penetration effect of convection, we discuss possible maximum and minimum thicknesses of the stable layer based on the radial distribution of power and its radial integral, respectively. We construct a 1-dimensional thermal and compositional balance model of the Earth's core with a larger value of thermal conductivity recently suggested by high-pressure experiments and first principle calculations, and estimate radial distributions of power for various values of core mantle boundary (CMB) heat flux Q_CMB. When Q_CMB > Q_sCMB no thermally stable layer can exist, where Q_sCMB is conductive heat flux along the adiabat at CMB. On the other hand, when Q_CMB < Q_sCMB, formation of an upper thermally stable layer becomes possible, depending on the extent of penetration of compositional convection excited below. When Q_CMB is sufficiently lower than Q_sCMB, a thermally stable layer survives the maximum penetration of compositional convection. The results show that a thermally stable layer becomes effectively thinner when the effect of compositional convection is considered compared with the results of previous studies where the existence of a stable layer is evaluated based on the convective flux only.

Flow instability in triangular lid-driven cavities with wall motion away from a rectangular corner

The linear stability of the two-dimensional steady flow in an infinite cavity with a right-angled triangular cross-section is investigated numerically by the finite-element method. We consider the case when one of the walls enclosing the right angle moves away from it. Neutral curves, eigenmodes and kinetic-energy production rates are computed. Five different instability modes are found, depending on the aspect ratio, i.e. the length ratio of the walls enclosing the right angle. The spatial structure of the kinetic-energy transfer between the basic flow and the critical modes indicates that three of the critical modes for very shallow cavities are due to an elliptic instability mechanism. Two other critical modes, for moderately shallow to deep cavities, arise due to a centrifugal mechanism. The instabilities found are discussed and compared with those arising in rectangular cavities.

Cyclic Turbulent Instabilities in a Thin Slab Mold. Part II: Mathematical Model

Mathematical simulations are employed to describe short- and large-scale flow distortions observed in a water model of a thin slab mold using a submerged entry nozzle (SEN) located at deep and shallow positions, operating at two casting speeds of 5 and 7 m/min. Two types of meniscus oscillations are identified; the first (high frequencies) has a relatively long life and short length scales, whereas the second (low frequencies) has a short life and its length scales are similar to those length scales in the mold. It was found, by turbulent flow principles, that the high-oscillation frequencies of the discharging jets are the same as those of the oscillating meniscus. Therefore, the discharging jets transfer vibrating momentum, with frequencies of 1.1 to 5 Hz, to the two upper roll flows during long periods of time, inducing those meniscus oscillations. The large-scale and short-life oscillations originate a dynamic distortion of the flow, forming deep meniscus depressions, especially for a casting speed of 7 m/min with the SEN in a shallow position. These dynamic distortions give origin to rotational flows in the lower boundaries of both jets, below the SEN tip, and even in the recirculatory eyes of the upper roll flows. The time scale of low-frequency oscillations agrees with the time scale of the production rate of kinetic energy along the jet’s length. Their origin is linked to a kinetic energy unbalance by the generation of a negative production rate. Because the flow must keep its energy budget, the fluid will transport, through mean convection and pressure–viscous mechanisms, further increases of momentum transfer during a short time, giving place to those dynamic distortions. Because of their large length scale, these dynamic and energetic distortions are the most dangerous to slab quality.

Influence of animals on turbulence in the sea

Analysis of data on the hydrodynamics of swimming by 100 species, ranging in body mass (M) from bacteria to blue whales, leads to a model of animal-induced turbulence in the ocean. Swimming speeds and Reynolds number (Re) are strongly correlated with body mass, both at typical cruising speeds and at escape speeds associated with predator-prey interactions. We find that animals operating at Re > 1000 typically form schools that are concentrated by many orders of magnitude above their average abundance. We calculate the rate of kinetic energy production by 11 representative species of schooling animals ranging in size from euphausiids to whales, and find it to be of the order of 10 -5 W kg -1 , regardless of animal size. Animal-induced turbulence is comparable in magnitude to rates of turbulent energy dissipation (e) that result from major storms. The horizontal length scale (10 to 1000 m) of energy production rate by animal schools is comparable to the observed fine-scale variability in e. We present detailed case studies of 4 species — Atlantic bluefin tuna, Norwegian herring, northern anchovy and Antarctic krill — all of which have schooling behavior that places them within the zone of maximum seasonal stratification where their energy production rate would be 3 to 4 orders of magnitude greater than the background average rate of turbulent energy dissipation. We conclude that schooling animals are an important source of fine-scale turbulent mixing in the ocean, especially in coastal regions during summer.

On the Dynamics and Energy Transformations in Steady-State Hurricanes

A dynamic model of the inflow layer in a steady mature hurricane is evolved, relating wind speed, pressure gradient, surface shearing stress, mass flow, and convergence. The low-level air trajectories are assumed to be logarithmic spirals. With this hypothesis, properties such as maximum wind and central pressure are determined through choice of a parameter depending on the inflow angle: a moderate hurricane arises with inflow angles of about 20°, while 25° gives an intense or extreme storm. Most of this study treats the moderate storm. In order to maintain its core pressure gradients, an oceanic source of sensible and latent heat is required. As a result, latent heat release in the inner hurricane area occurs at higher heat content (warmer moist adiabats) than mean tropical subcloud air. The heat transfer from the ocean and the release of latent heat in the core determine the pressure gradient along the trajectory, and this prescribes the particular trajectory selected by the air among an infinite number available from the logarithmic spiral family. This selection principle is evolved using recent work on “relative stability” of finite amplitude thermal circulations. Of an infinite number of dynamically possible spirals, the one is realized which maximizes the rate of kinetic energy production under the thermodynamic constraints, here formulated in terms of the relation between heat release and pressure gradient. Finally, rainfall, efficiency of work done by the storm, and kinetic energy budgets are examined in an attempt to understand the difference between the hurricane—a rare phenomenon—and the common sub-hurricane tropical storm. DOI: 10.1111/j.2153-3490.1960.tb01279.x

On the Dynamics and Energy Transformations in Steady-State Hurricanes

A dynamic model of the inflow layer in a steady mature hurricane is evolved, relating wind speed, pressure gradient, surface shearing stress, mass flow, and convergence. The low-level air trajectories are assumed to be logarithmic spirals. With this hypothesis, properties such as maximum wind and central pressure are determined through choice of a parameter depending on the inflow angle: a moderate hurricane arises with inflow angles of about 20°, while 25° gives an intense or extreme storm.&#x0D; Most of this study treats the moderate storm. In order to maintain its core pressure gradients, an oceanic source of sensible and latent heat is required. As a result, latent heat release in the inner hurricane area occurs at higher heat content (warmer moist adiabats) than mean tropical subcloud air. The heat transfer from the ocean and the release of latent heat in the core determine the pressure gradient along the trajectory, and this prescribes the particular trajectory selected by the air among an infinite number available from the logarithmic spiral family.&#x0D; This selection principle is evolved using recent work on “relative stability” of finite aniplitude thermal circulations. Of an infinite number of dynamically possible spirals, the one is realized which maximizes the rate of kinetic energy production under the thermodynamic constraints, here formulated in terms of the relation between heat release and pressure gradient.&#x0D; Finally, rainfall, efficiency of work done by the storm, and kinetic energy budgets are examined in an attempt to understand the difference between the hurricane—a rare phenomenon—and the common sub-hurricane tropical storm.