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1. Introduction Longuet-Higgins (1964) showed that there is a discrepancy between the definitions of energy flux in planetary (Rossby) waves based on the group velocity viewpoint and the pressure work viewpoint. The product of perturbation pressure and the horizontal velocity vector (sometimes referred to as the “pressure work” 1 ), is the natural energy flux definition in an energy equation for the linear, inviscid shallow-water equations. The derivation of group velocity, on the other hand
1. Introduction Longuet-Higgins (1964) showed that there is a discrepancy between the definitions of energy flux in planetary (Rossby) waves based on the group velocity viewpoint and the pressure work viewpoint. The product of perturbation pressure and the horizontal velocity vector (sometimes referred to as the “pressure work” 1 ), is the natural energy flux definition in an energy equation for the linear, inviscid shallow-water equations. The derivation of group velocity, on the other hand
1. Introduction As revealed by analysis of the Ocean Topography Experiment (TOPEX)/Poseidon data of sea surface height ( Chelton and Schlax 1996 ), the first-mode baroclinic Rossby waves emanating from the eastern boundary of the Pacific Ocean can propagate westward across the basin only in low-latitude regions (see their Fig. 4). In middle-latitude regions, the wave patterns of the sea level signals fade soon after they leave the coast and, at the same time, an eddy field emerges. To explain
1. Introduction As revealed by analysis of the Ocean Topography Experiment (TOPEX)/Poseidon data of sea surface height ( Chelton and Schlax 1996 ), the first-mode baroclinic Rossby waves emanating from the eastern boundary of the Pacific Ocean can propagate westward across the basin only in low-latitude regions (see their Fig. 4). In middle-latitude regions, the wave patterns of the sea level signals fade soon after they leave the coast and, at the same time, an eddy field emerges. To explain
modulation of Rossby wave amplitudes, giving rise to so-called wave packets or wave trains ( Lee and Held 1993 ; Chang and Yu 1999 ; Chang 1999 ). Such wave packets are dynamically relevant as they are associated with zonal (in particular downstream) transfer of energy and momentum ( Chang 1993 ). This may lead to localized downstream effects like surface cyclogenesis ( Chang 2005 ; Wirth and Eichhorn 2014 ) and severe weather events ( Martius et al. 2008 ; Shapiro and Thorpe 2004 ). The latter
modulation of Rossby wave amplitudes, giving rise to so-called wave packets or wave trains ( Lee and Held 1993 ; Chang and Yu 1999 ; Chang 1999 ). Such wave packets are dynamically relevant as they are associated with zonal (in particular downstream) transfer of energy and momentum ( Chang 1993 ). This may lead to localized downstream effects like surface cyclogenesis ( Chang 2005 ; Wirth and Eichhorn 2014 ) and severe weather events ( Martius et al. 2008 ; Shapiro and Thorpe 2004 ). The latter
1. Introduction Ray tracing is often used to explore the propagation of Rossby waves with stationary or near-stationary phase speeds. These ray trajectories indicate how information is communicated through the atmosphere over large distances, as well as the time scales over which this information is conveyed. Rossby wave ray tracing has provided insight into the atmospheric response to steady thermal and orographic forcing ( Hoskins and Karoly 1981 ), the response to low-frequency forcing ( Li
1. Introduction Ray tracing is often used to explore the propagation of Rossby waves with stationary or near-stationary phase speeds. These ray trajectories indicate how information is communicated through the atmosphere over large distances, as well as the time scales over which this information is conveyed. Rossby wave ray tracing has provided insight into the atmospheric response to steady thermal and orographic forcing ( Hoskins and Karoly 1981 ), the response to low-frequency forcing ( Li
; Wu and Zhang 2004 ), analyses ( Plougonven and Teitelbaum 2003 ), and radiosondes ( Plougonven et al. 2003 ). Such IGWs may be generated by flow imbalances in jet streaks, deep convection, frontal activity, and other situations. The detailed understanding and quantitative description of the different processes of IGW generation and propagation is an open question. Here, we study IGWs in the context of a poleward Rossby wave breaking event—a frequently observed phenomenon over northern Europe
; Wu and Zhang 2004 ), analyses ( Plougonven and Teitelbaum 2003 ), and radiosondes ( Plougonven et al. 2003 ). Such IGWs may be generated by flow imbalances in jet streaks, deep convection, frontal activity, and other situations. The detailed understanding and quantitative description of the different processes of IGW generation and propagation is an open question. Here, we study IGWs in the context of a poleward Rossby wave breaking event—a frequently observed phenomenon over northern Europe
