Coherent Structures On A Rayleigh Benard Boundary Layer

Author : Parvathi Madathil Kooloth
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (139 download)

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Download or read book Moist Potential Vorticity and Coherent Structures in the Atmosphere written by Parvathi Madathil Kooloth and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two different types of atmospheric flows: flows with clouds and phase changes and Rayleigh-Bénard convection were studied in this thesis. Our efforts led to the identification of coherent structures associated with potential vorticity conservation in the moist atmosphere and heat transport in transitional Rayleigh-Bénard convection. Moist atmospheric flows [Kooloth et al., 2022b,a]: One of the most important conservation laws in atmospheric and oceanic science is conservation of potential vorticity. The original derivation is approximately a century old, in the work of Rossby and Ertel, and it is related to the celebrated circulation theorems of Kelvin and Bjerknes. However, the laws apply to idealized fluids, and extensions to more realistic scenarios have been problematic. Here, these laws are extended to hold with additional fundamental complexities, including salinity in the ocean, or moisture and clouds in the atmosphere. In the absence of these additional complexities, it is known that potential vorticity is conserved following each fluid parcel; here, for a salty ocean or cloudy atmosphere, the general conserved quantity is potential vorticity integrated over certain pancake-shaped volumes. Furthermore, the conservation laws are also related to a symmetry in the Lagrangian, which brings a connection to the symmetry-conservation relationships seen in other areas of physics. Rayleigh-Bénard convection [Kooloth et al., 2021]: For two-dimensional (2D) Rayleigh-Bénard convection, classes of unstable, steady solutions were previously computed using numerical continuation [Waleffe et al. [2015], Sondak et al. [2015]]. The 'primary' steady solution bifurcates from the conduction state at Ra 9́8 1708, and has a characteristic aspect ratio (length/height) of approximately 2. The primary solution corresponds to one pair of counterclockwise-clockwise convection rolls with a temperature updraft in between and an adjacent downdraft on the sides. By adjusting the horizontal length of the domain, Waleffe et al. [2015], Sondak et al. [2015] also found steady, maximal heat transport solutions, with characteristic aspect ratio less than 2 and decreasing with increasing Ra. Compared to the primary solutions, optimal heat transport solutions have modifications to boundary layer thickness, the horizontal length scale of the plume, and the structure of the downdrafts. The current study establishes a direct link between these (unstable) steady solutions and transition to turbulence for Pr = 7 and Pr = 100. For transitional values of Ra, the primary and optimal-heat-transport solutions both appear prominently in appropriately-sized sub-fields of the time-evolving temperature fields. For Ra beyond transitional, our data analysis shows persistence of the primary solution for Pr = 7, while the optimal heat transport solutions are more easily detectable for Pr = 100. In both cases Pr = 7 and Pr = 100, the relative prevalence of primary and optimal solutions is consistent with the Nu vs. Ra scalings for the numerical data and the steady solutions.