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Turbulent diffusion is the transport of mass, heat, or momentum within a system due to random and chaotic time dependent motions. [1] It occurs when turbulent fluid systems reach critical conditions in response to shear flow, which results from a combination of steep concentration gradients, density gradients, and high velocities.
The transport of mass, energy, and momentum can be affected by the presence of external sources: An odor dissipates more slowly (and may intensify) when the source of the odor remains present. The rate of cooling of a solid that is conducting heat depends on whether a heat source is applied.
A turbulent flow is characterized by a hierarchy of scales through which the energy cascade takes place. Dissipation of kinetic energy takes place at scales of the order of Kolmogorov length η, while the input of energy into the cascade comes from the decay of the large scales, of order L. These two scales at the extremes of the cascade can ...
The compressible Euler equations consist of equations for conservation of mass, balance of momentum, and balance of energy, together with a suitable constitutive equation for the specific energy density of the fluid. Historically, only the equations of conservation of mass and balance of momentum were derived by Euler.
For isolated systems (closed to all mass and energy exchange), mass never disappears in the center of momentum frame, because energy cannot disappear. Instead, this equation, in context, means only that when any energy is added to, or escapes from, a system in the center-of-momentum frame, the system will be measured as having gained or lost ...
For example, the stress–energy tensor is a second-order tensor field containing energy–momentum densities, energy–momentum fluxes, and shear stresses, of a mass-energy distribution. The differential form of energy–momentum conservation in general relativity states that the covariant divergence of the stress-energy tensor is zero: T μ ...
Total energy is the sum of rest energy = and relativistic kinetic energy: = = + Invariant mass is mass measured in a center-of-momentum frame. For bodies or systems with zero momentum, it simplifies to the mass–energy equation E 0 = m 0 c 2 {\displaystyle E_{0}=m_{0}c^{2}} , where total energy in this case is equal to rest energy.
Analysis paralysis is a critical problem in athletics. It can be explained in simple terms as "failure to react in response to overthought". A victim of sporting analysis paralysis will frequently think in complicated terms of "what to do next" while contemplating the variety of possibilities, and in doing so exhausts the available time in which to act.