Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session L3: General Fluid Dynamics: Theory 
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Chair: Serafim Kalliadasis, Imperial College, UK Room: 102 
Monday, November 23, 2015 4:05PM  4:18PM 
L3.00001: A potential mechanism for a singular solution of the Euler Equations Michael Brenner, Sahand Hormoz, Alain Pumir We describe a potential mechanism for a singular solution of the Euler equation. The mechanism involves the interaction of vortex filaments, but occurs sufficiently quickly and at small enough scales that it could have plausibly evaded experimental and computational detection. Scaling estimates for the characteristics of this solution will be presented, as well as numerical simulations of the initial stages. [Preview Abstract] 
(Author Not Attending)

L3.00002: Existence and Smoothness of solution of NavierStokes equation on R3 Ognjen Vukovic NavierStokes equation has for a long time been considered as one of the greatest unsolved problems in three dimensions. This paper proposes a solution to the aforementioned equation on R3. It proves the existence and uniqueness of smooth solution. Firstly, the concept of turbulent solution is defined.It is proved that turbulent solutions become strong solutions after some time in NavierStokes set of equations. However in order to define the turbulent solution, the decay or blowup time of solution must be examined. Differential inequality was defined and it was proved that solution of NavierStokes equation exists in a finite time although it exhibits blowup solutions. The equation is introduced that establishes the distance between the strong solutions of NavierStokes equation and heat equation. As it is demonstrated, as the time goes to infinity, the solution of heat equation is identical to the solution of NS equation. As the solution of heat equation is defined in the heatsphere, after its analysis,it is proved that as the time goes to infinity, solution converges to the stationary state. The solution has a finite time and it exists when that implies that it exists and it is periodic. The aforementioned statement proves the existence and smoothness of solution of NS on R3. [Preview Abstract] 
Monday, November 23, 2015 4:31PM  4:44PM 
L3.00003: Kaluza's kinetic theory description of the classical Hall effect in a single component dilute gas within the ChapmanEnskog approximation A. SandovalVillalbazo, A.L. GarciaPerciante, A.R. SagacetaMejia Kinetic theory is used to establish the explicit form of the particle flux associated to the Hall effect for the case of a dilute single component charged gas, using the ChapmanEnskog method and the BGK approximation for the collision Kernel. It is shown that when the system evolves towards mechanical equilibrium, the standard treatment using the concept of external force fails to describe the Hall effect. It is also shown that the use of a fivedimensional curved spacetime in the description of the dynamics of the charged particle in the kinetic treatment (Kaluza's theory) formally solves the problem. The implications of this result are briefly discussed. [Preview Abstract] 
Monday, November 23, 2015 4:44PM  4:57PM 
L3.00004: Establishment of the thermoelectric effect in Kaluza's MHD through the kinetic theory A.R. SagacetaMejia, A.L. GarciaPerciante, A. SandovalVillalbazo The study of the behavior of charged gases in curved spacetimes is an active research area in which cross effects, such as thermoelectricity, have not been studied in depth. In our kinetic description of transport theory the electric charge is introduced into the fifth component of the particle velocity, following the idea first proposed by Kaluza in 1919. Using ChapmanEnskog's method, the first order in the gradients correction to the gas distribution function is established, noticing that some of the thermodynamic forces present in the system are associated with the spacetime curvature. It is shown that with this distribution function, it is possible to obtain the wellknown expressions that relate the heat flux with the electric field in a dilute gas, without resorting to the steady state approximation. This formalism corresponds to an extension of the result obtained for the case of the direct effect between the particle flux and the electric field within Kaluza's MHD (A. SandovalVillalbazo, A. R. SagacetaMej\'{\i}a, A. L. Garc\'{\i}a Perciante; Journal of NonEquilibrium Thermodynamics, 2015, Vol. 40, pp. 93101.) [Preview Abstract] 
Monday, November 23, 2015 4:57PM  5:10PM 
