DOCSLIB.ORG

The Influence of Magnetic Fields in Planetary Dynamo Models

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Influence of Magnetic Fields in Planetary Dynamo Models Earth and Planetary Science Letters 333–334 (2012) 9–20 Contents lists available at SciVerse ScienceDirect Earth and Planetary Science Letters journal homepage: www.elsevier.com/locate/epsl The influence of magnetic fields in planetary dynamo models Krista M. Soderlund a,n, Eric M. King b, Jonathan M. Aurnou a a Department of Earth and Space Sciences, University of California, Los Angeles, CA 90095, USA b Department of Earth and Planetary Science, University of California, Berkeley, CA 94720, USA article info abstract Article history: The magnetic fields of planets and stars are thought to play an important role in the fluid motions Received 7 November 2011 responsible for their field generation, as magnetic energy is ultimately derived from kinetic energy. We Received in revised form investigate the influence of magnetic fields on convective dynamo models by contrasting them with 27 March 2012 non-magnetic, but otherwise identical, simulations. This survey considers models with Prandtl number Accepted 29 March 2012 Pr¼1; magnetic Prandtl numbers up to Pm¼5; Ekman numbers in the range 10À3 ZEZ10À5; and Editor: T. Spohn Rayleigh numbers from near onset to more than 1000 times critical. Two major points are addressed in this letter. First, we find that the characteristics of convection, Keywords: including convective flow structures and speeds as well as heat transfer efficiency, are not strongly core convection affected by the presence of magnetic fields in most of our models. While Lorentz forces must alter the geodynamo flow to limit the amplitude of magnetic field growth, we find that dynamo action does not necessitate a planetary dynamos dynamo models significant change to the overall flow field. By directly calculating the forces in each of our simulations, rotating convection models we show that the traditionally defined Elsasser number, Li, overestimates the role of the Lorentz force in dynamos. The Coriolis force remains greater than the Lorentz force even in cases with Li C100, explaining the persistence of columnar flows in Li 41 dynamo simulations. We argue that a dynamic Elsasser number, Ld, better represents the Lorentz to Coriolis force ratio. By applying the Ld parametrization to planetary settings, we predict that the convective dynamics (excluding zonal flows) in planetary interiors are only weakly influenced by their large-scale magnetic fields. The second major point addressed here is the observed transition between dynamos with dipolar and multipolar magnetic fields. We find that the breakdown of dipolar field generation is due to the degradation of helicity in the flow. This helicity change does not coincide with the destruction of columnar convection and is not strongly influenced by the presence of magnetic fields. Force calculations suggest that this transition may be related to a competition between inertial and viscous forces. If viscosity is indeed important for large-scale field generation, such moderate Ekman number models may not adequately simulate the dynamics of planetary dynamos, where viscous effects are expected to be negligible. & 2012 Elsevier B.V. All rights reserved. 1. Introduction (e.g., Gaidos et al., 2010). Planetary magnetic fields result from dynamo action thought to be driven by convection in electrically Magnetic fields are common throughout the solar system; conducting fluid regions (e.g., Jones, 2011) and, therefore, are intrinsic magnetic fields have been detected on the Sun, Mercury, linked to the planets’ internal dynamics. Convection in these Earth, the giant planets, and the Jovian satellite Ganymede systems is subject to Coriolis forces resulting from planetary (Connerney, 2007). Evidence of extinct dynamos is also observed rotation. In electrically conducting fluids, these flows can be on the Moon and Mars (Connerney, 2007). In addition, it is unstable to dynamo action. Lorentz forces then arise, via Lenz’s expected that many extrasolar planets have magnetic fields law, that act to equilibrate magnetic field growth. Insight into the forces that govern the fluid dynamics of planetary interiors can be gained through numerical modeling: non-magnetic rotating convection models investigate the influ- n Corresponding author. Present address: Institute for Geophysics, John A. & ence of rotation on convection, and planetary dynamo models Katherine G. Jackson School of