Scaling laws of compressible turbulence

Abstract

The spatial scaling laws of velocity kinetic energy spectrum for compressible turbulence flow and its density-weighted counterpart have been formulated in terms of wavenumber, dissipation rate and Mach number by using dimensional analysis. We have applied the Barenblatt's incomplete similarity theory to both kinetic and density-weighted energy spectrum and showed that, within the initial subrange, both energy spectrums approach the -5/3 power law of the wavenumber, when the Mach number M tends to be naught, unity and infinity, respectively.

Universal Scaling Law for the Velocity of Dominoes Toppling Motion

“…Szirtes and Rozsa [6] studied domino by using dimensional analysis [15][16][17][18][19] for a domino with equal thickness δ, separation λ and height h. Hence the five variables and their diemsion are listed in Table I below:…”

Universal Scaling Laws of Origami Paper Springs

“…It is clear that this problem has no analytical solution, so numerical solutions and experimental methods have to be done approximately. However, since the numerical and experimental results can only be obtained for a specific case, it is very hard to predict the general scaling trends on the problem by using limited numerical results, it would be a natural attempts to find an alternative way -dimensional analysis [19][20][21][22][23].…”

“…Often, dimensional analysis is conducted without any explicit consideration for the actual equations that may govern a physical phenomenon. Only the variables that affect the problem are considered [19][20][21][22][23].…”

“…In the above relation, there are 7 quantities, two of them are dimensionless. Since only 3 dimensional basis L, M, T are used, so according to dimensional analysis [19,21], Eq. 2 produces two dimensionless quantities Π, the first one is:…”

“…Based on the Buckingham Π theorem [19][20][21], the scaling law must of the paper spring be expressed as follows:…”