Physics of Soft Impact and Cratering by Hiroaki Katsuragi

By Hiroaki Katsuragi

This ebook specializes in the effect dynamics and cratering of sentimental topic to explain its significance, trouble, and huge applicability to planetary-related difficulties. A complete advent to the dimensional research and constitutive legislation which are essential to speak about influence mechanics and cratering is first supplied. Then, specific insurance is given to the impression of granular subject, that's essentially the most an important elements for geophysics. whereas granular topic exhibits either solid-like and fluid-like behaviors, neither sturdy nor fluid dynamics is enough to absolutely comprehend the physics of granular topic. in an effort to show its primary houses, huge influence exams were conducted lately. the writer unearths the findings of those fresh experiences in addition to what continues to be unsolved when it comes to influence dynamics. effect crater morphology with a number of delicate subject affects is also mentioned intensively. a variety of experimental and observational effects as much as the hot Itokawa asteroid’s terrain and nanocrater are reviewed and defined generally via dimensional research. the writer discusses views of the relation among smooth subject physics and planetary technology, since it is a crucial step in the direction of unifying physics and planetary technology, in either one of which fields crater morphology has been studied independently.

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Let us begin with the Navier-Stokes equation derived in the previous section. Here we consider an incompressible fluid without body forces ( a D 0). Then, from Eqs. 36) All the quantities and operators in Eq. 36) have their own units. For instance, velocity has a unit of (length)/(time), namely, m/s in the SI unit system. A unit such as m/s is an artificial rule to measure a physical quantity. As discussed in Sect. 1, the governing physical law must be free from such an artificial rule. Of course, 28 2 Scaling and Dimensional Analysis Eq.

5). The relevant physical quantities in this stage are the released energy Eb , the radius of the blast wave front Rb , atmospheric density , its pressure p, its viscosity Á, and timescale to . 4. 4, three possibly relevant dimensionless numbers can be derived because the number of independent dimensionless numbers m is computed as m D n k D 6 3. 60) ˘1 , ˘2 , and ˘3 can be related by the form of Eq. 61) The relation of Eq. 61) is obtained routinely using the ˘ -groups method. We need additional deeper physical considerations to extract useful insight from the set of (˘1 , ˘2 , ˘3 ).

While Di (the impactor’s diameter) is usually employed for p the characteristic length scale of Re , here we use a particular length scale, l D U= g=Di , to consider the gravitational effect. Substituting this l, D t , and U D v0 into Eq. 41), we obtain the right-hand side of Eq. 83) as a type of Re . Note that Eq. 83) is an empirical relation and holds only for the impact drag. For the steady-state drag, CD is inversely proportional to Re (in the low Re ; Eq. 74)) or almost independent of Re (at high Re regime).

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