Geosciences, The University of Texas at Austin, incorporate the additional back reaction of the magnetic fields on Austin, TX 78758, USA. Tel.: þ1 218 349 3006; fax: þ1 512 471 8844. the fluid motions from which they arise. E-mail addresses: [email protected], [email protected] (K.M. Soderlund), [email protected] (E.M. King), The flows in non-magnetic rapidly rotating convection are [email protected] (J.M. Aurnou). organized by the Coriolis force into axial columns (e.g., Grooms 0012-821X/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.epsl.2012.03.038 10 K.M. Soderlund et al. / Earth and Planetary Science Letters 333–334 (2012) 9–20 et al., 2010; Olson, 2011; King and Aurnou, 2012). Under the forces (see Table 1). Thus, in rapidly rotating systems such as À extreme influence of rotation, the dominant force balance is planetary cores (where Et10 10), it is predicted that convection geostrophic—a balance between the Coriolis force and the pres- occurs as tall, thin columns. Flows in these columns are helical, sure gradient. Geostrophic flows are described by the Taylor– and these corkscrew-like motions are important for large-scale Proudman constraint, which predicts that fluid motions should magnetic field generation (e.g., Jones, 2011). not vary strongly in the direction of the rotation axis (e.g., Tritton, In planetary dynamos, however, magnetic fields are also 1998). Furthermore, linear asymptotic analyses predict that the thought to play an important dynamical role on the convection azimuthal wavenumber of these columns varies as m ¼ OðEÀ1=3Þ and zonal flows. It is often argued that the influence of magnetic as E-0(Roberts, 1968; Jones et al., 2000; Dormy et al., 2004). fields will be important when Li \1, where the traditional Here, m is non-dimensionalized by the shell thickness and the Elsasser number, Li, characterizes the relative strengths of the Ekman number, E, characterizes the ratio of viscous to Coriolis Lorentz and Coriolis forces (see Table 2). In the presence of dominant imposed magnetic fields and rotation, the first order force balance is magnetostrophic—a balance between the Corio- Table 1 lis, pressure gradient, and Lorentz terms. Studies of linear mag- Summary of non-dimensional control parameters. Symbols are defined in the text. netoconvection show that the azimuthal wavenumber of Parameter estimates for Earth’s core taken from King et al. (2010). convection decreases to m ¼ Oð1Þ when a strong magnetic field (L \Oð1Þ) is imposed in the limit E-0(Chandrasekhar, 1961; Definition Interpretation Model Earth’s i core Eltayeb and Roberts, 1970; Fearn and Proctor, 1983; Cardin and Olson, 1995). This behavior occurs because magnetic fields can w ¼ ri=ro Shell geometry 0.4 0.35 relax the Taylor–Proudman constraint, allowing global-scale 3 Buoyancy/diffusion 5 9 24 Ra ¼ agoDTD =nk 10 oRao10 10 motions that differ fundamentally from the small-scale axial À À À E ¼ n=2OD2 Viscous/Coriolis forces 10 3,10 4, 10 15 columns typical of non-magnetic, rapidly rotating convection. À5 10 Despite having strong magnetic fields, however, axial convec- Pr ¼ n=k Viscous/thermal diffusivities 1 À1 10 tive flow structures are maintained in many rotating magneto- Pm ¼ n=Z Viscous/magnetic 0, 2, 5 À6 10 convection and dynamo studies (e.g., Olson and Glatzmaier, 1995; diffusivities Zhang, 1995; Kageyama and Sato, 1997; Zhang et al., 1998; Table 2 Summary of non-dimensional diagnostic parameters. Symbols are defined in the text. In these definitions, ‘B ¼ðpD=2Þ=kB is assumed to be the characteristic quarter-wavelength of the magnetic field. Parameter Definition Interpretation 1 R Kinetic energy density EK ¼ u Á u dV 2V s c Axisymmetric Convective kinetic energy density EK ¼ EK ÀEK,Toroidal 1 R Magnetic energy density E ¼ B Á B dV M 2V P s l ¼ lðu Á u Þ=2E Characteristic degree of the flow u P l l K Characteristic degree of the B field lB ¼ PlðBl Á BlÞ=2EM mu ¼ P mðum Á umÞ=2EK Characteristic order of the flow mB ¼qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffimðBm Á BmÞ=2EM Characteristic order of the B field 2 2 Characteristic wavenumber of the ku ¼ lu þmu qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi flow 2 2 Characteristic wavenumber of the B kB ¼ lB þmB P field 9/ 0 S 9 x Á z^ z Axial vorticity columnarity s,f C ¼ P oz /9 09S x z s,f /H S Relative axial helicity Hrel ¼ z h z / S / S 1=2 ð uzuz h ozoz hÞ Nusselt number r qD Total heat transfer Nu ¼ o r C T i r ppkffiffiffiffiffiffiffiffiffiD Conductive heat transfer Reynolds number UD Inertial force Re ¼ n ¼ 2EK Viscous force