scholarly journals On the meaning of mixing efficiency for buoyancy-driven mixing in stratified turbulent flows

2015 ◽  
Vol 781 ◽  
pp. 261-275 ◽  
Author(s):  
Megan S. Davies Wykes ◽  
Graham O. Hughes ◽  
Stuart B. Dalziel
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Turbulent Flows ◽  
Density Profile ◽  
Direct Conversion ◽  
Density Field ◽  
Gravitational Potential Energy ◽  
Mixing Efficiency ◽  
Local Flow ◽  
Available Potential Energy

The concept of a mixing efficiency is widely used to relate the amount of irreversible diabatic mixing in a stratified flow to the amount of energy available to support mixing. This common measure of mixing in a flow is based on the change in the background potential energy, which is the minimum gravitational potential energy of the fluid that can be achieved by an adiabatic rearrangement of the instantaneous density field. However, this paper highlights examples of mixing that is primarily ‘buoyancy-driven’ (i.e. energy is released to the flow predominantly from a source of available potential energy) to demonstrate that the mixing efficiency depends not only on the specific characteristics of the turbulence in the region of the flow that is mixing, but also on the density profile in regions remote from where mixing physically occurs. We show that this behaviour is due to the irreversible and direct conversion of available potential energy into background potential energy in those remote regions (a mechanism not previously described). This process (here termed ‘relabelling’) occurs without requiring either a local flow or local mixing, or any other process that affects the internal energy of that fluid. Relabelling is caused by initially available potential energy, associated with identifiable parcels of fluid, becoming dynamically inaccessible to the flow due to mixing elsewhere. These results have wider relevance to characterising mixing in stratified turbulent flows, including those involving an external supply of kinetic energy.

Linking surface enthalpy fluxes to the forces driving the secondary circulation: towards a causal theory of tropical cyclone intensification

2020 ◽  
Author(s):  
Remi Tailleux ◽  
Bethan Harris ◽  
Christopher Holloway ◽  
Pier-Luigi Vidale
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Power Input ◽  
Causal Theory ◽  
Density Field ◽  
Secondary Circulation ◽  
Reference State ◽  
Available Potential Energy ◽  
Available Energy ◽  
Surface Enthalpy

<p>While it is well accepted that tropical cyclones (TCs) derive their energy from surface enthalpy fluxes over the ocean, there is still little understanding of the precise causes and effects by which the latter ends up as TC vortex kinetic energy. For example, Potential Intensity (PI) theory, which has been so far the main framework for predicting TC intensities, assumes a balance between the Carnot power input and the kinetic energy dissipated by surface friction, but says nothing of the detailed physical processes linking the two. A similar criticism pertains to the WISHE (Wind Induced Surface Heat Exchange) theory. To achieve a causal theory of TC intensification, the main difficulty is in linking the power input to kinetic energy production, rather than kinetic energy dissipation. Because kinetic energy is produced at the expense of available potential energy (APE), APE theory is arguably the most promising candidate framework for achieving a causal theory of TC intensification. However, in its current form, the usefulness of APE theory appears to be limited in a number of ways because of its reliance on a notional reference state of rest. First, APE production associated with standard reference states (i.e., horizontally averaged density field, density field of initial sounding, adiabatically sorted states, ...) is usually found to systematically overestimate the kinetic energy actually produced in ideal TC simulations, similarly as the Carnot theory of heat engines; moreover, the standard APE is only connected to vertical buoyancy forces, but says nothing of the radial forces required to drive the secondary circulation. To address these shortcomings, this work presents a new theory of available energy (AE) that is based on the use of an axisymmetric vortex reference state in gradient wind balance. This theory possesses the following advantages over previous frameworks:</p><p> </p><ul><li>The available energy (AE) thus constructed possesses both a mechanical and thermodynamic component. The thermodynamic component is analogous to the well-known Slantwise Convective Available Potential Energy (SCAPE), whereas the mechanical component is proportional to the anomalous azimuthal kinetic energy;</li> <li>The rate of AE production by surface enthalpy fluxes is found to be a very accurate predictor of the amount of potential energy actually converted into kinetic energy in idealised TC simulations based on the Rotunno and Emanuel (1986) axisymmetric model, although a few exceptions are found for cold SSTs;</li> <li>In addition to the expected thermodynamic efficiencies, the production term for AE also involves mechanical efficiencies predicting the fraction of the sinks/sources of angular momentum creating/destroying AE;</li> <li>The AE is related to a generalised buoyancy/inertial force that has both vertical and horizontal components; at low levels, such a generalised force has radially inward and vertically upward components, as required to drive the expected secondary circulation.</li> </ul><p>The new theory, therefore, appears to possess all the ingredients to form the basis for a causal theory of TC intensification.</p>

