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The approach is based on a derivative free, energetic formulation using one functional for elastic energy storage and one for the dissipation distance.
The latter is derived from a dissipation potential defining the dissipation distance between internal states and hence the Wasserstein distance between Young measures.
Modifications of the regularizing term and of the dissipation distance are introduced and their effect on the global response is investigated.
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Large-scale circular waves with two negative peaks, a large propagation velocity (3,457 m/s and 783 m/s), and strong dissipation (travelling distance is about 1,000 km) propagated in a radial direction from 06:00 UT to 06:15 UT.
It is found that the difference between 2D (χr) and 3D scalar dissipation increases with axial distance along the flame such that the ratio χ/χr may be as high as 2.6.
This model predicts the existence of multipeaked solitons which can travel long distances without dissipation.
This is expected as the proposed method ignores bedrock energy dissipation over the 80 km distance between FSK019 and MYG006.
This asymptotic behaviour is related to a functional inequality, which links the distance with its dissipation and ensures a spectral gap in Wasserstein distance.
Results of experiments are compared with the classical hydraulic jump, and significant effect of tall sill on dissipation of energy in shorter distance was confirmed.
By focusing energy dissipation within a very narrow distance in the regions adjacent to the screen, it was possible to generate local energy dissipation rates as high as 40,000 W/kg while maintaining the specific energy consumption rates below 0.2 kWh/t of liquid processed.
For illustrative purposes, it is helpful to compare the radiative "habitable" zone (HZ) to the "tidal" zone, the orbital distance at which tidal dissipation is likely to dominate the internal heat budget of the planet.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com