Convective Reynolds U D pffiffiffiffiffiffiffiffiffi Convective inertial force Re ¼ c ¼ 2Ec number c n K Viscous force Magnetic Reynolds UD Magnetic induction Rm ¼ ¼ Re Pm number Z Magnetic diffusion R Dipolarity 1=2 Dipole field strength ðr Þ BlR¼ 1ðr ¼ roÞBl ¼ 1ðr ¼ roÞ dA o f ¼ Total field strength ðr Þ Bðr ¼ roÞBðr ¼ roÞ dA o Imposed Elsasser B2 Lorentz force ¼ ¼ (low Rm) number Li EMPmE Coriolis force 2rmoZO Dynamic Elsasser B2 L D Lorentz force ¼ ¼ i (high Rm) number Ld Coriolisforce 2rmoOU‘B Rm ‘B Lehnert number B Lorentz force l ¼ pffiffiffiffiffiffiffiffiffi ¼ AL ðA ¼ Oð1ÞÞ 2‘ O rm d Coriolis force pB ffiffiffiffiffiffiffiffiffi oqffiffiffiffiffiffiffiffiffiffiffiffi Alfve´n number U rm 2 Flow speed A ¼ o ¼ Re EPm B Li Alfven wave speed K.M. Soderlund et al. / Earth and Planetary Science Letters 333–334 (2012) 9–20 11 Christensen et al., 1999; Zhang and Schubert, 2000; Jones, 2007; where u is the velocity vector, B is the magnetic induction, T is Jault, 2008; Busse and Simitev, 2011).
Load more

Recommended publications
  • Convection Heat Transfer
    Convection Heat Transfer Heat transfer from a solid to the surrounding fluid Consider fluid motion Recall flow of water in a pipe Thermal Boundary Layer • A temperature profile similar to velocity profile. Temperature of pipe surface is kept constant. At the end of the thermal entry region, the boundary layer extends to the center of the pipe. Therefore, two boundary layers: hydrodynamic boundary layer and a thermal boundary layer. Analytical treatment is beyond the scope of this course. Instead we will use an empirical approach. Drawback of empirical approach: need to collect large amount of data. Reynolds Number: Nusselt Number: it is the dimensionless form of convective heat transfer coefficient. Consider a layer of fluid as shown If the fluid is stationary, then And Dividing Replacing l with a more general term for dimension, called the characteristic dimension, dc, we get hd N ≡ c Nu k Nusselt number is the enhancement in the rate of heat transfer caused by convection over the conduction mode. If NNu =1, then there is no improvement of heat transfer by convection over conduction. On the other hand, if NNu =10, then rate of convective heat transfer is 10 times the rate of heat transfer if the fluid was stagnant. Prandtl Number: It describes the thickness of the hydrodynamic boundary layer compared with the thermal boundary layer. It is the ratio between the molecular diffusivity of momentum to the molecular diffusivity of heat. kinematic viscosity υ N == Pr thermal diffusivity α μcp N = Pr k If NPr =1 then the thickness of the hydrodynamic and thermal boundary layers will be the same.
    [Show full text]
  • Confinement of Rotating Convection by a Laterally Varying Magnetic Field
    This draft was prepared using the LaTeX style file belonging to the Journal of Fluid Mechanics 1 Confinement of rotating convection by a laterally varying magnetic field Binod Sreenivasan and Venkatesh Gopinath Centre for Earth Sciences, Indian Institute of Science, Bangalore 560012, India. (Received xx; revised xx; accepted xx) Spherical shell dynamo models based on rotating convection show that the flow within the tangent cylinder is dominated by an off-axis plume that extends from the inner core boundary to high latitudes and drifts westward. Earlier studies explained the formation of such a plume in terms of the effect of a uniform axial magnetic field that significantly increases the lengthscale of convection in a rotating plane layer. However, rapidly rotating dynamo simulations show that the magnetic field within the tangent cylinder has severe lateral inhomogeneities that may influence the onset of an isolated plume. Increasing the rotation rate in our dynamo simulations (by decreasing the Ekman number E) produces progressively thinner plumes that appear to seek out the location where the field is strongest. Motivated by this result, we examine the linear onset of convection in a rapidly rotating fluid layer subject to a laterally varying axial magnetic field. A cartesian geometry is chosen where the finite dimensions (x;z) mimic (f;z) in cylindrical coordinates. The lateral inhomogeneity of the field gives rise to a unique mode of instability arXiv:1703.08051v2 [physics.flu-dyn] 24 Apr 2017 where convection is entirely confined to the peak-field region. The localization of the flow by the magnetic field occurs even when the field strength (measured by the Elsasser number L) is small and viscosity controls the smallest lengthscale of convection.