Diagnosing mixing in stratified turbulent flows with a locally defined available potential energy

2014 ◽  
Vol 740 ◽  
pp. 114-135 ◽  
Author(s):  
Alberto Scotti ◽  
Brian White
Keyword(s):  
Potential Energy ◽  
Turbulent Flows ◽  
Boussinesq Approximation ◽  
Mixing Efficiency ◽  
Available Potential Energy ◽  
Energy Cycle ◽  
Lorenz Energy Cycle ◽  
The Mean ◽  
Definition Of ◽  
Special Circumstances

AbstractA local available potential energy (APE) density useful as suitable diagnostic tool in turbulent stratified flows is considered under the Boussinesq approximation. The local APE is positive, and in the limit of infinitesimal perturbation from an equilibrium state recovers the Lorenz energy cycle definition of APE. In a turbulent stratified flow, the APE can be Reynolds-decomposed into non-trivial mean and turbulent components, which are connected to the mean and turbulent kinetic energy by suitably defined fluxes. We show that the turbulent buoyancy flux $\overline{w'b'}$ and the rate of production of turbulent APE coincide only under very special circumstances. The framework is applied to derive some global bounds on the mixing efficiency of some representative flows.

scholarly journals Biases in Thorpe-Scale Estimates of Turbulence Dissipation. Part II: Energetics Arguments and Turbulence Simulations

2015 ◽  
Vol 45 (10) ◽  
pp. 2522-2543 ◽  
Author(s):  
Alberto Scotti
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Turbulent Flows ◽  
Companion Paper ◽  
Mean Flow ◽  
Available Potential Energy ◽  
Ozmidov Scale ◽  
Thorpe Scale ◽  
The Mean ◽  
Shear Driven Flows

AbstractThis paper uses the energetics framework developed by Scotti and White to provide a critical assessment of the widely used Thorpe-scale method, which is used to estimate dissipation and mixing rates in stratified turbulent flows from density measurements along vertical profiles. This study shows that the relevant displacement scale in general is not the rms value of the Thorpe displacement. Rather, the displacement field must be Reynolds decomposed to separate the mean from the turbulent component, and it is the turbulent component that ought to be used to diagnose mixing and dissipation. In general, the energetics of mixing in an overall stably stratified flow involves potentially complex exchanges among the available potential energy and kinetic energy associated with the mean and turbulent components of the flow. The author considers two limiting cases: shear-driven mixing, where mixing comes at the expense of the mean kinetic energy of the flow, and convective-driven mixing, which taps the available potential energy of the mean flow to drive mixing. In shear-driven flows, the rms of the Thorpe displacement, known as the Thorpe scale is shown to be equivalent to the turbulent component of the displacement. In this case, the Thorpe scale approximates the Ozmidov scale, or, which is the same, the Thorpe scale is the appropriate scale to diagnose mixing and dissipation. However, when mixing is driven by the available potential energy of the mean flow (convective-driven mixing), this study shows that the Thorpe scale is (much) larger than the Ozmidov scale. Using the rms of the Thorpe displacement overestimates dissipation and mixing, since the amount of turbulent available potential energy (measured by the turbulent displacement) is only a fraction of the total available potential energy (measured by the Thorpe scale). Corrective measures are discussed that can be used to diagnose mixing from knowledge of the Thorpe displacement. In a companion paper, Mater et al. analyze field data and show that the Thorpe scale can indeed be much larger than the Ozmidov scale.

Energetics and mixing in buoyancy-driven near-bottom stratified flow

2019 ◽  
Vol 869 ◽  
pp. 214-237
Author(s):  
Pranav Puthan ◽  
Masoud Jalali ◽  
Vamsi K. Chalamalla ◽  
Sutanu Sarkar
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Energy Loss ◽  
Convective Instability ◽  
Mixing Efficiency ◽  
Time Interval ◽  
Mean Flow ◽  
Available Potential Energy ◽  
Long Time ◽  
The Mean

