Viscous Dissipation Of Kinetic Energy Research Articles

The impact of atmospheric storminess on the sensitivity of Southern Ocean circulation to wind stress changes

The influence of changing the mean wind stress felt by the ocean through alteration of the variability of the atmospheric wind, as opposed to the mean atmospheric wind, on Southern Ocean circulation is investigated using an idealised channel model. Strongly varying atmospheric wind is found to increase the (parameterised) near-surface viscous and diffusive mixing. Analysis of the kinetic energy budget indicates a change in the main energy dissipation mechanism. For constant wind stress, dissipation of the power input by surface wind work is always dominated by bottom kinetic energy dissipation. However, with time-varying atmospheric wind, near surface viscous dissipation of kinetic energy becomes increasingly important as mean wind stress increases. This increased vertical diffusivity leads to thicker mixed layers and higher sensitivity of the residual circulation to increasing wind stress, when compared to equivalent experiments with the same wind stress held constant in time. This may have implications for Southern Ocean circulation in different climate change scenarios should the variability of the atmospheric wind change rather than the mean atmospheric wind.

Analysis of Head Losses in a Turbine Draft Tube by Means of 3D Unsteady Simulations

In this paper, Unsteady RANS (URANS) simulations and Large Eddy Simulations (LES) in the draft tube of a bulb turbine are presented with the objective to understand and locate the head losses in this turbine component. Three operating points of the turbine are considered. Numerical results are compared with experimental velocity measurements for validation. Thanks to a detailed analysis of the energy balance in the draft tube, the physical and hydrodynamic phenomena responsible for head losses in the draft tube are identified. Head losses are due to transfer of mean kinetic energy to the turbulent flow and viscous dissipation of kinetic energy. This occurs mainly in the central vortex structure and next to the walls in the draft tube. Head losses prediction is found to be dependent on the turbulence model used in the simulations, especially in URANS simulations. Using this analysis, the evolution of head losses between the three operating points is understood.

Kinetic energy budgets near the turbulent/nonturbulent interface in jets

The dynamics of the kinetic energy near the turbulent/nonturbulent (T/NT) interface separating the turbulent from the irrotational flow regions is analysed using three direct numerical simulations of turbulent planar jets, with Reynolds numbers based on the Taylor micro-scale across the jet shear layer in the range Reλ ≈ 120–160. Important levels of kinetic energy are already present in the irrotational region near the T/NT interface. The mean pressure and kinetic energy are well described by the Bernoulli equation in this region and agree with recent results obtained from rapid distortion theory in the turbulent region [M. A. C. Teixeira and C. B. da Silva, “Turbulence dynamics near a turbulent/non-turbulent interface,” J. Fluid Mech. 695, 257–287 (2012)]10.1017/jfm.2012.17 while the normal Reynolds stresses agree with the theoretical predictions from Phillips [“The irrotational motion outside a free turbulent boundary,” Proc. Cambridge Philos. Soc. 51, 220 (1955)]10.1017/S0305004100030073. The use of conditional statistics in relation to the distance from the T/NT interface allow a detailed study of the build up of kinetic energy across the T/NT interface, pointing to a very different picture than using classical statistics. Conditional kinetic energy budgets show that apart from the viscous dissipation of kinetic energy, the maximum of all the mechanisms governing the kinetic energy are concentrated in a very narrow region distancing about one to two Taylor micro-scales from the T/NT interface. The (total and fluctuating) kinetic energy starts increasing in the irrotational region by pressure-velocity interactions – a mechanism that can act at distance, and continue to grow by advection (for the total kinetic energy) and turbulent diffusion (for the turbulent kinetic energy) inside the turbulent region. These mechanisms tend to occur preferentially around the core of the large-scale vortices existing near T/NT interface. The production of turbulent kinetic energy then becomes the dominating mechanism and the so called “peak production” is located at about one Taylor micro-scale from the T/NT interface. Simple analytical estimates are given for the peaks of pressure strain, turbulent diffusion, and production near the T/NT interface. The growth of kinetic energy across the T/NT interface is an inertial process, since the viscous terms (diffusion and dissipation) are negligible during this process. The present results highlight the importance of the region near the T/NT interface in the entire jet development.

