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Application of Variational Method in Analysis of Flow in an Ideal Stratified Fluid System

Behzadi, Sima | 2021

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 56571 (09)
  4. University: Sharif University of Technology
  5. Department: Industrial Engineering
  6. Advisor(s): Jamali, Mirmosadegh
  7. Abstract:
  8. Using Variational Method, two important hydrodynamic phenomena, “internal gravity waves” and “gravity currents”, are modelled theoretically in this research. Variational method as a robust technique for modelling complicated problems related to fluid mechanics gives us the ability of finding closed-form formula for predicting the behavior of the flow in an ideal fluid system. In the first part of this research, focusing on the nonlinear resonant interaction between surface and internal waves, we model the evolution of interfacial waves on the interface of a two-layer fluid system. This phenomenon play an important role in the mixture of the fluid and cascade of energy in the environment. Finding short-form interaction coefficient for internal waves, we present a theoretical model to predict the behavior of the internal waves in both Harmonic and Sub-harmonic cases. The effect of different parameters such as internal wave angles, surface wave frequency, and density difference on the behavior of the internal waves are also examined. Good agreement between these results and previous experimental observations has been observed. In the second part, Variational technique is used for modelling the progress of internal gravity currents in a stratified fluid system. Height and speed of head of the current, as two important characteristics of the flow, are determined in both full-depth and partial-depth systems. A better agreement between the theoretical results and experimental observations in comparison to the results of the energy conservation method and shallow water theory shows the reliability of the new model for prediction of gravity current behavior
  9. Keywords:
  10. Variational Method ; Nonlinear Resonance ; Gravity Current ; Internal Waves ; Stratified Fluid ; Ideal Fluid ; Nonlinear Resonance Interaction

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