Physical Oceanography, Vol.
RECONSTRUCTION OF THE LINEAR DISTRIBUTION OF THE SQUARED
BUOYANCY FREQUENCY ACCORDING TO THE KNOWN DISPERSION
PROPERTIES OF THE FIELD OF INTERNAL WAVES
É. N. Potetyunko,
L. V. Cherkesov,
and D. S. Shubin
We propose a method for the solution of the inverse problem of reconstruction of the vertical
stratification of density in the ocean according to the known dispersion curves for internal gravity
waves. For the stratification of density modeled by a linear distribution, we determine the accu-
racy of its reconstruction for values of the frequency of oscillations and wave numbers given
with different degrees of accuracy. The posed problem is studied in the Boussinesq approxima-
tion for two traditionally used types of boundary conditions on the surface of the fluid. We de-
duce dispersion equations and focus our attention on their asymptotic analysis. An asymptotic
solution of the inverse problem is constructed and its sensitivity to the degree of accuracy of the
input data is investigated.
The investigation of the process of propagation of internal waves in the ocean is one of the principal prob-
lems of oceanology. To a great extent, this is explained by a significant role played by internal waves in the pro-
cesses of horizontal and vertical exchange in the ocean. Note that the existence of stable stratification of density
corresponding to the increase in the density of water in the direction of the gravity force is the principal factor
responsible for the existence of internal waves in the ocean and, therefore, the character and behavior of internal
gravity waves are largely determined by the distribution of density field in the ocean. This enables us to apply
the theory of internal waves to the solution of the problem of evaluation of density in the ocean. From the view-
point of the dynamics of internal waves, the distribution of the squared buoyancy frequency is the principal char-
acteristic of stratification of the ocean. It should be emphasized that each particular basin is characterized by its
own distribution of the squared buoyancy frequency. However, at present, there is no general method for the so-
lution of the posed inverse problem in the case of an arbitrary distribution of the squared buoyancy frequency.
For this reason, the attention of the researchers is focused on the solution of the posed problem for various parti-
cular regularities of the behavior of the Väisälä–Brunt frequency [1–14]. The results of construction of the func-
tion of squared buoyancy frequency according to the in-situ data are presented in [11, 15]. The approximation
δ-like functions is applied and the posed problem is solved by the method of joined asymptotic expansions in
. A piecewise constant approximation of the function of squared buoyancy frequency is studied in detail in
. In the present work, we use a linear approximation of the distribution of buoyancy frequency.
Note that the formulas deduced for the solution of the inverse problem studied in the present work require
the values of wave numbers and frequencies of oscillations as input data and, as a rule, these data are obtained
experimentally. The accuracy of reconstruction of the function of squared buoyancy frequency depends not only
on the accuracy of evaluation of the wave numbers and frequencies of oscillations but also on the range of dis-
Rostov-on-Don University, Rostov-on-Don.
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
27–40, March–April, 2003. Original article submitted March 16, 2001;
revision submitted January 8, 2002.
88 0928-5105/03/1302–0088 $25.00 © 2003 Plenum Publishing Corporation