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The hydro-kinetic theory of liquid helium II


Goodman, Seymour Evan (1970) The hydro-kinetic theory of liquid helium II. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/X8EM-S579.


In Part I the kinetic theory of excitations in flowing liquid He II is developed to a higher order than that carried out previously, by Landau and Khalatnikov, in order to demonstrate the existence of non-equilibrium terms of a new nature in the hydrodynamic equations. It is then shown that these terms can lead to spontaneous destabilization in counter currents when the relative velocity of the normal and super fluids exceeds a critical value that depends on the temperature, but not on geometry. There are no adjustable parameters in the theory. The critical velocities are estimated to be in the 14-20 m/sec range for T ≤ 2.0° K, but tend to zero as T → T_λ. The possibility that these critical velocities may be related to the experimentally observed "intrinsic" critical velocities is discussed.

Part II consists of a semi-classical investigation of rotonquantized vortex line interactions. An essentially classical model is used for the collision and the behavior of the roton in the vortex field is investigated in detail. From this model it is possible to derive the HVBK mutual friction terms that appear in the phenomenalogical equations of motion for rotating liquid He II. Estimates of the Hall and Vinen B and B' coefficients are in good agreement with experiments. The claim is made that the theory does not contain any arbitrary adjustable parameters.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Applied Mathematics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Saffman, Philip G.
Thesis Committee:
  • Unknown, Unknown
Defense Date:23 April 1970
Record Number:CaltechTHESIS:04032013-114325644
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7578
Deposited By: Benjamin Perez
Deposited On:03 Apr 2013 19:55
Last Modified:09 Nov 2022 19:20

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