Turbulence and mixing in a near-bottom convectively driven flow are examined by numerical simulations of a model problem: a statically unstable disturbance at a slope with inclination $\unicode[STIX]{x1D6FD}$ in a stable background with buoyancy frequency $N$ . The influence of slope angle and initial disturbance amplitude are quantified in a parametric study. The flow evolution involves energy exchange between four energy reservoirs, namely the mean and turbulent components of kinetic energy (KE) and available potential energy (APE). In contrast to the zero-slope case where the mean flow is negligible, the presence of a slope leads to a current that oscillates with $\unicode[STIX]{x1D714}=N\sin \unicode[STIX]{x1D6FD}$ and qualitatively changes the subsequent evolution of the initial density disturbance. The frequency, $N\sin \unicode[STIX]{x1D6FD}$ , and the initial speed of the current are predicted using linear theory. The energy transfer in the sloping cases is dominated by an oscillatory exchange between mean APE and mean KE with a transfer to turbulence at specific phases. In all simulated cases, the positive buoyancy flux during episodes of convective instability at the zero-velocity phase is the dominant contributor to turbulent kinetic energy (TKE) although the shear production becomes increasingly important with increasing  $\unicode[STIX]{x1D6FD}$ . Energy that initially resides wholly in mean available potential energy is lost through conversion to turbulence and the subsequent dissipation of TKE and turbulent available potential energy. A key result is that, in contrast to the explosive loss of energy during the initial convective instability in the non-sloping case, the sloping cases exhibit a more gradual energy loss that is sustained over a long time interval. The slope-parallel oscillation introduces a new flow time scale $T=2\unicode[STIX]{x03C0}/(N\sin \unicode[STIX]{x1D6FD})$ and, consequently, the fraction of initial APE that is converted to turbulence during convective instability progressively decreases with increasing $\unicode[STIX]{x1D6FD}$ . For moderate slopes with $\unicode[STIX]{x1D6FD}<10^{\circ }$ , most of the net energy loss takes place during an initial, short ( $Nt\approx 20$ ) interval with periodic convective overturns. For steeper slopes, most of the energy loss takes place during a later, long ( $Nt>100$ ) interval when both shear and convective instability occur, and the energy loss rate is approximately constant. The mixing efficiency during the initial period dominated by convectively driven turbulence is found to be substantially higher (exceeds 0.5) than the widely used value of 0.2. The mixing efficiency at long time in the present problem of a convective overturn at a boundary varies between 0.24 and 0.3.

Tracker-assisted modelling: simultaneous validation of the conservation law of energy and the work-energy theorem

2021 ◽  
Vol 57 (1) ◽  
pp. 015012
Author(s):  
Unofre B Pili ◽  
Renante R Violanda
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Conservation Law ◽  
Gravitational Potential Energy ◽  
Time Data ◽  
Home Based ◽  
Basic Physics ◽  
Free Falling ◽  
Work Done

Abstract The video of a free-falling object was analysed in Tracker in order to extract the position and time data. On the basis of these data, the velocity, gravitational potential energy, kinetic energy, and the work done by gravity were obtained. These led to a rather simultaneous validation of the conservation law of energy and the work–energy theorem. The superimposed plots of the kinetic energy, gravitational potential energy, and the total energy as respective functions of time and position demonstrate energy conservation quite well. The same results were observed from the plots of the potential energy against the kinetic energy. On the other hand, the work–energy theorem has emerged from the plot of the total work-done against the change in kinetic energy. Because of the accessibility of the setup, the current work is seen as suitable for a home-based activity, during these times of the pandemic in particular in which online learning has remained to be the format in some countries. With the guidance of a teacher, online or face-to-face, students in their junior or senior high school—as well as for those who are enrolled in basic physics in college—will be able to benefit from this work.

Study of the Mechanisms of Vortex Variability in the Lofoten Basin Based on the Energy Analysis

2021 ◽  
Vol 37 (3) ◽  
Author(s):  
V. S. Travkin ◽  
◽  
T. V. Belonenko ◽  
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Baroclinic Instability ◽  
Positive Trend ◽  
Barotropic Instability ◽  
Available Potential Energy ◽  
Conversion Rates ◽  
Order Of Magnitude ◽  
The Mean ◽  
Mean Kinetic Energy

Purpose. The Lofoten Basin is one of the most energetic zones of the World Ocean characterized by high activity of mesoscale eddies. The study is aimed at analyzing different components of general energy in the basin, namely the mean kinetic and vortex kinetic energy calculated using the integral of the volume of available potential and kinetic energy of the Lofoten Vortex, as well as variability of these characteristics. Methods and Results. GLORYS12V1 reanalysis data for the period 2010–2018 were used. The mean kinetic energy and the eddy kinetic one were analyzed; and as for the Lofoten Vortex, its volume available potential and kinetic energy were studied. The mesoscale activity of eddies in winter is higher than in summer. Evolution of the available potential energy and kinetic energy of the Lofoten Vortex up to the 1000 m horizon was studied. It is shown that the vortex available potential energy exceeds the kinetic one by an order of magnitude, and there is a positive trend with the coefficient 0,23⋅1015 J/year. It was found that in the Lofoten Basin, the intermediate layer from 600 to 900 m made the largest contribution to the potential energy, whereas the 0–400 m layer – to kinetic energy. The conversion rates of the mean kinetic energy into the vortex kinetic one and the mean available potential energy into the vortex available potential one (barotropic and baroclinic instability) were analyzed. It is shown that the first type of transformation dominates in summer, while the second one is characterized by its increase in winter. Conclusions. The vertical profile shows that the kinetic energy of eddies in winter is higher than in summer. The available potential energy of a vortex is by an order of magnitude greater than the kinetic energy. An increase in the available potential energy is confirmed by a significant positive trend and by a decrease in the vortex Burger number. The graphs of the barotropic instability conversion rate demonstrate the multidirectional flows in the vortex zone with the dipole structure observed in a winter period, and the tripole one – in summer. The barotropic instability highest intensity is observed in summer. The baroclinic instability is characterized by intensification of the regime in winter that is associated with weakening of stratification in this period owing to winter convection.

