Nonlinear viscous higher harmonics generation due to incident and reflecting internal wave beam collision

2017-09-01
Aksu, Anil A.
In this paper, we have considered the non-linear effects arising due to the collision of incident and reflected internal wave beams. It has already been shown analytically [Tabaei et al., "Nonlinear effects in reflecting and colliding internal wave beams," J. Fluid Mech. 526, 217-243 (2005)] and numerically [Rodenborn et al., "Harmonic generation by reflecting internal waves," Phys. Fluids 23, 026601 (2011)] that the internal wave beam collision generates the higher harmonics and mean flow in a linear stratification. In this paper, similar to previous analytical work, small amplitude wave theory is employed; however, it is formulated from energetics perspective which allows considering internal wave beams as the product of slowly varying amplitude and fast complex exponential. As a result, the mean energy propagation equation for the second harmonic wave is obtained. Finally, a similar dependence on the angle of incidence is obtained for the non-linear energy transfer to the second harmonic with previous analyses. A possible physical mechanism for this angle dependence on the second harmonic generation is also discussed here. In addition to previous studies, the viscous effects are also included in the mean energy propagation equation for the incident, the reflecting, and the second harmonic waves. Moreover, even though the mean flow obtained here is only confined to the interaction region, it is also affected by viscosity via the decay in the incident and the reflecting internal wave beams. Furthermore, a framework for the non-linear harmonic generation in non-linear stratification is also proposed here. Published by AIP Publishing.
PHYSICS OF FLUIDS

Suggestions

Nonlinear Static Aeroelastic Behaviour of Composite Missile Fin with Interlaminar Damage
Özkaya, Özge; Kayran, Altan (2017-09-22)
Nonlinear static aeroelastic behavior of a basic composite missile fin is analyzed by means of two-way coupled FSI simulation and the effects of composite damages are presented. The configuration has been simulated by coupling the two commercial solvers ANSYS CFX for the fluid mechanical simulation with ANSYS Mechanical for the structural simulation. 3D composite fin geometry is constructed using ANSYS ACP tool. Interlaminar damage cases were investigated and the influence of the damage locations on the sta...
Spatial sensitivity of seismic hazard results to different background seismic activity and temporal earthquake occurrence models
Yilmaz, Nazan; Yücemen, Mehmet Semih (Elsevier BV, 2011-07-01)
Spatial sensitivity of seismic hazard results to different models with respect to background seismic activity and earthquake occurrence in time is investigated. For the contribution of background seismic activity to seismic hazard, background area source with uniform seismicity and spatially smoothed seismicity models are taken into consideration. For the contribution of faults, through characteristic earthquakes, both the memoryless Poisson and the time dependent renewal models are utilized. A case study, ...
Radial basis function and dual reciprocity boundary element solutions of fluid dynamics problems
Gürbüz, Merve; Tezer Sezgin, Münevver; Department of Mathematics (2017)
In this thesis, the two-dimensional, laminar steady or unsteady flow of a viscous, incompressible, electrically conducting fluid is considered in channels of several geometries under the impact of a uniform magnetic field with different orientations. Magnetohydrodynamic (MHD) flow governed by the hydrodynamic and electromagnetic equations is solved numerically with or without Stokes approximation and with or without magnetic induction due to the large or small values of Reynolds and magnetic Reynolds number...
LONGITUDINAL ELASTIC-WAVE PROPAGATION AND ENERGY FLUX AT A DISCONTINUITY OF 2 DISSIMILAR SEMIINFINITE CIRCULAR RODS
Yıldırım, Raif Orhan (1994-10-01)
Elastic wave propagation through an area discontinuity of two dissimilar, bonded, semi-infinite circular rods is investigated analytically. In particular, the variations of the coefficients of stress reflection and transmission are determined in terms of the nondimensional cross sectional area and mechanical impedance parameters. The coefficients of energy flux reflection and transmission are also included. Then, the case is generalized to include a rigid mass attached at the discontinuity.
Dynamic frictional contact problems involving elastic coatings
BALCI, MEHMET NURULLAH; Dağ, Serkan (Elsevier BV, 2018-08-01)
This paper presents a general theory of dynamic frictional contact of elastic coatings pressed against by a rigid punch moving with a constant speed. Governing equations of elastodynamics are solved by applying Galilean and Fourier transformations. The contact problem is then reduced to a singular integral equation, which is solved numerically. Developed procedures are verified through comparisons made to the available computational and analytical results. Parametric analyses illustrate the influences of pu...
Citation Formats
A. A. Aksu, “Nonlinear viscous higher harmonics generation due to incident and reflecting internal wave beam collision,” PHYSICS OF FLUIDS, pp. 0–0, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64148.