1. Introduction A basic building block for the understanding of atmospheric and oceanic dynamics is the Rossby wave ( Rossby 1939 ). The mathematical solutions for Rossby waves have been motivated through descriptive models that appeal to physical intuition. The arguments developed here have also been developed to supplement physical interpretation of the mathematical solutions and do not appear to have been previously explicitly described in the literature. Holton and Hakim (2012 , their Fig
1. Introduction A basic building block for the understanding of atmospheric and oceanic dynamics is the Rossby wave ( Rossby 1939 ). The mathematical solutions for Rossby waves have been motivated through descriptive models that appeal to physical intuition. The arguments developed here have also been developed to supplement physical interpretation of the mathematical solutions and do not appear to have been previously explicitly described in the literature. Holton and Hakim (2012 , their Fig
between the large-scale circulation and perturbations is complicated, as it includes many nonlinear processes. Based on idealized models, two possible mechanisms maintaining recirculation gyres have been proposed. One is potential vorticity (PV) homogenization ( Rhines and Young 1982 , hereinafter RY82 ), and the other is the rectification of Rossby wave motion ( Haidvogel and Rhines 1983 , hereinafter HR83 ; Malanotte-Rizzoli et al. 1995 ; Hogg 1988 ). RY82 assumed that mesoscale perturbations
between the large-scale circulation and perturbations is complicated, as it includes many nonlinear processes. Based on idealized models, two possible mechanisms maintaining recirculation gyres have been proposed. One is potential vorticity (PV) homogenization ( Rhines and Young 1982 , hereinafter RY82 ), and the other is the rectification of Rossby wave motion ( Haidvogel and Rhines 1983 , hereinafter HR83 ; Malanotte-Rizzoli et al. 1995 ; Hogg 1988 ). RY82 assumed that mesoscale perturbations
1. Introduction Planetary or Rossby waves are long-period oscillations in the oceans and atmosphere, whose restoring mechanism is provided by the variation of the Coriolis parameter with latitude. In the oceans the anisotropy of energy transmission of these waves is responsible for a major feature of the general circulation, that is, the concentration of small-scale energy in the western portion of oceanic gyres (e.g., Pedlosky 1987 ). Rossby waves also constitute the prevalent mechanism by
1. Introduction Planetary or Rossby waves are long-period oscillations in the oceans and atmosphere, whose restoring mechanism is provided by the variation of the Coriolis parameter with latitude. In the oceans the anisotropy of energy transmission of these waves is responsible for a major feature of the general circulation, that is, the concentration of small-scale energy in the western portion of oceanic gyres (e.g., Pedlosky 1987 ). Rossby waves also constitute the prevalent mechanism by
. Chang et al. (1996) found northwestward-propagating waves of 8–9-day period that also originated near the equator. During periods that such disturbances had large variance, tropical cyclones were much more likely to form. Takayabu and Nitta (1993) identified mixed Rossby–gravity (MRG) waves in the central Pacific that turned away from the equator near 150°E and appeared to transition to “TD-type” disturbances (i.e., Rossby-type waves, also known as easterly waves). They showed one example of a
. Chang et al. (1996) found northwestward-propagating waves of 8–9-day period that also originated near the equator. During periods that such disturbances had large variance, tropical cyclones were much more likely to form. Takayabu and Nitta (1993) identified mixed Rossby–gravity (MRG) waves in the central Pacific that turned away from the equator near 150°E and appeared to transition to “TD-type” disturbances (i.e., Rossby-type waves, also known as easterly waves). They showed one example of a
zonal mean under the quasigeostrophic (QG) approximation. Hoskins et al. (1983) derived the 3D wave activity flux based on the horizontal velocity correlation tensor. While successfully representing the interaction between the time-mean flow and waves, their wave activity flux is not parallel to the group velocity of Rossby waves. Trenberth (1986) derived the 3D wave activity flux by adding the zonal and meridional derivatives of the perturbation kinetic energy to the zonal and meridional
zonal mean under the quasigeostrophic (QG) approximation. Hoskins et al. (1983) derived the 3D wave activity flux based on the horizontal velocity correlation tensor. While successfully representing the interaction between the time-mean flow and waves, their wave activity flux is not parallel to the group velocity of Rossby waves. Trenberth (1986) derived the 3D wave activity flux by adding the zonal and meridional derivatives of the perturbation kinetic energy to the zonal and meridional