L3.00005: Does relativistic kinetic theory predict a viscous analog of the nonequilibrium generalization of Tolman's law? J.H. MondragonSuarez, D. BrunBattistini, A. SandovalVillalbazo, A.L. GarciaPerciante In this paper tensor transport processes present in singlecomponent dilute fluids are discussed within the framework of irreversible thermodynamics using elements of general relativity. The formalism suggests the existence of a tensor analog of Tolman's effect. In this case, the traceless symmetric part of the local hydrodynamic velocity gradient is compensated (in principle) with the terms containing sources of curvature in the case of null entropy production. This result is obtained only if the field effects are included in the treatment of the Boltzmann equation through the use of geodesics [1]. \\[4pt] [1] A. SandovalVillalbazo, A. R. SagacetaMej\'ia, A. L. Garc\'ia Perciante; Journal of NonEquilibrium Thermodynamics, 2015, Vol. 40, pp. 93101. [Preview Abstract] 
Monday, November 23, 2015 5:10PM  5:23PM 
L3.00006: Heat~dissipation~in relativistic single charged fluids A. L. GarciaPerciante, A. SandovalVillalbazo, D. BrunBattistini When the temperature of a fluid is increased its out of equilibrium behavior is significantly modified. In particular kinetic theory predicts that~the heat~flux is not solely driven by a temperature gradient but can also be coupled to other thermodynamic vector forces. We explore the nature of~heat~conduction in a single component charged fluid in special relativity, where the electromagnetic field is introduced as an external force. We obtain an electrothermal effect, similar to the mixture's crosseffect, which is not present in the nonrelativistic simple fluid. The general lines of the corresponding calculation will be shown, emphasizing the importance of reference frame invariance and the origin of the extra~heat~sources, in particular the role of the modified inertia and the difference in fluid's and molecules' proper times. The constitutive equation for the heat flux obtained using ChapmanEnskog's expansion in Marle's approximation will be analyzed together with the corresponding transport coefficients.The impact of this effect in the overall dynamics of the system here considered will be briefly discussed. [Preview Abstract] 
Monday, November 23, 2015 5:23PM  5:36PM 
L3.00007: Dynamical density functional theory for arbitraryshape colloidal fluids including inertia and hydrodynamic interactions Miguel A. DuranOlivencia, Ben Goddard, Serafim Kalliadasis Over the last few decades the classical densityfunctional theory (DFT) and its dynamic extensions (DDFTs) have become a remarkably powerful tool in the study of colloidal fluids. Recently there has been extensive research to generalise all previous DDFTs finally yielding a general DDFT equation (for spherical particles) which takes into account both inertia and hydrodynamic interactions (HI) which strongly influence nonequilibrium properties. The present work will be devoted to a further generalisation of such a framework to systems of anisotropic particles. To this end, the kinetic equation for the Brownian particle distribution function is derived starting from the Liouville equation and making use of Zwanzig's projectionoperator techniques. By averaging over all but one particle, a DDFT equation is finally obtained with some similarities to that for spherical colloids. However, there is now an inevitable translationalrotational coupling which affects the diffusivity of asymmetric particles. Lastly, in the overdamped (high friction) limit the theory is notably simplified leading to a DDFT equation which agrees with previous derivations. [Preview Abstract] 
Monday, November 23, 2015 5:36PM  5:49PM 
L3.00008: Solutions to the NavierStokes Equation in the complex plane Jonathan Mestel, Florencia Boshier A Stokes series is a theoretically attractive approach to solving the NavierStokes equations. Essentially the solution is expressed as a power series in the Reynolds number, $R_e$. At each order, a linear problem needs to be solved, providing a series representation of the solution for all $R_e$. This method was pioneered by Van Dyke in the 1970s. However, typically this series has a finite radius of convergence, and the solution has singularities at complex values of $R_e$. The behaviour of the series can be enhanced using a generalsied Pad\'e approximant technique. This method also predicts complex solution branches, and identifies bifurcation points to multiple solutions. Solutions branches for complex $R_e$ can be followed back onto the real $R_e$axis. It is shown that in general the NavierStokes equations have more than one complex solution even for low (real) $R_e$. The intricate structure of complex solutions is followed in detail for Dean flows, and new branches are presented. [Preview Abstract] 
Monday, November 23, 2015 5:49PM  6:02PM 
