Nonlinear evolution of equatorial spreadF: 4. Gravity waves, velocity shear, and day-to-day variability

1996 ◽  
Vol 101 (A11) ◽  
pp. 24521-24532 ◽  
Author(s):  
Chao-Song Huang ◽  
Michael C. Kelley
Keyword(s):  
Gravity Waves ◽  
Nonlinear Evolution ◽  
Velocity Shear

On the nonlinear evolution of wind-driven gravity waves

2004 ◽  
Vol 16 (9) ◽  
pp. 3256-3268 ◽  
Author(s):  
A. Alexakis ◽  
A. C. Calder ◽  
L. J. Dursi ◽  
R. Rosner ◽  
J. W. Truran ◽  
...  
Keyword(s):  
Gravity Waves ◽  
Nonlinear Evolution

Nonlinear Evolution of Internal Gravity Waves in Cluster Cooling Flows

1995 ◽  
Vol 446 ◽  
pp. 529 ◽  
Author(s):  
Eric A. Lufkin ◽  
Steven A. Balbus ◽  
John F. Hawley
Keyword(s):  
Gravity Waves ◽  
Nonlinear Evolution ◽  
Internal Gravity Waves ◽  
Cooling Flows

scholarly journals On dispersion of directional surface gravity waves

2017 ◽  
Vol 812 ◽  
pp. 681-697 ◽  
Author(s):  
Tore Magnus A. Taklo ◽  
Karsten Trulsen ◽  
Harald E. Krogstad ◽  
José Carlos Nieto Borge
Keyword(s):  
Gravity Waves ◽  
Nonlinear Evolution ◽  
Laboratory Data ◽  
Surface Gravity ◽  
Linear Dispersion ◽  
Marine Research ◽  
Surface Gravity Waves ◽  
Linear Dispersion Relation ◽  
Directional Waves ◽  
Crest Length

Using a nonlinear evolution equation we examine the dependence of the dispersion of directional surface gravity waves on the Benjamin–Feir index (BFI) and crest length. A parameter for describing the deviation between the dispersion of simulated waves and the theoretical linear dispersion relation is proposed. We find that for short crests the magnitude of the deviation parameter is low while for long crests the magnitude is high and depends on the BFI. In the present paper we also consider laboratory data of directional waves from the Marine Research Institute of the Netherlands (MARIN). The MARIN data confirm the simulations for three cases of BFI and crest length.

Secondary Instabilities in Breaking Inertia–Gravity Waves

2012 ◽  
Vol 69 (1) ◽  
pp. 303-322 ◽  
Author(s):  
Mark D. Fruman ◽  
Ulrich Achatz
Keyword(s):  
Normal Mode ◽  
Gravity Waves ◽  
Singular Vector ◽  
Initial Conditions ◽  
Velocity Shear ◽  
Time Dependent ◽  
Unstable Wave ◽  
Singular Vectors ◽  
Secondary Instabilities ◽  
Inertia Gravity Waves

Abstract The three-dimensionalization of turbulence in the breaking of nearly vertically propagating inertia–gravity waves is investigated numerically using singular vector analysis applied to the Boussinesq equations linearized about three two-dimensional time-dependent basic states obtained from nonlinear simulations of breaking waves: a statically unstable wave perturbed by its leading transverse normal mode, the same wave perturbed by its leading parallel normal mode, and a statically stable wave perturbed by a leading transverse singular vector. The secondary instabilities grow through interaction with the buoyancy gradient and velocity shear in the basic state. Which growth mechanism predominates depends on the time-dependent structure of the basic state and the wavelength of the secondary perturbation. The singular vectors are compared to integrations of the linear model using random initial conditions, and the leading few singular vectors are found to be representative of the structures that emerge in the randomly initialized integrations. A main result is that the length scales of the leading secondary instabilities are an order of magnitude smaller than the wavelength of the initial wave, suggesting that the essential dynamics of the breaking might be captured by tractable nonlinear three-dimensional simulations in a relatively small triply periodic domain.

scholarly journals Existence, stability and formation of baroclinic tripoles in quasi-geostrophic flows

2015 ◽  
Vol 785 ◽  
pp. 1-30 ◽  
Author(s):  
Jean N. Reinaud ◽  
Xavier Carton
Keyword(s):  
Nonlinear Evolution ◽  
Baroclinic Instability ◽  
Steady States ◽  
Point Vortices ◽  
Velocity Shear ◽  
Vertical Shear ◽  
Finite Area ◽  
Geostrophic Flows ◽  
Vertically Aligned ◽  
Baroclinic Vortices

Hetons are baroclinic vortices able to transport tracers or species, which have been observed at sea. This paper studies the offset collision of two identical hetons, often resulting in the formation of a baroclinic tripole, in a continuously stratified quasi-geostrophic model. This process is of interest since it (temporarily or definitely) stops the transport of tracers contained in the hetons. First, the structure, stationarity and nonlinear stability of baroclinic tripoles composed of an upper core and two lower (symmetric) satellites are studied analytically for point vortices and numerically for finite-area vortices. The condition for stationarity of the point vortices is obtained and it is proven that the baroclinic point tripoles are neutral. Finite-volume stationary tripoles exist with marginal states having very elongated (figure-of-eight shaped) upper cores. In the case of vertically distant upper and lower cores, the latter can nearly join near the centre of the plane. These steady states are compared with their two-layer counterparts. Then, the nonlinear evolution of the steady states shows when they are often neutral (showing an oscillatory evolution); when they are unstable, they can either split into two hetons (by breaking of the upper core) or form a single heton (by merger of the lower satellites). These evolutions reflect the linearly unstable modes which can grow on the vorticity poles. Very tall tripoles can break up vertically due to the vertical shear mutually induced by the poles. Finally, the formation of such baroclinic tripoles from the offset collision of two identical hetons is investigated numerically. This formation occurs for hetons offset by less than the internal separation between their poles. The velocity shear during the interaction can lead to substantial filamentation by the upper core, thus forming small upper satellites, vertically aligned with the lower ones. Finally, in the case of close and flat poles, this shear (or the baroclinic instability of the tripole) can be strong enough that the formed baroclinic tripole is short-lived and that hetons eventually emerge from the collision and drift away.

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