Session HL: Waves II, Abstract no. HL.00002published_or_final_versio

Chow, KW

Ding, E

Grimshaw, RHJ

Shek, CM

HKU Scholars Hub

Title Interactions of breathers and solitons of the extended Korteweg- de Vries equationAuthor(s) Shek, CM; Grimshaw, RHJ; Ding, E; Chow, KWCitation The 58th Annual Meeting of the Division of Fluid Dynamics,Chicago, IL., 20-22 November 2005.Issued Date 2005URL http://hdl.handle.net/10722/57139Rights American Physical Society Bulletin. Copyright © AmericanPhysical Society.1:20PM HK.00001 A continuum model with microstructural evolution for Stokesian suspen-sions, viscoplastic dispersions and granular media , JOE GODDARD, University of California, San Diego — A special case ofthe “thixotropic” fluid proposed several years ago by this author (J. NonNewtonian Fluid Mech. 14 141-160,1984) is explored as a plausible model for the flowof homogeneous particle suspensions and dense granular media. The effect of deformation history is described by the shear-induced evolution of a second-rank“fabric” tensor, which serves to define a pair of non-negative fourth-rank tensors for viscosity and plasticity. The viscous model predicts qualitatively most ofthe time-dependent viscous shear-stress and normal-stress effects observed experimentally in Stokesian suspensions. The addition of plastic terms allows foryield stress arising from mechanical contact between particles, and the purely plastic form provides a model for quasi-static deformation of dry granular media.Addition of viscous effects to the latter provides a generalization of models currently being employed to describe dense, rapid granular flows, where the relevantmicrostructural time scale is associated with granular micro-inertia. A brief consideration is given to non-homogeneous (Acrivos-Leighton) models, of a typethat allow for particle segregation and possibly for material instability.1:33PM HK.00002 The rise velocity and shape of an air bubble moving in HASE fluid , E. SOTO,C. GOUJON, T. BEHAGHEL, R. ZENIT, IIM-UNAM, Mexico — Experiments were conducted to determine the shape and the rise velocity of an air bubblemoving in a HASE fluid. These type of non Newtonian materials can be classified as associative fluids, because their internal structure is formed by hydrophobicmolecules which associate or dissociate as a result of flow. In particular, the liquid used in this investigation has a nearly constant shear viscosity for a widerange of shear rates but shows significant elasticity above a certain critical shear rate. Millimetric size bubbles were released from rest in a tall cylindricalcontainer. Two types of images were obtained: high resolution photographs, from which the bubble shape and volume were obtained; and, low resolution highspeed videos were used to measure the bubble velocity. We found that the bubble velocity increases with the bubble volume; however, a sudden increase of thebubble velocity is observed as the bubble volume reaches a critical value. This phenomena, known as the bubble velocity discontinuity, has been observed inother non Newtonian fluids but, to our knowledge, has never been reported for associative fluids. Additionally, we identified that a significant change of thebubble shape occurs along with the appearance of the velocity discontinuity. Moreover, by performing PIV measurements we are able to relate the appearanceof the velocity jump with values of the local shear rate at which the elasticity of the fluid becomes important.1:46PM HK.00003 Electrorheology of single wall carbon nanotubes/silicone oil suspensionsunder AC fields , CHEN LIN, JERRY W. SHAN, Rutgers University — Electrorheological properties of single wall carbon nanotubes (SWNTs)suspended in silicone oil are experimentally investigated in this work. Nanotube alignment and the formation of strands and chains of nanotubes are observedin the suspensions when an alternating current (AC) electric field is applied. The rheological measurements show that the nominal viscosity of a 0.002%mass-fraction SWNT/silicone oil suspension increases by more than 15% at low shear rates under an AC field. The relationship between stress and strain rateis investigated for varying electric-field strengths and suspension concentrations.1:59PM HK.00004 Dynamics of nematic liquid crystal polymers in coupled flow and magneticfield , QI WANG, Florida State University, M.G. FOREST, UNC-Chapel Hill, RUHAI ZHOU, Old Dominion University, HONG ZHOU, Naval