    [Show full text]
  • Turning up the Heat in Turbulent Thermal Convection COMMENTARY Charles R
    COMMENTARY Turning up the heat in turbulent thermal convection COMMENTARY Charles R. Doeringa,b,c,1 Convection is buoyancy-driven flow resulting from the fluid remains at rest and heat flows from the warm unstable density stratification in the presence of a to the cold boundary according Fourier’s law, is stable. gravitational field. Beyond convection’s central role in Beyond a critical threshold, however, steady flows in myriad engineering heat transfer applications, it un- the form of coherent convection rolls set in to enhance derlies many of nature’s dynamical designs on vertical heat flux. Convective turbulence, character- larger-than-human scales. For example, solar heating ized by thin thermal boundary layers and chaotic of Earth’s surface generates buoyancy forces that plume dynamics mixing in the core, appears and per- cause the winds to blow, which in turn drive the sists for larger ΔT (Fig. 1). oceans’ flow. Convection in Earth’s mantle on geolog- More precisely, Rayleigh employed the so-called ical timescales makes the continents drift, and Boussinesq approximation in the Navier–Stokes equa- thermal and compositional density differences induce tions which fixes the fluid density ρ in all but the buoyancy forces that drive a dynamo in Earth’s liquid temperature-dependent buoyancy force term and metal core—the dynamo that generates the magnetic presumes that the fluid’s material properties—its vis- field protecting us from solar wind that would other- cosity ν, specific heat c, and thermal diffusion and wise extinguish life as we know it on the surface. The expansion coefficients κ and α—are constant.
    [Show full text]
  • Rotating Fluids
    26 Rotating fluids The conductor of a carousel knows about fictitious forces. Moving from horse to horse while collecting tickets, he not only has to fight the centrifugal force trying to kick him off, but also has to deal with the dizzying sideways Coriolis force. On a typical carousel with a five meter radius and turning once every six seconds, the centrifugal force is strongest at the rim where it amounts to about 50% of gravity. Walking across the carousel at a normal speed of one meter per second, the conductor experiences a Coriolis force of about 20% of gravity. Provided the carousel turns anticlockwise seen from above, as most carousels seem to do, the Coriolis force always pulls the conductor off his course to the right. The conductor seems to prefer to move from horse to horse against the rotation, and this is quite understandable, since the Coriolis force then counteracts the centrifugal force. The whole world is a carousel, and not only in the metaphorical sense. The centrifugal force on Earth acts like a cylindrical antigravity field, reducing gravity at the equator by 0.3%. This is hardly a worry, unless you have to adjust Olympic records for geographic latitude. The Coriolis force is even less noticeable at Olympic speeds. You have to move as fast as a jet aircraft for it to amount to 0.3% of a percent of gravity. Weather systems and sea currents are so huge and move so slowly compared to Earth’s local rotation speed that the weak Coriolis force can become a major player in their dynamics.
    [Show full text]
  • Chapter 5 Frictional Boundary Layers
    Chapter 5 Frictional boundary layers 5.1 The Ekman layer problem over a solid surface In this chapter we will take up the important question of the role of friction, especially in the case when the friction is relatively small (and we will have to find an objective measure of what we mean by small). As we noted in the last chapter, the no-slip boundary condition has to be satisfied no matter how small friction is but ignoring friction lowers the spatial order of the Navier Stokes equations and makes the satisfaction of the boundary condition impossible. What is the resolution of this fundamental perplexity? At the same time, the examination of this basic fluid mechanical question allows us to investigate a physical phenomenon of great importance to both meteorology and oceanography, the frictional boundary layer in a rotating fluid, called the Ekman Layer. The historical background of this development is very interesting, partly because of the fascinating people involved. Ekman (1874-1954) was a student of the great Norwegian meteorologist, Vilhelm Bjerknes, (himself the father of Jacques Bjerknes who did so much to understand the nature of the Southern Oscillation). Vilhelm Bjerknes, who was the first to seriously attempt to formulate meteorology as a problem in fluid mechanics, was a student of his own father Christian Bjerknes, the physicist who in turn worked with Hertz who was the first to demonstrate the correctness of Maxwell’s formulation of electrodynamics. So, we are part of a joined sequence of scientists going back to the great days of classical physics.