L3.00009: Experimental Confirmation of a Causal, Covariant, Relativistic Theory of Dissipative Fluid Flow Dillon Scofield, Pablo Huq Using newtonian viscous dissipation stress in covariant, relativistic fluid flow theories leads to a violation of the second law of thermodynamics and to acausality of their predictions. E.g., the Landau \& Lifshitz theory, a Lorentz covariant formulation, suffers from these defects. These problems effectively limit such theories to timeindependent flow r\'egimes. Thus, these theories are of little fundamental interest to astrophysical, geophysical, or thermonuclear flow modeling. We discuss experimental confirmation of the new geometrodynamical theory of fluids solving these problems (GTF, Fluid Dynamics, Research, 46, 055513,055514 (2014), Submitted 2015). This theory is derived from recent results of geometrodynamics showing current conservation implies gauge field creation; the vortex field lemma (Phys. Lett. A 374 347682 (2010)). [Preview Abstract] 
Monday, November 23, 2015 6:02PM  6:15PM 
L3.00010: On a difficulty in eigenfunction expansion solutions for the startup of fluid flow Ivan C. Christov Most mathematics and engineering textbooks describe the process of ``subtracting off'' the steady state of a linear parabolic partial differential equation as a technique for obtaining a boundaryvalue problem with homogeneous boundary conditions that can be solved by separation of variables (i.e., eigenfunction expansions). While this method produces the correct solution for the startup of the flow of, e.g., a Newtonian fluid between parallel plates, it can lead to erroneous solutions to the corresponding problem for a class of nonNewtonian fluids. We show that the reason for this is the nonrigorous enforcement of the startup condition in the textbook approach, which leads to a violation of the principle of causality. Nevertheless, these boundaryvalue problems can be solved correctly using eigenfunction expansions, and we present the formulation that makes this possible (in essence, an application of Duhamel's principle). The solutions obtained by this new approach are shown to agree identically with those obtained by using the Laplace transform in time only, a technique that enforces the proper startup condition implicitly (hence, the same error cannot be committed). [Preview Abstract] 
Monday, November 23, 2015 6:15PM  6:28PM 
L3.00011: Description of the nonequilibrium extension of Tolman's law in terms of kinetic theory: suppression of the acceleration term and the use of the geodesic in the treatment of Boltzmann's equation Dominique BrunBattistini, Jose Humberto MondragonSuarez, Alfredo SandovalVillalbazo, Ana Laura GarcĂaPerciante In 1936, Richard C. Tolman showed that in thermodynamic equilibrium a temperature gradient can be compensated by a gravitational potential gradient. In reference [1], in a linearized gravity approximation, Tolman's law was extended for inhomogeneous nonequilibrium systems, suggesting that the contribution of the gravitational field to heat flow can be seen as a cross effect. In this work this contribution to the heat flux for a dilute simple fluid in an isotropic Schwarzschild metric is analyzed. In this case, the effect of the field is contained in the covariant derivative, such that the molecules follow geodesics. The results show that the effect of the field on the heat flux does not vanish, in contrast with what is suggested by other authors [2]. [1] SandovalVillalbazo, A., GarciaPerciante, A. L. {\&} BrunBattistini D.; Phys Rev D 86, 085014 (2012) [2] Kremer, G. M.; J. Stat. Mech. P04016 (2013) [Preview Abstract] 
Monday, November 23, 2015 6:28PM  6:41PM 
L3.00012: The influence of inertia on the efflux velocity: From Daniel Bernoulli to a contemporary theory Andreas Malcherek In 1644 Evangelista Torricelli claimed that the outflow velocity from a vessel is equal to the terminal speed of a body falling freely from the filling level h, i.e. $v = \sqrt{2 g h}$. Therefore the largest velocities are predicted when the height in a vessel is at the highest position. As a consequence the efflux would start with the highest velocity directly from the initiation of motion which contradicts the inertia principle. In 1738 Daniel Bernoulli derived a much more sophisticated and instationary outflow theory basing on the conservation of potential and kinetic energy. As a special case Torricelli's law is obtained, when inertia is neglected and the cross section of the opening is small compared to the vessel's cross section. To the Authors knowledge, this theory was never applied or even mentioned in text books although it is superior to the Torricelli theory in many aspects. In this paper Bernoulli's forgotten theory will be presented. Deriving this theory using the state of the arts hydrodynamics results in a new formula $v = \sqrt{g h}$. Although this formula contradicts Torricelli's principle, it is confirmed by all kind of experiments stating that a discharge coefficient of about $\beta = 0.7$ is needed in Torricelli's formula $v = \beta \sqrt{2 g h}$. [Preview Abstract] 
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