Institute for Mathematics and its Applications - nonlinear instability
http://www.ima.umn.edu/Tags/nonlinear-instability
enNonlinear instabilities in multilayer shear flows
http://www.ima.umn.edu/2017-2018.3/W3.12-16.18/26728
<div class="field field-name-field-time field-type-datetime field-label-hidden"><div class="field-items"><div class="field-item even"><span class="date-display-single">Tuesday, March 13, 2018 - <span class="date-display-start" property="dc:date" datatype="xsd:dateTime" content="2018-03-13T10:00:00-05:00">10:00am</span> - <span class="date-display-end" property="dc:date" datatype="xsd:dateTime" content="2018-03-13T10:50:00-05:00">10:50am</span></span></div></div></div><div class="field field-name-field-location field-type-text field-label-hidden"><div class="field-items"><div class="field-item even">Lind 305</div></div></div><div class="field field-name-field-speakers field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><a href="https://www.imperial.ac.uk/people/d.papageorgiou" target="_blank">Demetrios Papageorgiou</a> (Imperial College London)</div></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"><div class="tex2jax">This talk will be in two parts. The first will describe some recent results<br />on the stability of multilayer shear flows of three or more immiscible viscous<br />fluids caused to flow by gravity and/or a pressure gradient. There are now at<br />least two free boundaries and asymptotic solutions will be described that<br />yield a system of coupled partial differential equations for the interfacial positions.<br />Some subtleties in the weakly nonlinear asymptotics will be pointed out.<br />The equations generically support instabilities even at zero Reynolds numbers<br />and these emerge physically from a resonance between the interfaces and manifest<br />themselves mathematically through hyperbolic to elliptic transitions of the flux part<br />of the equations. We use the theory of 2x2 systems of conservation laws to derive<br />a nonlinear stability criterion that can tell us whether a system which is linearly stable,<br />can (i) become nonlinearly unstable, i.e. a large enough initial condition produces<br />a large time nonlinear response, or (ii) remains nonlinearly stable, i.e. the solution decays<br />to zero irrespective of the initial amplitude of the perturbation.<br />Having described weakly nonlinear solutions we turn to fully nonlinear deformations are also <br />in the large surface tension limit giving rise to coupled Benney type equations. Their fluxes also<br />support hyperbolic-elliptic transitions and numerical solutions will be described giving<br />rise to intricate nonlinear stable traveling waves. Differences between weakly and strongly<br />nonlinear flows will be described to guide ideas for theory of coupled Benney equations.<br />The second part is concerned with three-dimensional instabilities of electrified falling<br />film flows and in particular the multidimensional electrified Kuramoto-Sivashinsky<br />equation which is the first in a hierarchy of nonlinear models. We will mostly present<br />computations and end with words of caution in using 2D models instead of 3D ones<br />in the presence of electric fields.</div></div></div></div><div class="field field-name-field-keywords field-type-taxonomy-term-reference field-label-above"><div class="field-label">Keywords: </div><div class="field-items"><div class="field-item even"><a href="/Tags/multilayer-flows" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">multilayer flows</a></div><div class="field-item odd"><a href="/Tags/nonlinear-instability" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">nonlinear instability</a></div><div class="field-item even"><a href="/Tags/electrified-falling-films" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">electrified falling films</a></div></div></div>Thu, 25 Jan 2018 16:15:01 +0000Anonymous41448 at http://www.ima.umn.edu