Yomtov Tal, Shira
MSc student
 shirayom@post.bgu.ac.il
 Office
 54/
 Research type
 Theoretical
Education

2020
now,
MSc
Forced inertial waves with full Coriolis forcing
with Yoav TsoriAbstract/Description: Inertial waves are a type of wave that arises in rotating fluids due to the Coriolis force, a restoring force related to the Earth’s rotation. When the
fluid includes stratification, it introduces the buoyancy force, transforming these waves into Internal waves . Inertial and Internal waves play a crucial
role in facilitating the transfer of heat, energy, and momentum within the ocean [1].
The vertical velocity both in the ocean and in the atmosphere is small (due to the shallowness of the ocean and atmosphere with respect to the Earth’s radius), justifying the omission of some components of the Coriolis force and taking into account only the vertical component of the Earth’s rotation vector. This thesis focuses on the effect of the neglected Coriolis force terms (coCoriolis terms) on inertial waves. This is done by comparing the properties of internal waves when the full Coriolis force is taken into account to the properties obtained when only the vertical component of the Earth’s rotation vector is taken into account. We perform our analysis when assuming a barotropic ocean and neglecting the nonlinear advection terms (under the assumption of a Rossby number that is much smaller than 1). Notably, our analysis includes forcing and viscosity terms.
First, we consider the case of a spatiotemporal periodic forcing. Under such forcing, the excited wave has the same wave vector and frequency as the driving force. We study how the maximum kinetic energy of the system varies as a function of the model’s parameters, mainly the external forcing frequency. Additionally, we observe distinct variations in the number of these maxima, as well as changes in their associated parameters and amplitudes, when accounting for the full Coriolis force. The amplitude of the kinetic
energy and its components varies as a function of the frequency of the driving force. We discuss the differences between the cases when the coCoriolis terms are neglected to when they are included. In this discussion, we show that for the case where coCoriolis terms are included, the kinetic energy is independent of the earth’s latitude θ, in contrast to the conventional case for which the coCoriolis terms are neglected. Another aspect discussed is the emergence of an additional maximum point for the contributions of the kinetic energy in the meridional and vertical directions in the full Coriolis case, which is absent when the coCoriolis terms are neglected.
Second, we consider a force that is periodic in space and stochastic in time, following the OrnsteinUhlenbeck process. The temporal part of the forcing resembles a Lorentzian in the frequency domain where its center is denoted by the parameter ωl. We chose such forcing because it provides a suitable representation of the stochastic nature of wind stress applied to the ocean’s surface [2]. We use Parseval’s theorem to calculate the temporal average of the kinetic energy. As in the spatiotemporal case, we show that the temporal
average of the kinetic energy is maximal as a function of the model’s parameters, mainly the external forcing Lorentzian’s center frequency ωl and the force’s wave vector direction φ. We find that the temporal average of the kinetic energy has maxima points as a function of φ when the Lorentzian’s center frequency ωl (or the dispersion relation) is near or equal to a natural frequency of the system. Again, the number of these maxima, their location, and their amplitude are different when the full Coriolis force is taken into
account in comparison to the conventional case for which only the vertical component of the Earth’s rotation vector is taken into account.
Our findings highlight the importance of including the full Coriolis force in the study of inertial waves. By doing so, we gain a better understanding of the dynamics of rotating fluids, which is essential for understanding the dynamics of the atmosphere, ocean, and planetary cores, as well as for the transport of energy and momentum within these systems.