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Jan 2007

Volume 19, Issue 1, Articles (01xxxx)

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back to top Geophysical Flows

Internal wave transmission in nonuniform flows

J. T. Nault and B. R. Sutherland

Phys. Fluids 19, 016601 (2007); http://dx.doi.org/10.1063/1.2424791 (8 pages) | Cited 10 times

Online Publication Date: 17 January 2007

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We compute transmission coefficients for internal waves propagating in a fluid with continuously varying stratification and background shear. In stationary fluid the transmission is characterized by the ratio of transmitted to incident energy. More generally, transmission across the shear is appropriately characterized by the ratio of transmitted to incident pseudoenergy flux. First, we examine the transmission and reflection of internal waves incident upon a weakly stratified layer in stationary fluid focusing upon the opposing limits of piecewise-linear theory and a heuristic application of Wentzel-Kramers-Brillouin (WKB) theory. We find the WKB prediction is reasonably accurate if the distance of transition from strong to weak stratification is as small as one sixth the vertical wavelength of the transmitted waves. In the limit of infinitesimally small transition distances the prediction of piecewise-linear theory is reproduced. Second, we consider the transmission of internal waves across a shear layer which initially is uniformly stratified. In particular, we show that significant transmission is possible across critical layers if the minimum gradient Richardson number is less than 1/4. Finally, we show that internal waves can partially transmit across a mixed region that results from the evolution of an unstable shear layer. Transmission across critical layers occurs for waves whose horizontal phase speed matches the background flow speed at levels where the gradient Richardson number is less than 1/4.
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47.35.De Shear waves
47.55.Hd Stratified flows
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)

Numerical simulation of the Benjamin-Feir instability and its consequences

Dmitry Chalikov

Phys. Fluids 19, 016602 (2007); http://dx.doi.org/10.1063/1.2432303 (15 pages) | Cited 7 times

Online Publication Date: 25 January 2007

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Full nonlinear equations for one-dimensional potential surface waves were used for investigation of the evolution of an initially homogeneous train of exact Stokes waves with steepness AK = 0.01–0.42. The numerical algorithm for the integration of nonstationary equations and the calculation of exact Stokes waves is described. Since the instability of the exact Stokes waves develops slowly, a random small-amplitude noise was introduced in initial conditions. The development of instability occurs in two stages: in the first stage the growth rate of disturbances was close to that established for small steepness by Benjamin and Feir [J. Fluid. Mech. 27, 417 (1967)] and for medium steepness [ McLean, J. Fluid Mech. 114, 315 (1982)] . For any steepness, the Stokes waves disintegrate and create random superposition of waves. For AK<0.13, waves do not show a tendency to breaking, which is recognized by approaching a surface to non-single-value shape. Sooner or later, if AK>0.13, one of the waves increases its height, and finally it comes to the breaking point. For large steepness of AK>0.35 the rate of growth is slower than for medium steepness. The data for spectral composition of disturbances and their frequencies are given.
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47.35.-i Hydrodynamic waves
47.20.-k Flow instabilities

Rotating multipoles on the f- and γ-planes

Z. Kizner, R. Khvoles, and J. C. McWilliams

Phys. Fluids 19, 016603 (2007); http://dx.doi.org/10.1063/1.2432915 (13 pages) | Cited 5 times

Online Publication Date: 25 January 2007

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A family of semianalytical solutions is presented describing multipolar vortical structures with zero total circulation in a variety of two-dimensional models. Analytics are used to determine the form of a multipole edge, or separatrix, and the solution outside this separatrix. The interior is solved using a Newton-Kantorovich (successive linearization) procedure combined with a collocation method. The models considered are the quasigeostrophic f- and γ-planes, with either the rigid-lid or free-surface conditions. A multipole, termed also an (m+1)-pole, is a vortical system that possesses an m-fold symmetry (m ≥ 2) and is comprised of a central core vortex and m satellite vortices surrounding the core. Fluid parcels in the core and the satellites revolve oppositely, and the multipole as a whole rotates steadily. The characteristics of the multipoles are examined as functions of m and a parameter that incorporates the Rossby deformation radius, γ-effect, and the vortex’s angular velocity. The analogy between the β-plane modons and γ-plane multipoles is tracked.
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47.32.C- Vortex dynamics
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