dissipationrate

Dissipation rate is the rate at which energy is irreversibly lost from a system and converted into heat by dissipative processes such as viscosity, thermal conduction, or friction. It is a key concept in thermodynamics and fluid dynamics for describing how stored or transported energy diminishes over time.

In turbulence, the dissipation rate per unit mass, often denoted ε, represents how quickly turbulent kinetic energy is converted into internal energy through viscous stresses. The dissipation has units of m^2 s^-3. A common local expression is ε = 2ν s_ij s_ij, where ν is the kinematic viscosity and s_ij is the rate-of-strain tensor defined by s_ij = 1/2(∂u_i/∂x_j + ∂u_j/∂x_i). The average value of ε is a central quantity in Kolmogorov’s theory of turbulence and governs the transfer of energy from large to small scales.

The concept also appears in other contexts. Per unit volume, the viscous dissipation rate is Φ = 2μ s_ij s_ij, where μ is dynamic viscosity. In heat transfer, dissipation may refer to the rate at which thermal energy is dissipated as heat due to conduction and internal friction. In electrical or magnetohydrodynamic settings, dissipation can be quantified by power losses such as J·E.

Measurement and estimation of dissipation rate can be experimental, via velocity field measurements and structure functions, or computational, through direct calculation from velocity gradients in simulations. Its value influences energy balance, flow stability, and heat generation, making it a fundamental parameter across engineering, physics, and astrophysical applications.