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On the Mechanism for the Formation of Garrett-Munk Spectrum in the Ocean.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	On the Mechanism for the Formation of Garrett-Munk Spectrum in the Ocean./
作者:	Dong, Wenjing.
面頁冊數:	1 online resource (109 pages)
附註:	Source: Dissertations Abstracts International, Volume: 84-06, Section: B.
Contained By:	Dissertations Abstracts International84-06B.
標題:	Fluid mechanics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29322418click for full text (PQDT)
ISBN:	9798357552235

On the Mechanism for the Formation of Garrett-Munk Spectrum in the Ocean.
Dong, Wenjing.

On the Mechanism for the Formation of Garrett-Munk Spectrum in the Ocean. - 1 online resource (109 pages)

Source: Dissertations Abstracts International, Volume: 84-06, Section: B.

Thesis (Ph.D.)--New York University, 2022.

Includes bibliographical references

This dissertation studies three problems in interactions between waves and mean flows: (1) The mean flows induced by small amplitude inertia-gravity waves in a vertically bounded domain (2) Frequency diffusion of waves by unsteady flows (3) Stationary inertia-gravity wave frequency spectra generated by geostrophic mean flow refraction.Fluid particles can be transported by Lagrangian velocity which consists of Stokes drift and Eulerian mean velocity. While Stokes drift can be computed directly from linear wave solutions, Eulerian mean velocity in general involves solving partial differential equations and is much more difficult to compute than Stokes drift. In Chapter 1, the Stokes drift and Lagrangian mean flows induced by inertia-gravity waves in a bounded domain are computed. The similar problems in two-dimensional space without rotation or infinite three-dimensional space have been investigated previously. Here, we extended previous studies by considering the problem in a three-dimensional vertically bounded space with rotation. We discovered two regimes of the Langrangian mean flows depending on the aspect ratio of wave vector and the ratio of Coriolis parameter (f) to buoyancy frequency (N). In the first regime, the barotropic component dominates the Lagrangian mean flow response and the baroclinic component is steady in the frame moving with the wavepacket. In the second regime, the baroclinic component consists of resonantly forced secondary inertia-gravity waves.The second and third problems are motivated to explain formation mechanism of the broadband inertia-gravity wave frequency spectrum. Inertia-gravity waves in the ocean are mainly generated by wind forcing, interaction of tides with bottom topography, and spontaneous generation (Shakespeare & Taylor, 2014). However, they are observed to have a broad frequency and the frequency spectrum agree with the Garrett-Munk spectrum reasonably well. There have been some hypotheses proposed to explain the broadband frequency spectra, e.g. interaction between internal tides and the balanced flows, nonlinear wave wave interactions, interactions between the internal waves and the balanced flows. In this thesis, I explore the interaction between internal waves and the balanced flows. In particular, I study the evolution of internal wave statistics under the Wentzel-Kramers-Brillouin (WKB) approximation.In Chapter 2, multi-scale analysis is applied to the transport equation of wave action density in a homogeneous stationary random background flow under the weak refraction approximation. We find that when some time-dependence in the mean flow is retained, wave action density diffuses both along and across surfaces of constant frequency in wavenumber-frequency space; this stands in contrast to previous results showing that diffusion occurs only along constant-frequency surfaces when the mean flow is steady. A self-similar random background velocity field is used to show that the magnitude of this frequency diffusion depends non-monotonically on the time scale of variation of the velocity field. Numerical solutions of the ray tracing equations for rotating shallow water illustrate and confirm our theoretical predictions. Notably, the mean intrinsic wave frequency increases in time, which by wave action conservation implies a concomitant increase of wave energy at the expense of the energy of the background flow.Chapter 3 investigates the evolution of wave statistics for the three-dimensional Boussinesq system. Initially the mean flow magnitude is much smaller than the group velocity of wave packets, so the weak refraction approximation is valid. Under this approximation, wave packets remain their intrinsic frequency by previous studies. However, numerical solutions of ray tracing solutions under quasi-geostrophic flows show that weak refraction approximation breaks down eventually. Moreover, a broadband frequency spectrum forms and becomes quasi-stationary. The stationary frequency spectrum obtained in the quasi-geostrophic flows is indistinguishable from the spectrum in synthetic flows constructed using the quasi-geostrophic flows. Numerical simulations of ray tracing equations in synthetic background flows demonstrate that the stationary frequency spectra are independent of initial conditions of wave packets and Rossby number $Ro$. The stationary frequency spectra can be approximated by power laws with slope between -1 and -2, which is slightly shallower than the Garrett-Munk spectrum.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798357552235Subjects--Topical Terms:

