Jump to content

Landau derivative

From Wikipedia, the free encyclopedia

In gas dynamics, the Landau derivative or fundamental derivative of gas dynamics, named after Lev Landau who introduced it in 1942,[1][2] refers to a dimensionless physical quantity characterizing the curvature of the isentrope drawn on the specific volume versus pressure plane. Specifically, the Landau derivative is a second derivative of specific volume with respect to pressure. The derivative is denoted commonly using the symbol or and is defined by[3][4][5]

where

is the sound speed;
is the specific volume;
is the density;
is the pressure;
is the specific entropy.

Alternate representations of include

For most common gases, , whereas abnormal substances such as the BZT fluids exhibit . In an isentropic process, the sound speed increases with pressure when ; this is the case for ideal gases. Specifically for polytropic gases (ideal gas with constant specific heats), the Landau derivative is a constant and given by

where is the specific heat ratio. Some non-ideal gases falls in the range , for which the sound speed decreases with pressure during an isentropic transformation.

See also

[edit]

References

[edit]
  1. ^ 1942, Landau, L.D. "On shock waves" J. Phys. USSR 6 229-230.
  2. ^ Thompson, P. A. (1971). A fundamental derivative in gasdynamics. The Physics of Fluids, 14(9), 1843-1849.
  3. ^ Landau, L. D., & Lifshitz, E. M. (2013). Fluid mechanics: Landau And Lifshitz: course of theoretical physics, Volume 6 (Vol. 6). Elsevier.
  4. ^ W. D. Hayes, in Fundamentals of Gasdynamics, edited by H. W. Emmons (Princeton University Press, Princeton, N.J., 1958), p. 426.
  5. ^ Lambrakis, K. C., & Thompson, P. A. (1972). Existence of real fluids with a negative fundamental derivative Γ. Physics of Fluids, 15(5), 933-935.