Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Articles Article Faculty Publications -Articles Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource The Rayleigh-Bard problem for water with maximum density effects Description An account of the resource Linear stability and weakly nonlinear stability analyses are developed for Rayleigh-Bard convection in water near 3.98 C subject to isothermal boundary conditions. The density-temperature relationship (equation of state) is approximated by a cubic polynomial, including linear, quadratic, and cubic terms. The continuity equation, the Navier-Stokes momentum equation, the equation of state, and the energy equation constitute the governing system. Linear stability analysis is used to investigate how the maximum density property of water affects the onset of convective instability and the choice of unstable wave number for four different types of boundary conditions. Then, a weakly nonlinear stability study is done using the spectral Fourier method for isothermal tangential stress-free boundary conditions to quantify the heat transport of the system and demonstrate the transition from regular/periodic convection to chaotic convection. A Stuart-Ginzburg-Landau equation is obtained using the multiscale expansion method. Streamlines and isotherms are presented and analyzed. The influence of maximum density has been shown to delay the onset of instability and is, therefore, a stabilizing mechanism for thermal instability. Due to the maximum density, the onset of chaotic convection is also delayed. Among four different boundaries, the impermeable rigid boundaries require the highest Rayleigh number for instability to begin. Increasing boundary temperatures advance the onset of chaotic convection and improve the heat transport situation. 2023 Author(s). Creator An entity primarily responsible for making the resource Basavarajappa M.; Bhatta D. Source A related resource from which the described resource is derived Physics of Fluids, Vol-35, No. 7 Publisher An entity responsible for making the resource available American Institute of Physics Inc. Date A point or period of time associated with an event in the lifecycle of the resource 2023-01-01 Identifier An unambiguous reference to the resource within a given context <a href="https://doi.org/10.1063/5.0155687" target="_blank" rel="noreferrer noopener">https://doi.org/10.1063/5.0155687</a> <br /><br /><a href="https://www.scopus.com/inward/record.uri?eid=2-s2.0-85165433727&amp;doi=10.1063%2F5.0155687&amp;partnerID=40&amp;md5=f5dfe2e3a559fca6c0aee9f292acc928" target="_blank" rel="noreferrer noopener">https://www.scopus.com/inward/record.uri?eid=2-s2.0-85165433727&amp;doi=10.1063%2f5.0155687&amp;partnerID=40&amp;md5=f5dfe2e3a559fca6c0aee9f292acc928</a> Rights Information about rights held in and over the resource Restricted Access Relation A related resource ISSN: 10706631; CODEN: PHFLE Format The file format, physical medium, or dimensions of the resource Online Language A language of the resource English Type The nature or genre of the resource Article Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Basavarajappa M., School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, Edinburg, 78539, TX, United States, Center of Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bangalore, India; Bhatta D., School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, Edinburg, 78539, TX, United States