Physical Oceanography, Vol.
INFLUENCE OF CURRENTS ON WEAKLY NONLINEAR TOPOGRAPHIC WAVES
A. A. Slepyshev
In the Boussinesq approximation, we consider trapped topographic waves in an inhomogeneous current
directed along isobaths. The influence of the current on the dispersion properties of trapped topographic
waves in the Norwegian Sea is studied. We determine the mean currents and nonoscillatory (on the time
scale of the waves) density corrections induced by the waves due to their nonlinearity. It is shown that
the influence of currents is significant in the short-wave region. Its influence leads to a decrease in the
wavelength for the constant period of waves, whereas the mean current caused by nonlinearity noticea-
bly varies, especially in the bottom layer.
The investigation of dynamic processes in the bottom layers of seas and oceans is required for understand-
ing the physical mechanisms of interaction of the wave motions and turbulence. In the bottom layer, we observe
the transportation of sediments especially pronounced in the coastal zone of the sea [1, 2]. Near the coast, the
influence of surface waves is predominant down to depths of about a half wavelength . At greater depths, the
intense action upon the bottom is exerted by internal and trapped topographic waves. The bottom waves whose
energy is concentrated at the bottom play the role of a powerful dynamic factor promoting the transition of bot-
tom sediments into the suspension and their transportation . The vertical and horizontal shears of the velocity
of bottom waves are responsible for the process of feeding of turbulent processes in the bottom layer with en-
ergy, which makes a significant contribution to the vertical and horizontal turbulent exchange specifying the
transport of admixtures and dissolved substances.
The barotropic topographic waves are fairly well studied [1, 5, 6]. The investigation of baroclinic topographic
waves encounters the well-known difficulties connected with the separation of horizontal and vertical structures of
motion caused by the slope of the bottom. For small slopes, the oscillations can be separated into modes if the bot-
tom is taken into account in the boundary condition [7, 8].
In the short-wave limit, the energy of baroclinic topographic waves in a stratified sea is concentrated at the
bottom, i.e., the waves are trapped by the bottom [7, 9]. For any slope of the bottom and a constant Brunt–
Väisälä frequency, the bottom waves were studied in the quasigeostrophic approximation in [1, 9, 10]. In the
trapped waves, the component of the velocity normal to the bottom is equal to zero. Their amplitude decreases
according to the exponential law as the distance from the bottom increases and the phase propagates leaving
shallower waters to the right in the Northern Hemisphere. For any slope of the bottom, the frequencies of the
trapped waves can be quite large, namely,
is the slope of the bottom and
is the Brunt–
Väisälä frequency .
As the physical cause of the existence of trapped bottom waves, we can mention the interaction of gravita-
tional and buoyancy forces, on the one hand, and the inhomogeneities of the bottom topography and Earth’s ro-
Marine Hydrophysical Institute, Ukrainian National Academy of Sciences, Sevastopol, Ukraine.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
30–44, July–August, 2010. Original article submitted April 2, 2009; revi-
sion submitted April 15, 2009..
266 0928–5105/10/2004–0266 © 2010 Springer Science+Business Media, Inc.