The role of coherent vortices near the turbulent/non-turbulent interface in a planar jet

The role of coherent vortices near the turbulent/non-turbulent (T/NT) interface in a turbulent plane jet is analysed by a direct numerical simulation (DNS). The coherent vortices near the jet edge consist of large-scale vortical structures (LSVSs) maintained by the mean shear and intense vorticity structures (IVSs) created by the background fluctuating turbulence field. The radius of the LSVS is equal to the Taylor micro-scale R(lsvs)≈λ, while the radius of the IVS is of the order of the Kolmogorov micro-scale R(ivs)~η. The LSVSs are responsible for the observed vorticity jump at the T/NT interface, being of the order of the Taylor micro-scale. The coherent vortices in the proximity of the T/NT interface are preferentially aligned with the tangent to the T/NT interface and are responsible for the viscous dissipation of kinetic energy near the T/NT interface and to the characteristic shape of the enstrophy viscous diffusion observed at that location.

Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets

The invariants of the velocity gradient (R and Q), rate-of-strain (RS and QS), and rate-of-rotation (QW) tensors are analyzed across the turbulent/nonturbulent (T/NT) interface by using a direct numerical simulation (DNS) of a turbulent plane jet at Reλ≈120. The invariants allow a detailed characterization of the dynamics, geometry and topology of the flow during the entrainment. The invariants Q and QS are almost equal and negative outside the turbulent region close to the T/NT interface, which shows the existence of high values of strain product (hence viscous dissipation of kinetic energy) at that location. Right at the T/NT interface, the invariants QW and QS show that virtually all flow points there are characterized by irrotational dissipation, with no discernible sign of the coherent structures which are known to exist deep inside the turbulent region. Moreover, the invariants of the velocity gradient tensor (Q and R) show that the classical “teardrop” shape of their associated phase map is not yet formed at the T/NT interface. All the invariants rapidly change after the T/NT interface is crossed into the turbulent region. For instance, the enstrophy density, proportional to QW, is zero in the irrotational flow region and high and more or less constant inside the turbulent region, after it undergoes a sharp jump near the T/NT interface. Inside the turbulent region, at a distance of only 1.7η from the T/NT interface, where η is the Kolmogorov microscale, the invariants QW and QS suggest that large scale coherent vortices already exist in the flow. Furthermore, the joint probability density function of Q and R already displays its well known teardrop shape at that location. Moreover, the geometry of the straining (or deformation) of the fluid elements during the turbulent entrainment process is preferentially characterized by biaxial expansion with αS:βS:γS=2:1:−3, where αS, βS, and γS are the eigenvalues of the rate-of-strain tensor arranged in descending order. Based on an analysis of the invariants, many aspects of the flow topology inside the turbulent region at a distance of only 1.7η from the T/NT interface are already similar to those observed deep inside the turbulent region.

Local normal-fluid helium II flow due to mutual friction interaction with the superfluid

Mutual friction, the scattering of rotons and phonons by quantized vortex lines, acts locally on the normal fluid component of helium II and is nonzero only in a volume very close to the quantized vortex line. We show that this localized mutual friction force forms a jetlike flow structure in the normal fluid, with a vortex dipole structure. The peak velocity of this normal fluid jet is a significant fraction of the velocity of the quantized vortex line and the width of the jet is on the order of 0.1 mm. The normal fluid jet velocity is highest at $T\ensuremath{\approx}1.9$ K and decreases to zero as the temperature goes to zero and also as the temperature approaches the lambda transition temperature. We report the circulation, energy per unit length, and the viscous dissipation of kinetic energy of this normal fluid flow structure as a function of temperature.

Topology of fine-scale motions in turbulent channel flow

An investigation of topological features of the velocity gradient field of turbulent channel flow has been carried out using results from a direct numerical simulation for which the Reynolds number based on the channel half-width and the centreline velocity was 7860. Plots of the joint probability density functions of the invariants of the rate of strain and velocity gradient tensors indicated that away from the wall region, the fine-scale motions in the flow have many characteristics in common with a variety of other turbulent and transitional flows: the intermediate principal strain rate tended to be positive at sites of high viscous dissipation of kinetic energy, while the invariants of the velocity gradient tensor showed that a preference existed for stable focus/stretching and unstable node/saddle/saddle topologies. Visualization of regions in the flow with stable focus/stretching topologies revealed arrays of discrete downstream-leaning flow structures which originated near the wall and penetrated into the outer region of the flow. In all regions of the flow, there was a strong preference for the vorticity to be aligned with the intermediate principal strain rate direction, with the effect increasing near the walls in response to boundary conditions.