scholarly journals Walking in simulated reduced gravity: mechanical energy fluctuations and exchange

1999 ◽  
Vol 86 (1) ◽  
pp. 383-390 ◽  
Author(s):  
Timothy M. Griffin ◽  
Neil A. Tolani ◽  
Rodger Kram
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Inverted Pendulum ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Metabolic Cost ◽  
Metabolic Energy ◽  
Gravitational Potential Energy ◽  
Reduced Gravity

Walking humans conserve mechanical and, presumably, metabolic energy with an inverted pendulum-like exchange of gravitational potential energy and horizontal kinetic energy. Walking in simulated reduced gravity involves a relatively high metabolic cost, suggesting that the inverted-pendulum mechanism is disrupted because of a mismatch of potential and kinetic energy. We tested this hypothesis by measuring the fluctuations and exchange of mechanical energy of the center of mass at different combinations of velocity and simulated reduced gravity. Subjects walked with smaller fluctuations in horizontal velocity in lower gravity, such that the ratio of horizontal kinetic to gravitational potential energy fluctuations remained constant over a fourfold change in gravity. The amount of exchange, or percent recovery, at 1.00 m/s was not significantly different at 1.00, 0.75, and 0.50 G (average 64.4%), although it decreased to 48% at 0.25 G. As a result, the amount of work performed on the center of mass does not explain the relatively high metabolic cost of walking in simulated reduced gravity.

scholarly journals Feedback of outflows in the Taurus Molecular Cloud

2012 ◽  
Vol 8 (S292) ◽  
pp. 47-47
Author(s):  
Huixian Li ◽  
Di Li ◽  
Rendong Nan
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Molecular Cloud ◽  
Feedback Effect ◽  
Total Kinetic Energy ◽  
Gravitational Potential Energy ◽  
Taurus Molecular Cloud

AbstractWe collected 27 outflows from the literature and found 8 new ones in the FCRAO CO maps of the Taurus molecular cloud. The total kinetic energy of the 35 outflows is found to be about 3% of the gravitational potential energy from the whole cloud. The feedback effect due to the outflows is minor in Taurus.

scholarly journals Rapidly rotating strange stars

2000 ◽  
Vol 177 ◽  
pp. 661-662 ◽  
Author(s):  
D. Gondek-Rosińska ◽  
P. Haensel ◽  
J. L. Zdunik ◽  
E. Gourgoulhon
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Quark Mass ◽  
Strange Quark ◽  
Gravitational Potential Energy ◽  
Rapid Rotation ◽  
Strange Stars ◽  
Absolute Value ◽  
Strange Quark Mass ◽  
Global Parameters

AbstractWe study effects of the strange quark mass,ms, and of the QCD interactions, calculated to lowest order inαc, on the rapid rotation of strange stars (SS). The influence of rotation on global parameters of SS is greater than in the case of the neutron stars (NS). We show that independently ofmsandαcthe ratio of the rotational kinetic energy to the absolute value of the gravitational potential energyT/Wfor a rotating SS is significantly higher than for an ordinary NS. This might indicate that rapidly rotating SS could be important sources of gravitational waves.

scholarly journals Differential Rotation and the v sin i Parameter

2004 ◽  
Vol 215 ◽  
pp. 21-22 ◽  
Author(s):  
J. Zorec ◽  
A. Domiciano de Souza ◽  
Y. Frémat
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Line Width ◽  
Differential Rotation ◽  
Rotation Velocity ◽  
Rigid Rotation ◽  
Gravitational Potential Energy ◽  
Aspect Angle ◽  
Energy Ratios

We study the effects of a differential rotation upon the determination of the v sin i parameter. The effects are studied for several values of the ratio t = kinetic energy/gravitational potential energy, which include energy ratios higher than permitted for critical rigid rotation and using an internal conservative rotation law that allows for a latitudinal differential rotation in the stellar surface. Two effects are outstanding: when differential rotation is dependent on the stellar latitude the v sin i parameter does not necessarily correspond to the equatorial rotation velocity; the line width is a double valued function of v sin i and it is dependent on t and the aspect angle i.

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