The purpose of this paper is to study how the geometry and the spatial distribution of energy fluctuations of different length scales in a spiral vortex layer are related to each other in a time-dependent way. The numerical solution of Krasny [J. Comput. Phys. 65, 292 (1986)], corresponding to the development of the Kelvin-Helmholtz instability, is analyzed in order to determine some geometrical features necessary for the analysis of Lundgren's unstrained spiral vortex. The energy distribution of the asymptotic solution of Lundgren characterized by a similar geometry is investigated analytically (1) in the wavelet radius-scale space, with a wavelet selective in the radial direction, and (2) in the wavelet azimuth-scale space, with a wavelet selective in the azimuthal direction. Energy in the wavelet radius-scale space is organized in "blobs" distributed in a way determined by the Kolmogorov capacity of the spiral D(K) in [1,2] (which determines the rate of accumulation of spiral turns). As time evolves these blobs move towards the small scale region of the wavelet radius-scale space, until their scale is of the order of the diffusive length scale square root[nut], where t is the time and nu is the kinematic viscosity. In contrast, energy in the wavelet azimuth-scale space is not localized, and is characterized by a shear-augmented viscous cutoff proportional to sqaure root[nut(3)]. An accelerated viscous dissipation of the enstrophy and energy of Lundgren's spiral vortex is found for D(K) > 1.75, but not for D(K) < or =1.75.
2006-07-29 23:58:05
·
answer #1
·
answered by Anonymous
·
0⤊
0⤋
A four sided figure where all sides are equal in length. Also, if you square a number you multiply it by itself so, 5 squared is 5 times 5 so 5 squared is 25.
2006-07-26 11:35:06
·
answer #2
·
answered by Anonymous
·
0⤊
0⤋
According to the best MK TEXT Books here in Uganda a square has many meaning and here are some of them
1, in geometry it means a four sided polygon with equal sides
2, while in arithmetic it means multiplying a number by its self e,g 2x2=4 so two squared is equal to four
2006-07-26 11:51:05
·
answer #3
·
answered by abiola 1
·
0⤊
0⤋
square means a number times it self like 2 squared means 2 times 2
2006-07-26 11:38:42
·
answer #4
·
answered by china 1
·
0⤊
0⤋
The means of square in mathematics is the both sides are equal
2006-07-26 11:37:13
·
answer #5
·
answered by Bobby k 1
·
0⤊
0⤋
it depends:
in geometry it typically means a four sided 2-dimensional shape where all sides are equal in length and the angles connecting segments are all 90 degrees
In general arithmetic it means to multiply the number by itself... for example the square of 2 is 4, 5 is 25 etc.
2006-07-26 11:37:42
·
answer #6
·
answered by David K 1
·
0⤊
0⤋
multipy the number by itself.
ie. the square of 4 means 4 X 4. that would be 16!
the square of 8 means 8 X 8. that would be 64!
2006-07-26 12:39:34
·
answer #7
·
answered by ndyou 3
·
0⤊
0⤋
A square is a quadrilateral, that is a closed figure with four sides.
The length of it's four sides are equal; also the measure of it's four angles are equal, i.e. 90degrees. The opposite sides of a square are parralel to each other. And it's adjacent sides are perpendicular to each other,i.e. the angle between them is 90 degrees. The sum of it's angles is 360 degrees, like any other quadrilateral, and the sum of it's opposite angles is 180 degrees.
P.S. I hope it's not complex for you.
2006-07-26 11:40:22
·
answer #8
·
answered by Anonymous
·
0⤊
0⤋
A 4-sided 2-dimensional object with sides of equal length and opposite sides are parallel to one another.
2006-07-26 12:33:52
·
answer #9
·
answered by Anonymous
·
0⤊
0⤋
A 4-sided 2-dimensional object with sides of equal length and opposite sides are parallel to one another.
2006-07-26 11:35:39
·
answer #10
·
answered by Blunt Honesty 7
·
0⤊
0⤋