ROSSBY WAVES IN THE OCEAN

IN THE OCEANROSSBY WAVES

SRIHARI S

Rossby waves are formed in rotating fluids. In earth, it’s found in both oceans and atmosphere. It owes its existence to the Coriolis force which is due to the rotation of the Earth. Atmospheric Rossby waves are easily observed in the atmosphere as they are large enough and exist as meanders of the mid-latitude jet Stream which are responsible for the Weather patterns. Ocean Rossby waves are quite different. Rossby waves are the large scale dynamic response of ocean to atmospheric forcing and buoyancy forcing at the eastern ocean boundaries. They are slow moving and have small amplitudes at the surface and have large wavelengths which make them difficult to be detected. They always move in the westward direction and travel across a large stretch of an ocean basin. Horizontal speeds vary across latitudes. They are faster at the equator and reduce speed exponentially with increasing latitudes. Vertical speeds are slower at the surface but are atleast 100 times more at the deeper parts of the thermocline. Rossby waves hold the key to the ocean circulation process. They are responsible in establishing the phenomena of Western Intensification of ocean gyres which is a fundamental feature of large-scale Ocean circulation. Western intensification is the reason why there are stronger Currents in the western parts of an ocean basin or the east coast of a landmass. Let’s understand western intensification in the Northern hemisphere. Higher latitudes experience stronger Coriolis force as they are closer to the poles. As a result, the eastward flowing current of an ocean gyre deflects to the equator quite early. Near the equator, the westward current faces less Coriolis force and hence the deflection doesn’t happen unless they have reached the western most side of the gyre or ocean basin. The currents at the eastern part of the ocean gyre are spread out over a wider area whereas the western boundaries are narrow. This results in a very fast flow at the western boundaries and a much slower flow at the eastern boundaries. It is analogous to the continuity equation in water which implies water moves at a faster rate when the area of cross section is more and vice versa for the same quantity of water. Here, the volume of water remains same but the boundary areas are very different at both the sides and hence the difference in speeds. Gulf Stream is a strong ocean current that brings warm water from the Gulf of Mexico into the Atlantic Ocean. It extends all the way up the eastern cost of the United States and Canada. The Sea Surface Height values, obtained from Satellite altimetry have confirmed the narrowing of channels along the western boundaries. The sea surface levels are higher along the US east coast and the ocean is deeper. This Gulf Stream greatly influences the climate of the US east coast. Spanish explorers in the 16th Century noticed the presence of a Strong current in the west Atlantic Ocean.

The Gulf Stream is extremely useful for seafarers, fishermen etc. The warm water brings a lot of fish for fishing vessels adding to the advantage. The high speed current helps in ship movement. Ships can use the current and move at their registered speed but with a lower power requirement. Some Ships say they save upto 10- 15% of fuel when sailing along the Gulf Stream. Small fishing vessels with low speeds can use the current efficiently and reduce CO2 emission. Study of currents is hence immensely useful.

Western Boundary Intensification

As already mentioned, Rossby waves arise due to the perpendicular component of the Coriolis force and buoyancy and atmospheric forcing in the eastern boundaries. They are heavily influenced by local winds, local temperature changes and most importantly perturbations caused due to local topography. There exists a standard theory for freely propagating, linear Rossby waves. It can be derived from linearization of the unforced equations for large-scale, low frequency motion about a state of rest which results in a wave equation for the vertical normal modes. The restoring force is the beta-effect of latitudinal variation of the Earth’s rotation vector. The curvature of the Earth’s surface along with the rotation is thus essential to the existence of Rossby Waves. The normal modes can be determined numerically by applying the appropriate Boundary and Bottom conditions. Infinite number of Rossby wave normal modes with decreasing phase speeds exist. The lowest order mode is the Barotropic mode which are too fast and can’t be detected properly. The next higher mode is the 1st Baroclinic mode. They are slow and their speed decreases with increasing latitude. Here, the variations in the surface height is mirrored as thermocline depth variations of opposite signs with about three orders magnitude of greater amplitude. A 5 cm variation in sea level will correspond to thermocline displacement of about 50m. Such large variations of upper ocean thermal structure have important implications about the role of the ocean in short-term climate variations. The higher order Baroclinic modes are much slower and do not contribute significantly in Ocean Circulation. Hence, for all analysis purposes, only the lowest order Baroclinic Rossby waves are analysed.

Observing Ocean Rossby Waves

Observation of Rossby waves have always have been tough due to various factors. The development of satellite altimetry in the 1970s helped in observing Rossby Waves. The initial altimeters couldn’t generate a clean observation pattern for Rossby waves because of various Geographical factors particularly tidal aliasing. The Topex/Poseidon altimeter in early 1990s could detect them. This altimeter took in account tidal aliasing and gave results with good accuracy. After collecting data for 3 years, the results were compared to the predicted results using the Rossby Wave theory. Wavelengths and phase speeds are much higher at the tropics near the equator as compared to even mid latitudes. The fall in speed is huge. Waves within 2 degree of the equator are distinctly different from the extratropical waves. The observations prove that they are west propagating but there are sudden changes in the energy levels which indicate local topography has a key role in affecting these waves. Also, the phase speeds increase by a large margin in the western basins. Data also shows that in equator, there are slow eastward propagating signals which are referred to as Kelvin Waves. In the equator region, the positive and negative signals are coherent. This coherence is lost outside of the tropics and the signals fluctuate a lot but they are still westward propagating. This indicates the effects of distortions of freely propagated waves by local wind forcing or bottom topography. Outside 10-degree S and 10-degree N, observed phase speeds are significantly higher than the predicted speeds. The discrepancies are too large and corrections have to be done in the theory. The effects of topography have to be studied in more detail to understand its effects as well as any other OceanAtmospheric phenomena causing these discrepancies. The data obtained from the Altimeter clearly indicates that the Rossby wave theory is inadequate to understand Global ocean circulation accurately.