    [Show full text]
  • Rotating Convection-Driven Dynamos at Low Ekman Number
    PHYSICAL REVIEW E 66, 056308 ͑2002͒ Rotating convection-driven dynamos at low Ekman number Jon Rotvig* and Chris A. Jones School of Mathematical Sciences, University of Exeter, Exeter EX4 4QE, England ͑Received 10 October 2001; revised manuscript received 18 July 2002; published 22 November 2002͒ We present a fully 3D self-consistent convection-driven dynamo model with reference to the geodynamo. A relatively low Ekman number regime is reached, with the aim of investigating the dynamical behavior at low viscosity. This regime is computationally very demanding, which has prompted us to adopt a plane layer model with an inclined rotation vector, and to make use of efficiently parallelized code. No hyperdiffusion is used, all diffusive operators are in the classical form. Our model has infinite Prandtl number, a Rayleigh number that scales as EϪ1/3 (E being the Ekman number͒, and a constant Roberts number. The optimized model allows us to study dynamos with Ekman numbers in the range ͓10Ϫ5,10Ϫ4͔. In this regime we find strong-field dynamos where the induced magnetic fields satisfy Taylor’s constraint to good accuracy. The solutions are characterized by ͑i͒ a MAC balance within the bulk, i.e., Coriolis, pressure, Lorentz, and buoyancy forces are of comparable magnitude, while viscous forces are only significant in thin boundary layers, ͑ii͒ the Elsasser number is O(10), ͑iii͒ the strong magnetic fields cannot prevent small-scale structures from becoming dominant over the large- scale components, ͑iv͒ the Taylor-Proudman effect is detectable, ͑v͒ the Taylorization decreases as the Ekman number is lowered, and ͑vi͒ the ageostrophic velocity component makes up 80% of the flow.
    [Show full text]
  • On the Inverse Cascade and Flow Speed Scaling Behavior in Rapidly Rotating Rayleigh-Bénard Convection
    This draft was prepared using the LaTeX style file belonging to the Journal of Fluid Mechanics 1 On the inverse cascade and flow speed scaling behavior in rapidly rotating Rayleigh-B´enardconvection S. Maffei1;3y, M. J. Krouss1, K. Julien2 and M. A. Calkins1 1Department of Physics, University of Colorado, Boulder, USA 2Department of Applied Mathematics, University of Colorado, Boulder, USA 3School of Earth and Environment, University of Leeds, Leeds, UK (Received xx; revised xx; accepted xx) Rotating Rayleigh-B´enardconvection is investigated numerically with the use of an asymptotic model that captures the rapidly rotating, small Ekman number limit, Ek ! 0. The Prandtl number (P r) and the asymptotically scaled Rayleigh number (Raf = RaEk4=3, where Ra is the typical Rayleigh number) are varied systematically. For sufficiently vigorous convection, an inverse kinetic energy cascade leads to the formation of a depth-invariant large-scale vortex (LSV). With respect to the kinetic energy, we find a transition from convection dominated states to LSV dominated states at an asymptotically reduced (small-scale) Reynolds number of Ref ≈ 6 for all investigated values of P r. The ratio of the depth-averaged kinetic energy to the kinetic energy of the convection reaches a maximum at Ref ≈ 24, then decreases as Raf is increased. This decrease in the relative kinetic energy of the LSV is associated with a decrease in the convective correlations with increasing Rayleigh number. The scaling behavior of the convective flow speeds is studied; although a linear scaling of the form Ref ∼ Ra=Pf r is observed over a limited range in Rayleigh number and Prandtl number, a clear departure from this scaling is observed at the highest accessible values of Raf .
