Science@Berkeley Lab nameplate Berkeley Lab logo
August 5, 2005

Lubricating the Wind
A New Mathematical Model Links Hurricane Winds to Ocean Spray

Everyone knows that if you lubricate a wheel, it will spin faster. Apparently the same holds true for the winds of a hurricane. Mathematicians with Lawrence Berkeley National Laboratory and the University of California at Berkeley have used the equations that describe turbulence in fluids to link high-speed hurricane winds to ocean spray.

Hurricane Frances, which pounded the east coast of Florida last summer, at one point stretched nearly 400 miles across its storm front. A new mathematical model links the hundred-mile-an-hour winds of hurricanes, which can gust to 200 miles per hour, to the lubricating effects of ocean spray.

According to their flow model, droplets of water, sucked up into the vortex of a building storm, act as a lubricant to substantially accelerate wind speeds. Without the lubrication of the spray, wind speeds would not progress beyond those of a tropical depression.

"We have demonstrated that the mechanism of turbulence-suppression by water drops in the ocean spray can substantially accelerate the flow of air, so that the speeds of wind characteristic of the strongest hurricanes can be reached," said Alexandre Chorin, a principal investigator with the Mathematics Department of Berkeley Lab's Computational Research Division and an award-winning professor of mathematics at UC Berkeley.

Grigory Barenblatt, who is also a researcher with Berkeley Lab holding a joint faculty appointment with UC Berkeley, Chorin, and Valeriy Prostokishin of the Shirshov Institute of Oceanology in Moscow, formerly a visiting Berkeley Lab researcher, describe their work in the June 25, 2005 edition of the Proceedings of the National Academy of Sciences (PNAS).

By any name — hurricane, typhoon, or tropical cyclone — the awesome power of these oceanic storms is unmistakable. Massive columns of swirling clouds, torrential rains, giant waves, and violent winds that can reach sustained speeds in excess of 150 miles per hour are the trademarks of these true forces of nature, which can flatten coastal cities and flood inland areas far removed from the sea.

The formation of these storms is well understood. It starts with a region of intense low pressure over warm ocean pools. Water evaporating off the ocean's surface releases heat as it condenses to form clouds, and this heat causes the low-pressure area to grow. Winds generated by the expanding low-pressure area begin to spiral inward, forming the cloud-free eye at the center of the storm.

Turbulence, the seemingly random fluctuations that disrupt the orderly flow of a gas or liquid, should slow the acceleration of a hurricane's winds. However, the flow model developed by Barenblatt, Chorin, and Prostokishin shows that when ocean spray, swept up into the storm off the tops of cresting waves, rains back to the sea as droplets of water about 20 microns in diameter, it counteracts the effects of turbulence, much like a lubricant counteracts the effects of friction. According to Chorin and his colleagues, the friction between the air and water is reduced by a factor of a thousand, and the winds are free to accelerate to speeds approximately eight times faster than they could in the presence of turbulence.

" We concentrated on a single effect, flow acceleration in an ocean spray that carries large water droplets, and left aside the influence of the Coriolis force and the cooling effects due to the evaporation of the droplets," Chorin said. "However, we demonstrated that flow acceleration by droplets is very significant by itself, and the effects of air cooling by evaporation and of the Coriolis force can be easily included in numerical models."

Barenblatt, Chorin, and Prostokishin developed their flow model from the "sandwich model" of tropical cyclones proposed by Sir James Lighthill, one of the greatest applied mathematicians of our times. In Lighthill's model, ocean spray forms a cloud of droplets that can be viewed as a third fluid, sandwiched between the fluid layers of sea and air.

Mathematicians have shown that large water droplets thrown into the air by cresting waves in storm-tossed seas suppress the friction-enhancing effects of turbulence and allow wind speeds to accelerate dramatically.

At a social gathering, Lighthill suggested to Barenblatt that the droplets could lubricate the interactions between sea and air. Lighthill himself focused on the thermodynamic issues involved, the variation of flow energy due to the evaporation of the droplets and the subsequent cooling of the air. Lighthill's death from a swimming accident in 1998 at the age of 74 cut short his efforts, but his friends Chorin and Barenblatt took up the challenge.

Chorin and Barenblatt are both experts in the development of computational methods for studying the flow of fluids and solving problems involving turbulence, considered to be one of most difficult in all of applied mathematics. The authors dedicated their PNAS paper to Lighthill.

In the paper, Barenblatt, Chorin, and Prostokishin noted that in ancient times sailors carried oil on their vessels to pour onto the waves to calm a rising storm. They speculate that the spread of the oil could have prevented the formation of turbulence-damping ocean spray droplets.

"Possibly hurricanes can be similarly prevented or damped by having airplanes deliver fast decaying harmless surfactants to the right places on the sea surface," the authors write.

Additional information