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- Author or Editor: P. B. Rhines x

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## Abstract

This paper describes qualitative features of the generation of jetlike concentrated circulations, wakes, and blocks by simple mountainlike orography, both from idealized laboratory experiments and shallow-water numerical simulations on a sphere. The experiments are unstratified with barotropic lee Rossby waves, and jets induced by mountain orography. A persistent pattern of lee jet formation and lee cyclogenesis owes its origins to arrested topographic Rossby waves above the mountain and potential vorticity (PV) advection through them. The wake jet occurs on the equatorward, eastern flank of the topography. A strong upstream blocking of the westerly flow occurs in a Lighthill mode of long Rossby wave propagation, which depends on *βa*
^{2}/*U*, the ratio of Rossby wave speed based on the scale of the mountain, to zonal advection speed, *U* (*β* is the meridional potential vorticity gradient, *f* is the Coriolis frequency, and *a* is the diameter of the mountain). Mountains wider (north–south) than the east–west length scale of stationary Rossby waves will tend to block the oncoming westerly flow. These blocks are essentially *β* plumes, which are illustrated by their linear Green function. For large *βa*
^{2}/*U*, upwind blocking is strong; the mountain wake can be unstable, filling the fluid with transient Rossby waves as in the numerical simulations of Polvani et al. For small values, *βa*
^{2}/*U* ≪ 1 classic lee Rossby waves with large wavelength compared to the mountain diameter are the dominant process. The mountain height, *δh*, relative to the mean fluid depth, *H*, affects these transitions as well. Simple lee Rossby waves occur only for such small heights, *δh*/*h* ≪ *aβ*/*f*, that the *f*/*h* contours are not greatly distorted by the mountain. Nongeostrophic dynamics are seen in inertial waves generated by geostrophic shear, and ducted by it, and also in a texture of finescale, inadvertent convection. Weakly damped circulations induced in a shallow-water numerical model on a sphere by a lone mountain in an initially simple westerly wind are also described. Here, with *βa*
^{2}/*U* ∼1, potential vorticity stirring and transient Rossby waves dominate, and drive zonal flow acceleration. Low-latitude critical layers, when present, exert strong control on the high-latitude waves, and with no restorative damping of the mean zonal flow, they migrate poleward toward the source of waves. While these experiments with homogeneous fluid are very simplified, the baroclinic atmosphere and ocean have many tall or equivalent barotropic eddy structures owing to the barotropization process of geostrophic turbulence.

## Abstract

This paper describes qualitative features of the generation of jetlike concentrated circulations, wakes, and blocks by simple mountainlike orography, both from idealized laboratory experiments and shallow-water numerical simulations on a sphere. The experiments are unstratified with barotropic lee Rossby waves, and jets induced by mountain orography. A persistent pattern of lee jet formation and lee cyclogenesis owes its origins to arrested topographic Rossby waves above the mountain and potential vorticity (PV) advection through them. The wake jet occurs on the equatorward, eastern flank of the topography. A strong upstream blocking of the westerly flow occurs in a Lighthill mode of long Rossby wave propagation, which depends on *βa*
^{2}/*U*, the ratio of Rossby wave speed based on the scale of the mountain, to zonal advection speed, *U* (*β* is the meridional potential vorticity gradient, *f* is the Coriolis frequency, and *a* is the diameter of the mountain). Mountains wider (north–south) than the east–west length scale of stationary Rossby waves will tend to block the oncoming westerly flow. These blocks are essentially *β* plumes, which are illustrated by their linear Green function. For large *βa*
^{2}/*U*, upwind blocking is strong; the mountain wake can be unstable, filling the fluid with transient Rossby waves as in the numerical simulations of Polvani et al. For small values, *βa*
^{2}/*U* ≪ 1 classic lee Rossby waves with large wavelength compared to the mountain diameter are the dominant process. The mountain height, *δh*, relative to the mean fluid depth, *H*, affects these transitions as well. Simple lee Rossby waves occur only for such small heights, *δh*/*h* ≪ *aβ*/*f*, that the *f*/*h* contours are not greatly distorted by the mountain. Nongeostrophic dynamics are seen in inertial waves generated by geostrophic shear, and ducted by it, and also in a texture of finescale, inadvertent convection. Weakly damped circulations induced in a shallow-water numerical model on a sphere by a lone mountain in an initially simple westerly wind are also described. Here, with *βa*
^{2}/*U* ∼1, potential vorticity stirring and transient Rossby waves dominate, and drive zonal flow acceleration. Low-latitude critical layers, when present, exert strong control on the high-latitude waves, and with no restorative damping of the mean zonal flow, they migrate poleward toward the source of waves. While these experiments with homogeneous fluid are very simplified, the baroclinic atmosphere and ocean have many tall or equivalent barotropic eddy structures owing to the barotropization process of geostrophic turbulence.

