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  • Author or Editor: R. M. Samelson x
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R. M. Samelson

Abstract

The growth of linear disturbances to stable and unstable time-periodic basic states is analyzed in an asymptotic model of weakly nonlinear, baroclinic wave–mean interaction. In this model, an ordinary differential equation for the wave amplitude is coupled to a partial differential equation for the zonal-flow correction. Floquet vectors, the eigenmodes for linear disturbances to the oscillatory basic states, split into wave-dynamical and decaying zonal-flow modes. Singular vectors reflect the structure of the Floquet vectors: the most rapid amplification and decay are associated with the wave-dynamical Floquet vectors, while the intermediate singular vectors closely follow the decaying zonal-flow Floquet vectors. Singular values depend strongly on initial and optimization times. For initial times near wave amplitude maxima, the Floquet decomposition of the leading singular vector depends relatively weakly on optimization time. For the unstable oscillatory basic state in the chaotic regime, the leading Floquet vector is tangent to the large-scale structure of the attractor, while the leading singular vector is not. However, corresponding inferences about the accessibility of disturbed states rely on the simple attractor geometry, and may not easily generalize. The primary mechanism of disturbance growth on the wave timescale in this model involves a time-dependent phase shift along the basic wave cycle. The Floquet vectors illustrate that modal disturbances to time-dependent basic states can have time-dependent spatial structure, and that the latter need not indicate nonmodal dynamics. The dynamical splitting reduces the “butterfly effect,” the ability of small-scale disturbances to influence the evolution of an unstable large-scale flow.

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R. M. Samelson

Abstract

A model for hydraulically supercritical atmospheric marine-layer flow along a smoothly varying coastline is formulated and solved numerically. The model is motivated by a recent comparison of CODE observations to a simple hydraulic theory, which suggested the presence of an expansion fan and a compression jump downstream of topographic features. The marine layer is modeled as a homogeneous rotating fluid layer decelerated by surface friction and forced by imposed upper-level pressure gradients. The equations are solved by a characteristic-based gridpoint scheme. The results indicate that the expansion fan is a robust feature that persists under most conditions in the present more realistic model, but is dramatically altered in structure by the presence of friction, while the jump may weaken rapidly offshore due mainly to offshore variations of the layer height upstream of the jump. The agreement between observations and model predictions is good enough to suggest that a first-order description of the dynamics has been attained in which friction dramatically alters the character of the supercritical flow features. The supercritical flow features cause variations in wind stress of 10%–50% over tens of kilometers.

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A. M. Rogerson
and
R. M. Samelson

Abstract

Motivated by recent observations along the west coast of the United States, the authors investigate the generation and propagation of coastal-trapped disturbances in the marine atmospheric boundary layer. Analytic solutions are obtained in a linear, shallow water, reduced-gravity model of the flow subject to forcing by upper-level pressure disturbances and dissipation in the form of wind stress at the sea surface. It is found that unless the mean alongshore flow is to the south with speeds larger than the gravity wave phase speed, a northward propagating coastal-trapped response develops. The superposition of cross-shore propagating forcing and the northward propagating response in marine-layer thickness can give rise to surface pressure ridges at the coast with both narrow and broad cross-shore extent. Wind reversals associated with the disturbance lead the change in surface pressure at the coast. The magnitude of the response increases for weaker inversion strength, greater undisturbed marine-layer depth, and, to some extent, with weaker dissipation. For periodic forcing, the near-resonant response propagates steadily up the coast with the inviscid free Kelvin wave phase speed and has a cross-shore length scale equal to the Rossby deformation radius, while the off-resonant response possesses cross-shore length scales that differ from the Rossby radius, and propagates unsteadily up the coast with an average speed determined by forcing parameters. It is also found that the alongshore length scale of the disturbance depends on the propagation speed of the forcing, and may appear more mesoscale-like for fast-moving pressure systems. The results illustrate that unsteady propagation of the coastal-trapped disturbance can result from the linear response to synoptic forcing.

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R. M. Samelson
and
C. L. Wolfe

Abstract

An unstable, nonlinear baroclinic wave-mean oscillation is found in a strongly supercritical quasigeostrophic f-plane numerical channel model with 3840 Fourier components. The growth of linear disturbances to this time-periodic oscillation is analyzed by computing time-dependent normal modes (Floquet vectors). Two different Newton–Picard methods are used to compute the unstable solution, the first based on direct computation of a large set of Floquet vectors, and the second based on an efficient iterative solver. Three different growing normal modes are found, which modify the wave structure of the wave-mean oscillation in two essentially different ways. The dynamics of the instabilities are qualitatively similar to the baroclinic dynamics of the wave-mean oscillation. The results provide an example of time-dependent normal mode instability of a strongly nonlinear time-dependent baroclinic flow.

