The Response of Buoyant Coastal Plumes to Upwelling-Favorable Winds

Steven Lentz Woods Hole Oceanographic Institution, Woods Hole, Massachusetts

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Abstract

To better understand the response of a buoyant coastal plume to wind-induced upwelling, a two-dimensional theory is developed that includes entrainment. The primary assumption is that competition between wind-driven vertical mixing and lateral buoyancy forcing in the region where the isopycnals slope upward to intersect the surface results in continual entrainment at the offshore edge of the plume. The theory provides estimates of the buoyant plume characteristics and offshore displacement as a function of time t, given the wind stress, the characteristics of the buoyant plume prior to the onset of the wind forcing, and a critical value for the bulk Richardson number (Ric). The theory predicts that, for t/ts, the plume density anomaly decreases as (1 + )−1, the thickness increases as (1 + )1/3, the width increases as (1 + )2/3, and the plume average entrainment rate decreases as (1 + )−2/3. Here ts = 2Ao/(RicUE) is the time for entrainment to double the cross-sectional area of the plume Ao at the onset of the wind forcing, where UE is the Ekman transport. The theory reproduces results from 20 numerical model runs by Fong and Geyer, including their estimates of the plume-average entrainment rate (correlations greater than 0.98 and regression coefficients approximately 1 for plume characteristics and 1.7 for the entrainment rate). The theory, modified to allow for time-variable wind stress, also reproduces the observed response of the buoyant coastal plume from Chesapeake Bay during an 11-day period of upwelling winds in August 1994.

Corresponding author address: Dr. Steve Lentz, MS21, Woods Hole Oceanographic Institution, Woods Hole, MA 02543. Email: slentz@whoi.edu

Abstract

To better understand the response of a buoyant coastal plume to wind-induced upwelling, a two-dimensional theory is developed that includes entrainment. The primary assumption is that competition between wind-driven vertical mixing and lateral buoyancy forcing in the region where the isopycnals slope upward to intersect the surface results in continual entrainment at the offshore edge of the plume. The theory provides estimates of the buoyant plume characteristics and offshore displacement as a function of time t, given the wind stress, the characteristics of the buoyant plume prior to the onset of the wind forcing, and a critical value for the bulk Richardson number (Ric). The theory predicts that, for t/ts, the plume density anomaly decreases as (1 + )−1, the thickness increases as (1 + )1/3, the width increases as (1 + )2/3, and the plume average entrainment rate decreases as (1 + )−2/3. Here ts = 2Ao/(RicUE) is the time for entrainment to double the cross-sectional area of the plume Ao at the onset of the wind forcing, where UE is the Ekman transport. The theory reproduces results from 20 numerical model runs by Fong and Geyer, including their estimates of the plume-average entrainment rate (correlations greater than 0.98 and regression coefficients approximately 1 for plume characteristics and 1.7 for the entrainment rate). The theory, modified to allow for time-variable wind stress, also reproduces the observed response of the buoyant coastal plume from Chesapeake Bay during an 11-day period of upwelling winds in August 1994.

Corresponding author address: Dr. Steve Lentz, MS21, Woods Hole Oceanographic Institution, Woods Hole, MA 02543. Email: slentz@whoi.edu

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