## Abstract

A scatter diagram may be constructed by choosing an appropriate closed or open horizontal curve in physical space and plotting the value of any scalr quantity *q* against the geostrophic streamfunction ψ for each data point on the curve. The area enclosed on the scatter diagram is equal to the net geostrophic advective flux of *q* across the chosen curve in physical space. When *q* is the (quasi-geostrophic) potential vorticity *Q*, and suitable normalizations are adopted, this result may he exploited to derive measures of departure from free-mode form *Q*)= Q(ψ) along the curve in physical space. For a certain class of open space curves, an appropriate measure is the width-to-length ratio of the circuit in (ψ, *Q*) space. Most scatter diagrams that have appeared in the literature included the (ψ, *Q*) points corresponding to all the data or grid points within a given horizontal domain. The significance of the area enclosed on these diagrams is less clear, but the spread about some curve *Q*) = Q(ψ) is evidently a qualitative measure of the extent to which the flow deviates from free-mode form. For steady or time-averaged flows which are approximately of this form, the gradient *dQ*/*d*ψ of the scatter diagram may be used to infer some properties of the forcing and dissipative processes acting. When dissipation is principally due to *Q*transfer by transient eddy motion (or viscosity), the key diagnostic relation iswhere *S* is the potential vorticity forcing, *K* the lateral eddy (or viscous) v the horizontal velocity, and the integrals are taken over and around any region enclosed by a mean streamline. Hence *dQ*/*d*ψis often negative. corresponding to two common properties of quasi-geostrophic circulations: that the eddy motion (or viscosity) transport *Q* down its mean gradient (K > 0) and that the circulation integral have the same sign as the potential vorticity forcing. Two sets of examples, both involving (*Q*,ψ) scatter diagrams constructed from numerically simulated data, are presented. One relates to steady baroclinic wave motion in a rotating annulus system, and the other to the time-averaged circulation in an ocean basin.

## Abstract

A scatter diagram may be constructed by choosing an appropriate closed or open horizontal curve in physical space and plotting the value of any scalr quantity *q* against the geostrophic streamfunction ψ for each data point on the curve. The area enclosed on the scatter diagram is equal to the net geostrophic advective flux of *q* across the chosen curve in physical space. When *q* is the (quasi-geostrophic) potential vorticity *Q*, and suitable normalizations are adopted, this result may he exploited to derive measures of departure from free-mode form *Q*)= Q(ψ) along the curve in physical space. For a certain class of open space curves, an appropriate measure is the width-to-length ratio of the circuit in (ψ, *Q*) space. Most scatter diagrams that have appeared in the literature included the (ψ, *Q*) points corresponding to all the data or grid points within a given horizontal domain. The significance of the area enclosed on these diagrams is less clear, but the spread about some curve *Q*) = Q(ψ) is evidently a qualitative measure of the extent to which the flow deviates from free-mode form. For steady or time-averaged flows which are approximately of this form, the gradient *dQ*/*d*ψ of the scatter diagram may be used to infer some properties of the forcing and dissipative processes acting. When dissipation is principally due to *Q*transfer by transient eddy motion (or viscosity), the key diagnostic relation iswhere *S* is the potential vorticity forcing, *K* the lateral eddy (or viscous) v the horizontal velocity, and the integrals are taken over and around any region enclosed by a mean streamline. Hence *dQ*/*d*ψis often negative. corresponding to two common properties of quasi-geostrophic circulations: that the eddy motion (or viscosity) transport *Q* down its mean gradient (K > 0) and that the circulation integral have the same sign as the potential vorticity forcing. Two sets of examples, both involving (*Q*,ψ) scatter diagrams constructed from numerically simulated data, are presented. One relates to steady baroclinic wave motion in a rotating annulus system, and the other to the time-averaged circulation in an ocean basin.

## Abstract

Results from new experiments on baroclinic instability of a coastal jet demonstrate that this almost balanced flow spontaneously emits inertial waves when the Rossby radius of deformation is relatively small such that the characteristics of baroclinic meanders match the dispersion relation for the inertial waves. The energy of the waves is small compared to the energy of the flow. A single event of wave emission is identified in the experiment with larger radius of deformation and is interpreted in terms of vorticity dynamics. The flows are generated on a laboratory polar *β* plane where the Coriolis parameter varies quadratically with latitude. A new method for imaging the rotating flows, which the authors call “altimetric imaging velocimetry,” is employed. Optical color coding of slopes of the free-surface elevation field allows the authors to derive the fields of pressure, surface elevation, geostrophic velocity, or the “gradient wind” velocity with very high spatial resolution (typically several million vectors) limited largely by the pixel resolution of the available imaging sensors. The technique is particularly suited for the investigations of small-amplitude waves, which are often difficult to detect by other methods.

## Abstract

Results from new experiments on baroclinic instability of a coastal jet demonstrate that this almost balanced flow spontaneously emits inertial waves when the Rossby radius of deformation is relatively small such that the characteristics of baroclinic meanders match the dispersion relation for the inertial waves. The energy of the waves is small compared to the energy of the flow. A single event of wave emission is identified in the experiment with larger radius of deformation and is interpreted in terms of vorticity dynamics. The flows are generated on a laboratory polar *β* plane where the Coriolis parameter varies quadratically with latitude. A new method for imaging the rotating flows, which the authors call “altimetric imaging velocimetry,” is employed. Optical color coding of slopes of the free-surface elevation field allows the authors to derive the fields of pressure, surface elevation, geostrophic velocity, or the “gradient wind” velocity with very high spatial resolution (typically several million vectors) limited largely by the pixel resolution of the available imaging sensors. The technique is particularly suited for the investigations of small-amplitude waves, which are often difficult to detect by other methods.