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R. M. Samelson
and
E. D. Skyllingstad

Abstract

A numerical simulation is analyzed that resolves the full range of motions from rotationally dominated, growing baroclinic waves to quasi-isotropic, three-dimensional shear instabilities. The results confirm a 40-yr-old prediction, made by B. Hoskins and F. Bretherton, that frontogenetic collapse of cross-frontal spatial scales, driven by baroclinic-wave deformation fields, will continue to the Kelvin–Helmholtz (K–H) turbulent transition. This process of frontal collapse followed by K–H transition provides a mechanism for spontaneous loss of balance in an initially geostrophic flow, and a direct, spectrally nonlocal pathway for downscale energy transfer that is phenomenologically distinct from traditional concepts of turbulent cascades and can contribute substantially to total kinetic energy dissipation. These results, which neglect surface drag and several other potentially relevant atmospheric processes, would suggest that the turbulence associated with collapsing fronts in the atmosphere can extend upward from the surface through roughly one-third of the troposphere.

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R. M. Samelson
and
S. J. Lentz

Abstract

The horizontal momentum balance in the marine atmospheric boundary layer during the Coastal Ocean Dynamics Experiment (CODE) is analyzed, using meteorological data from an array of surface moorings. Previous studies have indicated the presence of orographically generated mesoscale features that are induced by strong southward flow around Point Arena. The present analysis demonstrates that during periods of strong southward flow, the cross-shore momentum equation is dominated by a balance between the ageostrophic acceleration associated with the flow curvature around Point Arena, and the cross-shore pressure gradient, while the along-shore momentum equation is dominated by a balance between vertical stress divergence and alongshore pressure gradient. These balances are consistent with results from a shallow water model of the marine layer. The calculations provide evidence for orographic modification of the horizontal structure of the boundary layer under a broader range of southward flow conditions than had been indicated by previous studies.

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Jeffrey Shaman
,
R. M. Samelson
, and
Eli Tziperman

Abstract

This paper presents a methodology for performing complex wavenumber ray tracing in which both wave trajectory and amplitude are calculated. This ray-tracing framework is first derived using a scaling in which the imaginary wavenumber component is assumed to be much smaller than the real wavenumber component. The approach, based on perturbation methods, is strictly valid when this scaling condition is met. The framework is then used to trace stationary barotropic Rossby waves in a number of settings. First, ray-traced Rossby wave amplitude is validated in a simple, idealized system for which exact solutions can be calculated. Complex wavenumber ray tracing is then applied to both solid-body rotation on a sphere and observed climatological upper-tropospheric fields. These ray-tracing solutions are compared with similarly forced solutions of the linearized barotropic vorticity equation (LBVE). Both real and complex wavenumber ray tracings follow trajectories matched by LBVE solutions. Complex wavenumber ray tracings on observed two-dimensional zonally asymmetric atmospheric fields are found to follow trajectories distinct from real wavenumber Rossby waves. For example, complex wavenumber ray tracings initiated over the eastern equatorial Pacific Ocean during boreal summer propagate northward and northeastward into the subtropics over the Atlantic Ocean, as well as southeastward into the Southern Hemisphere. Similarly initiated real wavenumber ray tracings remain within the deep tropics and propagate westward. These complex wavenumber Rossby wave trajectories and ray amplitudes are generally consistent with LBVE solutions, which indicates this methodology can identify Rossby wave effects distinct from traditional real wavenumber tracings.

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Stephen D. Burk
,
Tracy Haack
, and
R. M. Samelson

Abstract

A mesoscale atmospheric model is used to address the characteristics of stratified flow bounded by a side wall along a varying coastline. Initial Froude number values are varied through alteration of marine inversion strength, permitting examination of supercritical, subcritical, and transcritical flow regimes encountering several coastal configurations. Consistent with shallow water models, sharp drops in boundary layer depth and flow acceleration occur in flow rounding convex bends; however, significant flow response occurs in the stratified layer aloft, which is unexplained by conventional shallow water theory. The strongest flow acceleration occurs in the transcritical case while, regardless of inversion strength, the deformation of the isentropes aloft shows general structural similarity.

Advection of horizontal momentum is an important component of the horizontal force balance. A simulation having several coastline bends exhibits a detached, oblique hydraulic jump upwind of a concave bend that strongly blocks the flow. For the single-bend case, a shallow water similarity theory for stratified flow provides qualitative, and partial quantitative, agreement with the mesoscale model, in the boundary layer and aloft. Horizontal structure functions for these similarity solutions satisfy a set of equivalent shallow water equations. This comparison provides a new perspective on previous shallow water models of supercritical flow around coastal bends and suggests that the existence of the supercritical flow response may depend more on the presence of a low-level jet than on a sharp boundary layer inversion.

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