528155
Fluid mechanics.
Subjects--Index Terms:

Garrett-Munk spectrumIndex Terms--Genre/Form:

542853
Electronic books.

On the Mechanism for the Formation of Garrett-Munk Spectrum in the Ocean.
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520 $a This dissertation studies three problems in interactions between waves and mean flows: (1) The mean flows induced by small amplitude inertia-gravity waves in a vertically bounded domain (2) Frequency diffusion of waves by unsteady flows (3) Stationary inertia-gravity wave frequency spectra generated by geostrophic mean flow refraction.Fluid particles can be transported by Lagrangian velocity which consists of Stokes drift and Eulerian mean velocity. While Stokes drift can be computed directly from linear wave solutions, Eulerian mean velocity in general involves solving partial differential equations and is much more difficult to compute than Stokes drift. In Chapter 1, the Stokes drift and Lagrangian mean flows induced by inertia-gravity waves in a bounded domain are computed. The similar problems in two-dimensional space without rotation or infinite three-dimensional space have been investigated previously. Here, we extended previous studies by considering the problem in a three-dimensional vertically bounded space with rotation. We discovered two regimes of the Langrangian mean flows depending on the aspect ratio of wave vector and the ratio of Coriolis parameter (f) to buoyancy frequency (N). In the first regime, the barotropic component dominates the Lagrangian mean flow response and the baroclinic component is steady in the frame moving with the wavepacket. In the second regime, the baroclinic component consists of resonantly forced secondary inertia-gravity waves.The second and third problems are motivated to explain formation mechanism of the broadband inertia-gravity wave frequency spectrum. Inertia-gravity waves in the ocean are mainly generated by wind forcing, interaction of tides with bottom topography, and spontaneous generation (Shakespeare & Taylor, 2014). However, they are observed to have a broad frequency and the frequency spectrum agree with the Garrett-Munk spectrum reasonably well. There have been some hypotheses proposed to explain the broadband frequency spectra, e.g. interaction between internal tides and the balanced flows, nonlinear wave wave interactions, interactions between the internal waves and the balanced flows. In this thesis, I explore the interaction between internal waves and the balanced flows. In particular, I study the evolution of internal wave statistics under the Wentzel-Kramers-Brillouin (WKB) approximation.In Chapter 2, multi-scale analysis is applied to the transport equation of wave action density in a homogeneous stationary random background flow under the weak refraction approximation. We find that when some time-dependence in the mean flow is retained, wave action density diffuses both along and across surfaces of constant frequency in wavenumber-frequency space; this stands in contrast to previous results showing that diffusion occurs only along constant-frequency surfaces when the mean flow is steady. A self-similar random background velocity field is used to show that the magnitude of this frequency diffusion depends non-monotonically on the time scale of variation of the velocity field. Numerical solutions of the ray tracing equations for rotating shallow water illustrate and confirm our theoretical predictions. Notably, the mean intrinsic wave frequency increases in time, which by wave action conservation implies a concomitant increase of wave energy at the expense of the energy of the background flow.Chapter 3 investigates the evolution of wave statistics for the three-dimensional Boussinesq system. Initially the mean flow magnitude is much smaller than the group velocity of wave packets, so the weak refraction approximation is valid. Under this approximation, wave packets remain their intrinsic frequency by previous studies. However, numerical solutions of ray tracing solutions under quasi-geostrophic flows show that weak refraction approximation breaks down eventually. Moreover, a broadband frequency spectrum forms and becomes quasi-stationary. The stationary frequency spectrum obtained in the quasi-geostrophic flows is indistinguishable from the spectrum in synthetic flows constructed using the quasi-geostrophic flows. Numerical simulations of ray tracing equations in synthetic background flows demonstrate that the stationary frequency spectra are independent of initial conditions of wave packets and Rossby number $Ro$. The stationary frequency spectra can be approximated by power laws with slope between -1 and -2, which is slightly shallower than the Garrett-Munk spectrum.
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