ISSN 1027-4510, Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques, 2017, Vol. 11, No. 4, pp. 749–755. © Pleiades Publishing, Ltd., 2017.
Original Russian Text © V.I. Vysotskii, A.A. Kornilova, T.B. Krit, M.V. Vysotskyy, 2017, published in Poverkhnost’, 2017, No. 7, pp. 74–81.
On the Long-Range Detection and Study of Undamped Directed
Temperature Waves Generated during the Interaction
between a Cavitating Water Jet and Targets
V. I. Vysotskii
*, A. A. Kornilova
, T. B. Krit
, and M. V. Vysotskyy
Taras Shevchenko National University of Kyiv, Kyiv, 01033 Ukraine
Moscow State University, Moscow, 119991 Russia
Received December 27, 2016
Abstract―The features of the propagation of undamped thermal (temperature) waves in air are investigated.
The presence of these waves is a consequence of solution of the heat equation taking into account the relax-
ation of local thermal perturbation. It is shown that such waves can exist only in media with a finite (nonzero)
time of local thermal relaxation, and their frequencies are determined by this time. The time of relaxation in
air depends on the gas composition, its temperature and increases with a decrease in pressure. Under normal
conditions, the minimum frequency of undamped waves in air corresponds to 70–80 MHz. One of the meth-
ods for exciting these waves is associated with pulsed heating of the surface of a medium bordering air. Pulsed
heating on account of the application of shock waves generated during water jet cavitation is used. It is shown
for the first time that these waves with frequencies in the range of 70–500 MHz can propagate in air without
damping over a distance of up to 2 m.
Keywords: thermal (temperature) waves, shock waves, undamped waves, interaction of waves on a surface,
acoustic detector, cavitation
DOI: 10.1134/S10274510170 40140
INTRODUCTION: SOLVING THE HEAT
EQUATION FOR A SYSTEM WITH THERMAL
RELAXATION AND THE PHYSICAL BASIS
OF UNDAMPED THERMAL WAVES
The traditional concept of the laws of thermody-
namics is based on the fairly substantiated assumption
that the propagation of thermal excitations is of a
purely diffusive (incoherent and irreversible) nature.
The same concepts typically relate to the particular
features of thermal (temperature) wave propagation
which is related directly to heat equations.
Mathematical description of these processes is
based on the joint usage of two basic equations: the
Fourier law for a nonstationary heat f lux q(r, t)
and the equation of continuity (really, the law of
energy conservation for a local region), which, in the
absence of distributed heat sources in a medium with
the volume density ρ and the heat capacity , has the
From these two equations, the classical parabolic
partial differential equation for a spatial-temporal
variation in the temperature field follows:
More detailed analysis shows that this “standard”
way is not versatile and implicitly relies on two import-
ant assumptions: the principle of locality and the
hypothesis of local thermodynamic equilibrium.
The first of them makes it possible to pass from the
equation of energy conservation in the integral form to
that in the differential (local) form, while the second
one assumes (without adequate grounds) that the
non-equilibrium system under study can be presented
as many small locally-balanced subsystems. In the
explicit form, this circumstance manifests itself in the
structure of Eq. (2), which can be interpreted from the
viewpoint of synchronicity (simultaneity) of the flux
of thermal energy q(r, t) and a change in locally homo-
geneous temperature. It is obvious that the last
assumption is valid only for rather slow processes, in
which the time (τ) of subsystem relaxation to the equi-
librium state is significantly shorter than the charac-
teristic time of a particular process, which determines
the thermal-field characteristics (including the dura-
(,) grad( (,))tTt=−λqr r
div ( , ).
div grad[ ( , )] .