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Yomtov Tal, Shira

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

Education

  • 2020- now, MSc Forced inertial waves with full Coriolis forcing
    with Yoav Tsori

    Abstract/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 (co-Coriolis 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 co-Coriolis terms are neglected to when they are included. In this discussion, we show that for the case where co-Coriolis terms are included, the kinetic energy is independent of the earth’s latitude θ, in contrast to the conventional case for which the co-Coriolis 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 co-Coriolis terms are neglected.

    Second, we consider a force that is periodic in space and stochastic in time, following the Ornstein-Uhlenbeck 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.