    [Show full text]
  • Rayleigh-Bernard Convection Without Rotation and Magnetic Field
    Nonlinear Convection of Electrically Conducting Fluid in a Rotating Magnetic System H.P. Rani Department of Mathematics, National Institute of Technology, Warangal. India. Y. Rameshwar Department of Mathematics, Osmania University, Hyderabad. India. J. Brestensky and Enrico Filippi Faculty of Mathematics, Physics, Informatics, Comenius University, Slovakia. Session: GD3.1 Core Dynamics Earth's core structure, dynamics and evolution: observations, models, experiments. Online EGU General Assembly May 2-8 2020 1 Abstract • Nonlinear analysis in a rotating Rayleigh-Bernard system of electrical conducting fluid is studied numerically in the presence of externally applied horizontal magnetic field with rigid-rigid boundary conditions. • This research model is also studied for stress free boundary conditions in the absence of Lorentz and Coriolis forces. • This DNS approach is carried near the onset of convection to study the flow behaviour in the limiting case of Prandtl number. • The fluid flow is visualized in terms of streamlines, limiting streamlines and isotherms. The dependence of Nusselt number on the Rayleigh number, Ekman number, Elasser number is examined. 2 Outline • Introduction • Physical model • Governing equations • Methodology • Validation – RBC – 2D – RBC – 3D • Results – RBC – RBC with magnetic field (MC) – Plane layer dynamo (RMC) 3 Introduction • Nonlinear interaction between convection and magnetic fields (Magnetoconvection) may explain certain prominent features on the solar surface. • Yet we are far from a real understanding of the dynamical coupling between convection and magnetic fields in stars and magnetically confined high-temperature plasmas etc. Therefore it is of great importance to understand how energy transport and convection are affected by an imposed magnetic field: i.e., how the Lorentz force affects convection patterns in sunspots and magnetically confined, high-temperature plasmas.
    [Show full text]
  • Arxiv:1903.08882V2 [Physics.Flu-Dyn] 6 Jun 2019
    Lattice Boltzmann simulations of three-dimensional thermal convective flows at high Rayleigh number Ao Xua,∗, Le Shib, Heng-Dong Xia aSchool of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China bState Key Laboratory of Electrical Insulation and Power Equipment, Center of Nanomaterials for Renewable Energy, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China Abstract We present numerical simulations of three-dimensional thermal convective flows in a cubic cell at high Rayleigh number using thermal lattice Boltzmann (LB) method. The thermal LB model is based on double distribution function ap- proach, which consists of a D3Q19 model for the Navier-Stokes equations to simulate fluid flows and a D3Q7 model for the convection-diffusion equation to simulate heat transfer. Relaxation parameters are adjusted to achieve the isotropy of the fourth-order error term in the thermal LB model. Two types of thermal convective flows are considered: one is laminar thermal convection in side-heated convection cell, which is heated from one vertical side and cooled from the other vertical side; while the other is turbulent thermal convection in Rayleigh-B´enardconvection cell, which is heated from the bottom and cooled from the top. In side-heated convection cell, steady results of hydrodynamic quantities and Nusselt numbers are presented at Rayleigh numbers of 106 and 107, and Prandtl number of 0.71, where the mesh sizes are up to 2573; in Rayleigh-B´enardconvection cell, statistical averaged results of Reynolds and Nusselt numbers, as well as kinetic and thermal energy dissipation rates are presented at Rayleigh numbers of 106, 3×106, and 107, and Prandtl numbers of arXiv:1903.08882v2 [physics.flu-dyn] 6 Jun 2019 ∗Corresponding author Email address: [email protected] (Ao Xu) DOI: 10.1016/j.ijheatmasstransfer.2019.06.002 c 2019.
    [Show full text]
  • Dynamic Similarity, the Dimensionless Science
    Dynamic similarity, the dimensionless feature science Diogo Bolster, Robert E. Hershberger, and Russell J. Donnelly Dimensional analysis, a framework for drawing physical parallels between systems of disparate scale, affords key insights into natural phenomena too expansive and too energetic to replicate in the lab. Diogo Bolster is an assistant professor of civil engineering and geological sciences at the University of Notre Dame in Notre Dame, Indiana. Robert Hershberger is a research assistant in the department of physics at the University of Oregon in Eugene. Russell Donnelly is a professor of physics at the University of Oregon. Many experiments seem daunting at first glance, in accordance with general relativity, is deflected as it passes owing to the sheer number of physical variables they involve. through the gravitational field of the Sun. Assuming the Sun To design an apparatus that circulates fluid, for instance, one can be treated as a point of mass m and that the ray of light must know how the flow is affected by pressure, by the ap- passes the mass with a distance of closest approach r, dimen- paratus’s dimensions, and by the fluid’s density and viscosity. sional reasoning can help predict the deflection angle θ.1 Complicating matters, those parameters may be temperature Expressed in terms of mass M, length L, and time T, the and pressure dependent. Understanding the role of each variables’ dimensions—denoted with square brackets—are parameter in such a high-dimensional space can be elusive or prohibitively time consuming. Dimensional analysis, a concept historically rooted in Box 1. A brief history of dimensional analysis the field of fluid mechanics, can help to simplify such prob- Going back more than 300 years, discussions of dimensional lems by reducing the number of system parameters.