Thermodynamic aspects of thermoacoustic theory

The study of thermoacoustic phenomena has a long history, and a fluid mechanics description of them has been developed in this century. Thermodynamic aspects of the thermoacoustic theory are discussed in this paper. Work flux, heat flux and energy conversion are introduced. Two thermodynamic media (a solid and an oscillating fluid) are regarded as catalysts for the heat flow and energy conversion. Three basic equations of fluid mechanics in Lagrange's frame are linearized in terms of three oscillating variables, namely pressure, entropy and displacement or velocity of the fluid element. The energy conversion is shown to consist of viscous dissipation of kinetic energy and the trajectory area in the temperature-entropy space. The entropy oscillation is discussed using the general equation of heat transport and the second law of thermodynamics. Finally the heat flux and energy conversion are expressed in terms of oscillating pressure and displacement or velocity. Transverse inhomogeneity of oscillating entropy or temperature, including phase lag, results in standing components of energy conversion W stand and heat flux Q stand, in addition to the pressure induced dissipation W P and displacement enhanced heat conduction Q D .

The dissipation of kinetic energy in a warm‐core ring

Profiles of the rate of viscous dissipation of kinetic energy in a Gulf Stream warm‐core ring show large rates in the thermocline and in the entrainment region near the edge of the ring. The thermostad has very low levels of dissipation except where that region is in contact with the Gulf Stream. Dissipation rates in the thermocline are independent of the large scale vertical shear and are consistent with the concept of near‐inertial wave trapping by the ring's geostrophic shear. Near the edge, to depths of 1000 m, turbulence is associated with entrainment and interleaving. The e‐fold decay scale for the dissipation of the ring's total energy is 2 to 3 years, but is only 140 days for the kinetic energy, so energy conversion from potential to kinetic must be occurring on time scales of 10 to 30 days. The vertical eddy diffusivity of the ring is 0.1 × 10−4 m2/s except in the thermostad where it is smaller by approximately a factor of 10. The eddy viscosity is more than 10 × 10−4 m2/s; hence tubulent diffusion is relaxing the velocity field faster than the thermal field.

The thermal problem for a submerged stream

The general solution of the thermal problem of convective heat conduction with volume heat dissipation caused by viscous dissipation of kinetic energy of the fluid, whose velocity field is determined by the exact solution /1/ of the Navier-Stokes equations, is considered for a submerged stream. The possible formulation of the heat problem and the characteristic behaviour of the solutions are investigated. The solutions obtained have a special feature, namely the existence, under specified conditions, of two regimes of convective heat exchange.

Stellar convection. I - Modal equations in spheres and spherical shells

view Abstract Citations (19) References (21) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Stellar convection. I. Modal equations in spheres and spherical shells. Marcus, P. S. Abstract In the present paper, a set of nonlinear modal equations is derived to describe convection in self-gravitating spheres and spherical shells of Boussinesq fluids with internal heat sources that are functions of radius. (In a Boussinesq fluid, the depth is much less than its pressure scale-height and viscous dissipation of kinetic energy is absent.) The velocity field is written as a sum of two parts - the toroidal field generated from a pseudo-scalar and the poloidal field generated from a scalar. The nonlinear terms on the modal equations are written in terms of the scalar and pseudo-scalar. The nonlinear three-eddy interactions are parametrized with a set of dimensionless B-numbers and C-numbers. These numbers are calculated for several sets of planforms. Publication: The Astrophysical Journal Pub Date: July 1979 DOI: 10.1086/157178 Bibcode: 1979ApJ...231..176M Keywords: Convective Heat Transfer; Spheres; Spherical Shells; Stellar Envelopes; Stellar Models; Stellar Rotation; Angular Momentum; Boussinesq Approximation; Fluid Boundaries; Scalars; Turbulent Diffusion; Velocity Distribution; Astrophysics; Convection:Stars full text sources ADS |

Turbulent entrainment across stable density step structures

This paper is a summary of a research on the properties of the turbulent entrainment across stable density-stratified layers, a phenomenon commonly observed in geophysical fluid dynamics. A turbulent environment is created by oscillating grids in quasi-homogeneous layers of slightly different density separated by thin sheets of fluid containing a strong density gradient. The buoyancy flux across thin stable layers is found to be a function of the Richardson and Prandtl numbers. Theoretical and experimental studies are made, leading to a determination of the order of magnitude of the four terms expressing the balance of energy in physical space. It is shown that the turbulent energy flux is of the same order of magnitude as the viscous dissipation of kinetic energy in the quasi-homogeneous layers where the slight density gradient is not altogether negligible because a small but measurable fraction of the turbulent energy flux goes into maintaining the buoyancy flux. Data taken in the stable layer show the simultaneous existence of large internal waves and patchy turbulence. Some properties of these waves as functions of the Richardson number are determined.

