158
6 Rotational Effects
firs analytically described by Eady (1949). The source of this instability is a depthvariation of horizontal geostrophic f ow in a stratifie ocean associated with tilted
density interfaces. Disturbances in such a baroclinic geostrophic f ow leads to watercolumn stretching and squeezing at different locations of the disturbance. This generates self-enforcing patterns of relative vorticity and disturbances grow in time.
It can be shown that perturbations of a wavelength of about fourfold the internal
deformation radius have the greatest initial growth rate. Cushman-Roisin (1994)
presents the theory describing this instability process.
The baroclinic instability mechanism is the origin of the large mid-latitude
cyclones and anticyclones that make our weather so variable and creates eddies in
the ocean. Geostrophic frontal fl ws, such as those inherent with western boundary
currents, exhibit the steepest slopes of density interfaces and are therefore subtle to
the baroclinic instability mechanism. In the real situation, frontal fl ws can become
unstable to both barotropic instability owing to lateral current shear and baroclinic
instability owing to vertical current shear. It is often difficul to tell which mechanism was the major cause of instability development.
Is has been long thought that fl ws in the deep ocean are generally weak. This,
however, is not always the case. Frontal instabilities of western boundary currents,
for instance, trigger mesoscale eddies that produce swift f ow in the abyssal ocean,
referred to as benthic storms, f rst observed by Rowe and Menzies (1968). Benthic
storms can attain speeds >50 cm/s on timescales of 20 days and are capable of
eroding sediment from the abyssal seafloo . Hence, the hypothesis that the deep
oceans are quiescent, as suggested by the baroclinic compensation process, is not
valid in these frontal regions.
The theory behind the baroclinic instability process is complex and therefore not
included in this book. Nevertheless, we can employ the multi-layer model, developed in previous exercises, to investigate this process.
6.15 Exercise 21: Frontal Instability
6.15.1 Aim
The aim of this exercise is to explore frontal instabilities of quasi-geostrophic f ows
in an ocean of two superimposed layers of different densities.
6.15.2 Task Description
The model domain has a length of 200 km, a width of 100 km, and a depth of 500 m
with closed boundaries in the north and in the south. Cyclic boundary conditions
are used at the western and eastern boundaries of the model domain. Lateral grid
spacings are set to Δx = Δy = 2 km. The ocean is approximated by a two-layer
system. Density of the top layer is chosen at ρ 1 = 1027.25 kg m
−3
. Density of the
bottom layer is set to ρ 2 = 1028 kg m
−3
.
6 Rotational Effects
firs analytically described by Eady (1949). The source of this instability is a depthvariation of horizontal geostrophic f ow in a stratifie ocean associated with tilted
density interfaces. Disturbances in such a baroclinic geostrophic f ow leads to watercolumn stretching and squeezing at different locations of the disturbance. This generates self-enforcing patterns of relative vorticity and disturbances grow in time.
It can be shown that perturbations of a wavelength of about fourfold the internal
deformation radius have the greatest initial growth rate. Cushman-Roisin (1994)
presents the theory describing this instability process.
The baroclinic instability mechanism is the origin of the large mid-latitude
cyclones and anticyclones that make our weather so variable and creates eddies in
the ocean. Geostrophic frontal fl ws, such as those inherent with western boundary
currents, exhibit the steepest slopes of density interfaces and are therefore subtle to
the baroclinic instability mechanism. In the real situation, frontal fl ws can become
unstable to both barotropic instability owing to lateral current shear and baroclinic
instability owing to vertical current shear. It is often difficul to tell which mechanism was the major cause of instability development.
Is has been long thought that fl ws in the deep ocean are generally weak. This,
however, is not always the case. Frontal instabilities of western boundary currents,
for instance, trigger mesoscale eddies that produce swift f ow in the abyssal ocean,
referred to as benthic storms, f rst observed by Rowe and Menzies (1968). Benthic
storms can attain speeds >50 cm/s on timescales of 20 days and are capable of
eroding sediment from the abyssal seafloo . Hence, the hypothesis that the deep
oceans are quiescent, as suggested by the baroclinic compensation process, is not
valid in these frontal regions.
The theory behind the baroclinic instability process is complex and therefore not
included in this book. Nevertheless, we can employ the multi-layer model, developed in previous exercises, to investigate this process.
6.15 Exercise 21: Frontal Instability
6.15.1 Aim
The aim of this exercise is to explore frontal instabilities of quasi-geostrophic f ows
in an ocean of two superimposed layers of different densities.
6.15.2 Task Description
The model domain has a length of 200 km, a width of 100 km, and a depth of 500 m
with closed boundaries in the north and in the south. Cyclic boundary conditions
are used at the western and eastern boundaries of the model domain. Lateral grid
spacings are set to Δx = Δy = 2 km. The ocean is approximated by a two-layer
system. Density of the top layer is chosen at ρ 1 = 1027.25 kg m
−3
. Density of the
bottom layer is set to ρ 2 = 1028 kg m
−3
.