In thermal power cycles including concentrating solar thermal (CST) plants, natural draft cooling towers (NDCTs) are widely used heat-dumping facilities. One inherent drawback of NDCTs is that their cooling performance can be compromised by changes in ambient conditions, particularly temperature, which inevitably reduces the net power output of the cycles. Current methods resolving this issue are limited in a few options including inlet air pre-cooling, exit air heating, and fan assistance, each with considerable operational or initial cost. To more economically reduce energy efficiency losses of the power cycles due to inefficient cooling, this paper proposes a new concept of swirling plume method for both dry- and wet-type NDCTs. The method is to rotate the plume strongly like a tornado in the tower upper part and above the towers to increase the overall tower updraft capacity (pressure). The swirling plume is induced by high-speed air jets distributed at certain locations using a much smaller flow rate. A numerical investigation on a 20 m-tall dry-type NDCT model has been conducted verifying that this concept increases the airflow and the water temperature drop of the heat exchanger by at least 53.6% and 3.57 degrees C (39.2%), respectively, under 35 degrees C ambient temperature. This cooling performance enhancement enables a half megawatt-scale sCO(2)-based CST power cycle to recover its net power output, by 4.98%, to the level almost same as that at 30 degrees C ambient temperature. The air jet to create such a swirling plume consumes only 1/7 of the recovered power roughly. Compared with a traditional fan-forced cooler working under exactly the same condition, this concept requires significantly smaller energy in long-term operations as it would run only during temperature extremes. A simplified analytical modelling has found that the cooling tower performance is improved due to that the swirling plume creates an equivalent extra draft height on top of the tower which is attributed to two different vortical effects. The overall angular momentum of the swirl is a critical factor in these effects.