Dissipation and Diffusion by Turbulence and Irregular Winds near 100 km

A review is given of some recent measurements of the following energy balance parameters in the 90–110 km height region: ε0, the viscous dissipation of kinetic energy by shears in the mean winds; εd, the viscous dissipation of kinetic energy by shears in the turbulent winds; εs, the transfer of kinetic energy from the mean motion to the turbulent motion; εg, the transfer of turbulent kinetic energy to potential energy by buoyancy action; and εw, the rate of dissipation of wave energy of tides and irregular winds interpreted as gravity waves. Some measurements of the growth rates of globular structure on chemical release clouds and the growth rate of interglobular distances are presented. These data indicate that the diffusion mechanism is a mixture of the 〈v2〉t2 variation expected for the diffusion of a point from its initial position with the εdt3 variation expected for the variation of the separation between pairs of points.

Dynamical tides in close binary systems

Differential equations governing the dynamical tides in close binary systems consisting of centrally condensed components of viscous gas are split up (Section 2) in their real and imaginary parts, the ratio of which defines the tidal lag. In Sections 3 and 4 these equations will be particularized to a case in which the central mass-point of each star is surrounded by an evanescent envelope the density of which decreases as the inverse square of the central distance. It is shown that self-gravitating configurations built up in accordance with this model are incapable of performing free nonradial oscillations with a frequency ω comprised between 0 ⩽ ω2 ⩽ ∞; but explicit expressions for forced oscillations representing dynamical tides are given for an arbitrary form of the external field of force. Equations for the imaginary components of the displacement, constructed for the same model in Section 4, disclose that if the viscosity of stellar material is identified with that of hydrogen plasma, the tidal lag due to a viscous dissipation of kinetic energy may produce dynamical effects, the cumulative outcome of which becomes appreciable on the Kelvin time-scale, but over short intervals of time their stationary photometric effects should be negligible. The latter can become observationally significant only for stars in which turbulent viscosity under near-adiabatic conditions becomes and important factor.

A solution of the Navier-Stokes and energy equations illustrating the response of skin friction and temperature of an infinite plate thermometer to fluctuations in the stream velocity

An exact solution of the Navier-Stokes equations for incompressible flow is derived under the conditions: (i) the flow is two-dimensional and is bounded by an infinite, plane, porous wall; (ii) the flow is independent of the distance parallel to the wall; (iii) the component of velocity parallel to the wall at a large distance from it fluctuates in time about a constant mean; (iv) the component of velocity normal to the wall is constant. It is found that the skin-friction fluctuations illustrate Lighthill’s (1954) theory of the behaviour of boundary layers subject to fluctuating pressure gradients. The amplitude of the skin-friction fluctuations rises with frequency, while the phase lead of the skin-friction over the main-stream-velocity fluctuation rises from zero at zero frequency to 7r/4 at very high frequencies. The velocity profile in the boundary layer fluctuates, and under certain transient conditions resembles that of a separated boundary layer, that is, a boundary layer with reverse flow close to the wall. With viscous dissipation of kinetic energy taken into account, the corresponding exact solution of the energy equation for an incompressible fluid with constant physical properties is derived under a condition of zero heat transfer between the fluid and the wall—the so-called ‘thermometer’ or ‘kinetic temperature’ problem. Whereas the velocity field consists of a mean flow and a first-harmonic fluctuation, the temperature field contains additionally a second-harmonic fluctuation. It is found that the mean temperature of the wall rises with frequency, and is ultimately proportional to the square root of the frequency. The first-harmonic fluctuation of the wall temperature lags behind the main-stream-velocity fluctuation by an amount which rises from zero at zero frequency to 1/4n at high frequencies, while the phase lag of the second-harmonic rises from zero at zero frequency but drops again to zero at high frequencies. The amplitude of the first-harmonic fluctuation tends to zero at high frequencies, whereas the amplitude of the second-harmonic fluctuation tends to a non-zero limit. Thus the residual temperature fluctuation of the wall at high frequencies has a frequency which is twice that of the fluctuating stream.