Figure 1.
A three-dimensional depiction of the experimental set-up.
Temperature fluctuations potentially causing convective currents in the test aquarium were suppressed by placing it into an outer aquarium of constant temperature, which is not shown here.
Figure 2.
An illustration of different metrics in characterizing swimming trajectories.
The mean displacement is the mean of distances traveled between two subsequent observations (black dots). The net displacement
is the straight-line distance between the initial and final locations, and the gross displacement is the sum of distances
. The mean turning angle is the trigonometric mean of angles
formed by changes in direction between observations [32].
Figure 3.
An illustration of swimming patterns of Daphnia.
The swimming patterns can be distinguished based on NGDR values specified.
Figure 4.
A 3D schematic diagram that illustrates the method of estimating the volume of dissipation rates.
The gridded windows indicate the field of view at different time stamps across the laser light sheet while smaller grids represents spatial window of the interrogation area (). A Daphnia swims in the
-direction, and three different grid colors indicate different levels of dissipation rates induced by the swimming Daphnia. The
-coordinate was determined as the product of Daphnia swimming velocity (
) and time taken to passed through field of view (
) while the trail cross-sectional area was computed by the total area of patches of
above our threshold for each PIV image. The three-dimensional distribution of energy dissipation rates in the trails was reconstructed by the product of
-coordinate and the trail cross-sectional areas. Blue dashed lines represent the boundary of the trail.
Table 1.
Summary of analyzed data and results.
Figure 5.
Observed trail dimensions vs. Reynolds number.
(A) Observed trail length (squares) and trail diameter (triangles) vs. Reynolds number. Distinct colors of square markers indicate different age groups (cyan-5 days, red-20 days, and black-35 days). Daphnia length (green lines) and the length of corresponding sphere wakes (Equation 4) are shown for mean Reynolds number of the three age groups. (B) Observed trail volume vs. Reynolds number. Symbol color indicates age group, filled markers represent wakes and open markers jets. Distinct swimming patterns are indicated by square (cruising), triangle (hopping and sinking), and circle (looping). The line represents a proportionality to the .
Figure 6.
Trail-averaged viscous dissipation rates and total dissipated power within the trail vs. Reynolds number.
(A) Trail-averaged viscous dissipation rates (total dissipated power/trail volume) vs. Reynolds number. Distinct colors indicate age groups (cyan-5 days, red-20 days, and black-35 days), filled markers represent wakes and open markers jets. Different swimming patterns are indicated by square (cruising), triangle (hopping and sinking), and circle (looping). (B) Total dissipated power within the trail vs. Reynolds number. Colors indicate age groups. The blue line shows dissipated power estimated according to Huntley and Zhou [9] (Equation 3), and the orange line the modified approach for a sphere (Equation 4).
Figure 7.
Trail length estimated from observed dissipation rates (equation 6) vs. observed wake length
.
Distinct colors of square markers stand for age groups (cyan-5 days, red-20 days, and black-35 days) and the line represents a 1∶1 relationship.
Figure 8.
Comparison of Daphnia with other zooplankton.
(A) Comparison of swimming speed. Regions for and
are denoted by light and dark pink colors. Lines show the empirical relationships for cruising and escape speeds for aquatic organisms as a function of organism size obtained by Huntely and Zhou [9]. Labeled boxes in color indicate the range of organism size and swimming speed for three zooplankton species considered in the analysis of Huntley and Zhou, as well as the present results for Daphnia (figure adopted from [10] with modifications). (B) Comparison of total dissipated power of Daphnia with empirical estimates for other zooplankton [9]. Labeled colored boxes indicate the range of organism size and dissipated power. Shaded area indicates a potential domain for dissipated power (
) of kinetic energy produced by swimming zooplankton of different size.