Tropical cyclone momentum and energy fluxes

Abstract

Many modeling studies of tropical cyclones use the bulk aerodynamic formulae to determine angular momentum and enthalpy fluxes at the sea surface. These results show that the intensification of a hurricane is very sensitive to the values of the coefficients defined in these formulae (Emanuel, 1995). Using these formulae allows the model to make bulk estimates of these fluxes as a function of wind speed, without having to consider the full complexity of the physics of the air-sea interface. Generally, a complete treatment of fluxes would require modeling a number of small-scale physical processes, e.g. wave field response to the duration and fetch of the wind, sea spray processes, and convective stability of the boundary layer. The coefficients to these equations, Cd and Ck, have been empirically determined in previous studies, either by direct measurements on platforms and ships (Large and Pond, 1981), or by budget analyses from airborne data. However, these studies do not provide results for the high winds speeds encountered in strong hurricanes. Previous work has suggested that the coefficients do not remain constant, but rather are a function of wind speed. Producing values for these coefficients at high wind speeds will improve the accuracy of the numerical models. Recent advances in dropsonde technology (Hock and Franklin, 1999) provide improved range and accuracy from earlier methods, with reliable measurements of wind and thermodynamic variables down to within 10m of the surface. Three cases of strong hurricanes have been selected for this study, allowing analysis of these coefficients for conditions with up to 65 ms- 1 surface winds. The values of the drag coefficient, Cd, are demonstrated to reach a maximum value at about hurricane force, then maintain that value with higher wind speeds. The values of Ck, the heat flux coefficient, do not show variation with wind speed. These coefficients are calculated both at the standard 10m, so that they may be compared with existing literature, and at the top of the boundary layer, so that models which do not explicitly resolve the physics of the boundary layer may nonetheless make use of this data. The budget calculations in this study have shown that the 10m drag coefficient has a value of 0.0026 to 0.0030 for wind speeds in the 40-60 ms- 1 range. Eddy fluxes of total energy and entropy are also shown to be significant. With this effect added, budget calculations have shown that the 10m enthalpy transfer coefficient ranges from 0.0029 to 0.0036 under these conditions for Floyd and Georges. Thus, the ratio of Ck/Cd is slightly larger than 1.0. At the gradient wind level, Cd is 0.0019 ± 0.0010 and Ck is approximately 0.0018.