Toroidal and poloidal energy in rotating Rayleigh-B\'enard convection

We consider rotating Rayleigh-B\'enard convection of a fluid with a Prandtl number of $Pr = 0.8$ in a cylindrical cell with an aspect ratio $\Gamma = 1/2$. Direct numerical simulations were performed for the Rayleigh number range $10^5 \leq Ra \leq 10^9$ and the inverse Rossby number range $0 \leq 1/Ro \leq 20$. We propose a method to capture regime transitions based on the decomposition of the velocity field into toroidal and poloidal parts. We identify four different regimes. First, a buoyancy dominated regime occurring as long as the toroidal energy $e_{tor}$ is not affected by rotation and remains equal to that in the non-rotating case, $e^0_{tor}$. Second, a rotation influenced regime, starting at rotation rates where $e_{tor} > e^0_{tor}$ and ending at a critical inverse Rossby number $1/Ro_{cr}$ that is determined by the balance of the toroidal and poloidal energy, $e_{tor} = e_{pol}$. Third, a rotation dominated regime, where the toroidal energy $e_{tor}$ is larger than both, $e_{pol}$ and $e^0_{tor}$. Fourth, a geostrophic turbulence regime for high rotation rates where the toroidal energy drops below the value of non-rotating convection

Jump Rope Vortex in Liquid Metal Convection

Understanding large scale circulations (LSCs) in turbulent convective systems is important for the study of stars, planets and in many industrial applications. The canonical model of the LSC is quasi-planar with additional horizontal sloshing and torsional modes [Brown E, Ahlers G (2009) J. Fluid Mech. 638:383--400; Funfschilling D, Ahlers G (2004) Phys. Rev. Lett. 92(19):194502; Xi HD et al. (2009) Phys. Rev. Lett. 102(4):044503; Zhou Q et al. (2009) J. Fluid Mech. 630:367--390]. Using liquid gallium as the working fluid, we show via coupled laboratory-numerical experiments that the LSC in a tank with aspect ratios greater than unity takes instead the form of a "jump rope vortex", a strongly three-dimensional mode that periodically orbits around the tank following a motion much like a jump rope on a playground. Further experiments show that this jump rope flow also exists in more viscous fluids such as water, albeit with a far smaller signal. Thus, this new jump rope mode is an essential component of the turbulent convection that underlies our observations of natural systems

Mean Temperature Profiles in Turbulent Thermal Convection

To predict the mean temperature profiles in turbulent thermal convection, the thermal boundary layer (BL) equation including the effects of fluctuations has to be solved. In Shishkina et al., Phys. Rev. Lett. 114 (2015), the thermal BL equation with the fluctuations taken into account as an eddy thermal diffusivity has been solved for large Prandtl-number fluids for which the eddy thermal diffusivity and the velocity field can be approximated respectively as a cubic and a linear function of the distance from the plate. In the present work we make use of the idea of Prandtl's mixing length model and relate the eddy thermal diffusivity to the stream function. With this proposed relation, we can solve the thermal BL equation and obtain a closed-form expression for the dimensionless mean temperature profile in terms of two independent parameters for fluids with a general Prandtl number. With a proper choice of the parameters, our predictions of the temperature profiles are in excellent agreement with the results of our direct numerical simulations for a wide range of Prandtl numbers from 0.01 to 2547.9 and Rayleigh numbers from 10^7 to 10^9.Comment: 8 pages, 4 figure

Myofaskiakäsittelyjen ja myofaskiaalisen liikeharjoittelun vaikutus epikondyliitin hoidossa : systemaattinen kirjallisuuskatsaus

