On the generation and evolution of numerically simulated large-amplitude internal gravity wave packets

被引:5
作者
Abdilghanie, Ammar M. [2 ]
Diamessis, Peter J. [1 ]
机构
[1] Cornell Univ, Sch Civil & Environm Engn, Ithaca, NY 14853 USA
[2] Univ Washington, Dept Mech Engn, Seattle, WA 98195 USA
关键词
Stratified flows; Internal gravity wave packets; Wave generation and propagation; Wave-driven mean flow; INSTABILITY; FLOW;
D O I
10.1007/s00162-011-0222-1
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
Numerical simulations of internal gravity wave (IGW) dynamics typically rely on wave velocity and density fields which are either generated through forcing terms in the governing equations or are explicitly introduced as initial conditions. Both approaches are based on the associated solution to the inviscid linear internal wave equations and, thus, assume weak-amplitude, space-filling waves. Using spectral multidomain-based numerical simulations of the two-dimensional Navier-Stokes equations and focusing on the forcing-driven approach, this study examines the generation and subsequent evolution of large-amplitude IGW packets which are strongly localized in the vertical in a linearly stratified fluid. When the vertical envelope of the forcing terms varies relatively rapid when compared to the vertical wavelength, the associated large vertical gradients in the Reynolds stress field drive a nonpropagating negative horizontal mean flow component in the source region. The highly nonlinear interaction of this mean current with the propagating IGW packet leads to amplification of the wave, a significant distortion of its rear flank, and a substantial decay of its amplitude. Scaling arguments show that the mean flow is enhanced with a stronger degree of localization of the forcing, larger degree of hydrostaticity, and increasing wave packet steepness. Horizontal localization results in a pronounced reduction in mean flow strength mainly on account of the reduced vertical gradient of the wave Reynolds stress. Finally, two techniques are proposed toward the efficient containment of the mean flow at minimal computational cost. The findings of this study are of particular value in overcoming challenges in the design of robust computational process studies of IGW packet (or continuously forced wave train) interactions with a sloping boundary, critical layer, or caustic, where large wave amplitudes are required for any instabilities to develop. In addition, the detailed description of the dynamics of the wave generation region may offer a first probe into the underlying physics of disruptive near-source nonlinearities observed in laboratory experiments of persistently forced IGW beams. Finally, the question arises as to whether a highly vertically compact IGW packet, which has propagated far from its source but still maintains its original structure and amplitude, can indeed occur in nature.
引用
收藏
页码:205 / 224
页数:20
相关论文
共 36 条
[1]  
Abdilghanie A. M., 2010, THESIS CORNELL U
[2]  
[Anonymous], 2011, INTRO GEOPHYS FLUID
[3]  
[Anonymous], 2005, TURBULENT OCEAN
[4]   INTERNAL GRAVITY-WAVES GENERATED BY OSCILLATIONS OF A SPHERE [J].
APPLEBY, JC ;
CRIGHTON, DG .
JOURNAL OF FLUID MECHANICS, 1987, 183 :439-450
[5]  
Boyd JohnP, 2001, CHEBYSHEV FOURIER SP
[6]   Ray methods for internal waves in the atmosphere and ocean [J].
Broutman, D ;
Rottman, JW ;
Eckermann, SD .
ANNUAL REVIEW OF FLUID MECHANICS, 2004, 36 :233-253
[7]   Nonlinear critical-layer evolution of a forced gravity wave packet [J].
Campbell, LJ ;
Maslowe, SA .
JOURNAL OF FLUID MECHANICS, 2003, 493 :151-179
[8]  
Diamessis P.J., 2010, J FLUID MEC IN PRESS
[9]   A spectral multidomain penalty method model for the simulation of high Reynolds number localized incompressible stratified turbulence [J].
Diamessis, PJ ;
Domaradzki, JA ;
Hesthaven, JS .
JOURNAL OF COMPUTATIONAL PHYSICS, 2005, 202 (01) :298-322
[10]   Numerical and laboratory generation of internal waves from turbulence [J].
Dohan, K ;
Sutherland, BR .
DYNAMICS OF ATMOSPHERES AND OCEANS, 2005, 40 (1-2) :43-56