PostgraduateSchool, SARTHOK SIRCAR, Florida State University — We study the hydrodynamics of the nematic liquid crystals in coupled flow and magnetic field. Wefocus on two prototypes of the idealized flow geometries: general linear planar flows and elongational flows. For both flows, we give a complete flow phasediagram for all flow strength and the strength of the imposed magnetic field. For the elongational flows, we show rigorously that the magnetic field mustcoincide with one of the principle axes of the second moment of the probability density function for the distribution of the nematic polymers.2:12PM HK.00005 The application of non-Newtonian models to thin film flow , TIM MYERS, Universityof Cape Town — In this talk I will describe an investigation into the use of lubrication models on thin film flow. Power law, Ellis and Carreau models will becompared for free surface flow and flow within a channel. It will be shown that the Ellis law (or a slight modification) can give very similar viscosity curves toCarreau. The three models will then be compared for thin film flow with a constant height free surface. For low shear rates the power law model can give veryinaccurate predictions. Having shown Carreau and Ellis may produce similar results I will then study flow in a channel for Ellis and power law fluids. Again thepower law can give inaccurate results due to the high viscosity around the turning point for the velocity.Monday, November 21, 2005 1:20PM - 2:25PM —Session HL Waves II Hilton Chicago Astoria1:20PM HL.00001 The Effects of Surfactants on Wind Waves1 , X. LIU, M. TAVAKOLINEJAD, J.H. DUNCAN,University of Maryland — The effects of surfactants on wind waves are studied experimentally in a tank that is 11.8 m long, 1.1 m wide and 1.8 m high. Thewater depth is 1.0 m and the top 0.8 meters of the tank contains air flowing with speeds up to 10 m/s. A mechanical wave maker, which resides at the upwindend of the tank, is used in some cases to superimpose a monochromatic wavetrain with frequencies of about 2 Hz on the wind wave system. Wave profilesare measured along the center plane of the tank with an LIF technique that utilizes a high-speed digital camera. The measurement system is mounted on aninstrument carriage that can be set to move along the tank with various speeds. Measurements were performed with clean water and with water mixed withTriton X-100, a soluble surfactant. The results show that in clean water strong and active gravity-capillary wave phenomena are observed at the leeward sideof wind wave crests. In the presence of Triton X-100, these capillary wave phenomena become weaker and eventually disappear as the surfactant concentration(Triton X-100) is increased. The detailed experiments to quantify these features are undergoing.1Supported by the Ocean Sciences Division of the National Science Foundation1:33PM HL.00002 Interactions of breathers and solitons of the extended Korteweg de Vriesequation1 , C.M. SHEK, University of Hong Kong, R.H.J. GRIMSHAW, Loughborough University, E. DING, K.W. CHOW, University of Hong Kong —A popular model for the evolution of weakly nonlinear, weakly dispersive waves in the ocean is the extended Korteweg – de Vries equation (eKdV), whichincorporates both quadratic and cubic nonlinearities. The case of positive cubic nonlinearity allows for both solitons of elevation and depression, as well asbreathers (pulsating modes). Multi-soliton solutions are computed analytically, and will yield expressions for breather-soliton interactions. Both the soliton andbreather will retain their identities after interactions, but suffer phase shifts. However, the details of the interaction process will depend on the polarity of theinteracting soliton, and have been investigated by a computer algebra software. This highly time dependent motion during the interaction process is importantin nonlinear science and physical oceanography. As the dynamics of the current and an evolving internal oceanic tide can be modeled by eKdV, this knowledgeis relevant to the temporal and spatial variability observed in the oceanic internal soliton fields.1supported by Research Grants Council HKU7184/04E, 7123/05E

Interactions of breathers and solitons of the extended Korteweg - de Vries equation

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Interactions of breathers and solitons of the extended Korteweg - de Vries equation

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