Epikondyliitin hoidossa käytettyjä fysikaalisia ja manuaalisia hoitomenetelmiä on useita, mutta yhtenäistä, vahvaan tutkimusnäyttöön perustuvaa hoitosuositusta ei ole. Opinnäytetyön tarkoituksena oli systemaattisen kirjallisuuskatsauksen avulla tutkia ja arvioida myofaskiakäsittelyjen ja myofaskiaalisen liikeharjoittelun vaikutusta epikondyliitin hoidossa. Yläraajan rasitussairauksilla tarkoitetaan kyynärvarren, ranteen ja käden kiputiloja, jotka liittyvät raajan liialliseen kuormitukseen. Näihin lukeutuvat muun muassa lateraalinen ja mediaalinen epikondyliitti. Tutkimushaku toteutettiin ennalta määritetyn hakustrategian mukaan CINAHL-, Cochrane-, Embase-, PEDro- ja PubMed-viitetietokannoista. Kirjallisuuskatsaukseen valikoitui 7 tutkimusta, jotka täyttivät sisäänottokriteerit. Tutkimusten laatu arvioitiin PEDro Scale -asteikon avulla. Tutkimusten keskimääräinen laatu oli kohtalainen, keskiarvon ollessa PEDro-asteikolla 5,3/10 (vaihteluväli 4–6/10). Tiedonhaussa ilmeni, että tutkimuksia, joissa myofaskiakäsittelyjä ja myofaskiaalista liikeharjoittelua verrataan muihin fysioterapeuttisiin hoitomuotoihin löytyi melko vähän. Myös tutkimusotannat olivat pieniä, ja faskioista puhuttaessa yhtenäinen termistö puuttuu. Kolmessa tutkimuksessa esiintyi eksentristen harjoitteiden myönteinen vaikutus epikondyliitin hoitoon. Johtopäätöksiä siitä, onko myofaskiakäsittelyistä tai myofaskiaalisesta liikeharjoittelusta hyötyä vaivan hoidossa ei voi näin pienellä otannalla todentaa. Tutkimushaun tulosten perusteella jatkotutkimus on tarpeen ja lisää laadukkaita tutkimuksia tarvitaan.Several different physical and manual methods are used in the treatment of epicondylitis, however homogenous treatment recommendation based on hard scientific evidence, is absent. The purpose of the thesis was to study and evaluate the effect of myofascial treatments and myofascial exercise therapy in the treatment of epicondylitis with a systematic literature review. Repetitive strain injuries of the upper extremities are defined as pain, caused by excessive strain, in the forearm, wrist and hand. For example, medial and lateral epicondylitis. The literature search was carried out according to a predetermined search strategy from the CINAHL, Cochrane, Embase, PEDro and PubMed databases. Seven studies, which met the inclusion criteria, were selected and then evaluated using the PEDro scale. The average quality of the studies was fair and the mean average of PEDro scale was 5,3/10 (range of 4–6/10). Systematic review revealed that there are only few studies comparing myofascial treatments and myofascial exercise therapy with other physiotherapeutic treatments. Study samplings were small and coherent terminology was missing. In three studies, a positive effect of eccentric exercises on the treatment of epicondylitis occured. Based on the review and the small study samplings, it is not possible to verify whether myofascial treatment or myofascial exercise is effective on treating epicondylitis. Further research and more high-quality studies are needed

Thermoelectric Precession in Turbulent Magnetoconvection

We present laboratory measurements of the interaction between thermoelectric currents and turbulent magnetoconvection. In a cylindrical volume of liquid gallium heated from below and cooled from above and subject to a vertical magnetic field, it is found that the large scale circulation (LSC) can undergo a slow axial precession. Our experiments demonstrate that this LSC precession occurs only when electrically conducting boundary conditions are employed, and that the precession direction reverses when the axial magnetic field direction is flipped. A thermoelectric magnetoconvection (TEMC) model is developed that successfully predicts the zeroth-order magnetoprecession dynamics. Our TEMC magnetoprecession model hinges on thermoelectric current loops at the top and bottom boundaries, which create Lorentz forces that generate horizontal torques on the overturning large-scale circulatory flow. The thermoelectric torques in our model act to drive a precessional motion of the LSC. This model yields precession frequency predictions that are in good agreement with the experimental observations. We postulate that thermoelectric effects in convective flows, long argued to be relevant in liquid metal heat transfer and mixing processes, may also have applications in planetary interior magnetohydrodynamics

Oscillatory thermal-inertial flows in liquid metal rotating convection

We present the first detailed thermal and velocity field characterization of convection in a rotating cylindrical tank of liquid gallium, which has thermophysical properties similar to those of planetary core fluids. Our laboratory experiments, and a closely associated direct numerical simulation, are all carried out in the regime prior to the onset of steady convective modes. This allows us to study the oscillatory convective modes, sidewall modes and broadband turbulent flow that develop in liquid metals before the advent of steady columnar modes. Our thermo-velocimetric measurements show that strongly inertial, thermal wind flows develop, with velocities reaching those of comparable non-rotating cases. Oscillatory bulk convection and wall modes coexist across a wide range of our experiments, along with strong zonal flows that peak in the Stewartson layer, but that extend deep into the fluid bulk in the higher supercriticality cases. The flows contain significant time-mean helicity that is anti-symmetric across the midplane, demonstrating that oscillatory liquid metal convection contains the kinematic components to sustain system-scale dynamo generation.Comment: 29 pages, 12 figure