    [Show full text]
  • Scottish Fluid Mechanics Meeting Wednesday 30 Th May 2012
    25 th Scottish Fluid Mechanics Meeting Wednesday 30 th May 2012 Book of Abstracts Hosted by School of Engineering and Physical Sciences & School of the Built Environment Sponsored by Dantec Dynamics Ltd. 25 th Scottish Fluid Mechanics Meeting, Heriot-Watt University, 30 th May 2012 Programme of Event: 09:00 – 09:30 Coffee and registration* 09:30 – 09:45 Welcome (Wolf-Gerrit Früh)** 09:45 – 11:00 Session 1 (5 papers) (Chair: Wolf-Gerrit Früh)** 11:00 – 11:30 Coffee break & Posters*** 11:30 – 12:45 Session 2 (5 papers) (Chair: Stephen Wilson) 12:45 – 13:45 Lunch & Posters 13:45 – 15:00 Session 3 (5 papers) (Chair: Yakun Guo) 15:00 – 15:30 Coffee break & Posters 15:30 – 17:00 Session 4 (6 papers) (Chair: Peter Davies) 17:00 – 17:10 Closing remarks (Wolf-Gerrit Früh) 17:10 – 18:00 Drinks reception * Coffee and registration will be outside Lecture Theatre 3, Hugh Nisbet Building. ** Welcome and all sessions will be held in Lecture Theatre 3, Hugh Nisbet Building. *** All other refreshments (morning and afternoon coffee breaks, lunch and the drinks reception) and posters will be held in NS1.37 (the Nasmyth Common room and Crush Area), James Nasmyth Building. 25 th Scottish Fluid Mechanics Meeting, Heriot-Watt University, 30 th May 2012 Programme of Oral Presentations (* denotes presenting author) Session 1 (09:40 – 11:00): 09:45 – 10:00 Flow control for VATT by fixed and oscillating flap Qing Xiao, Wendi Liu* & Atilla Incecik, University of Strathclyde 10:00 – 10:15 Shear stress on the surface of a mono-filament woven fabric Yuan Li* & Jonathan
    [Show full text]
  • Time-Periodic Cooling of Rayleigh–Bénard Convection
    fluids Article Time-Periodic Cooling of Rayleigh–Bénard Convection Lyes Nasseri 1 , Nabil Himrane 2, Djamel Eddine Ameziani 1 , Abderrahmane Bourada 3 and Rachid Bennacer 4,* 1 LTPMP (Laboratoire de Transports Polyphasiques et Milieux Poreux), Faculty of Mechanical and Proceeding Engineering, USTHB (Université des Sciences et de la Technologie Houari Boumedienne), Algiers 16111, Algeria; [email protected] (L.N.); [email protected] (D.E.A.) 2 Labo of Energy and Mechanical Engineering (LEMI), Faculty of Technology, UMBB (Université M’hamed Bougara-Boumerdes, Boumerdes 35000, Algeria; [email protected] 3 Laboratory of Transfer Phenomena, RSNE (Rhéologie et Simulation Numérique des Ecoulements) Team, FGMGP (Faculté de génie Mécaniques et de Génie des Procédés Engineering), USTHB (Université des Sciences et de la Technologie Houari Boumedienne), Bab Ezzouar, Algiers 16111, Algeria; [email protected] 4 CNRS (Centre National de la Recherche Scientifique), LMT (Laboratoire de Mécanique et Technologie—Labo. Méca. Tech.), Université Paris-Saclay, ENS (Ecole National Supérieure) Paris-Saclay, 91190 Gif-sur-Yvette, France * Correspondence: [email protected] Abstract: The problem of Rayleigh–Bénard’s natural convection subjected to a temporally periodic cooling condition is solved numerically by the Lattice Boltzmann method with multiple relaxation time (LBM-MRT). The study finds its interest in the field of thermal comfort where current knowledge has gaps in the fundamental phenomena requiring their exploration. The Boussinesq approximation is considered in the resolution of the physical problem studied for a Rayleigh number taken in the range 103 ≤ Ra ≤ 106 with a Prandtl number equal to 0.71 (air as working fluid).
    [Show full text]