Auxiliary material for Paper 2010GL042715

Vertical Heat Flux and Lateral Mass Transport in Nonlinear Internal Waves

Emily L. Shroyer, James N. Moum, and Jonathan D. Nash
College of Oceanic and Atmospheric Sciences, Oregon State University


Shroyer, E. L., J. N. Moum, J. D. Nash (2010), Vertical heat flux and lateral 
mass transport in  nonlinear internal waves, Geophys. Res. Lett., 37, L08601, 
doi:10.1029/2010GL042715.


Introduction

The auxiliary material details the merit of the w_c^2 criteria used in this 
study to identify nonlinear internal waves in the fixed adcp record. 




1. 2010gl042715-fs01.tif

Shown is one day's time series of temperature, onshore velocity, and vertical 
velocity at mooring SW29. Times selected using w_c^2 = 4e-4 m^2 s^-2 are 
marked in black at top; less/more restrictive measures (2e-4 m^2 s^-2/8e-4 
m^2 s^-2) are shown in grey below/above the black markers. Note w_c^2=4e-4 
m^2 s^-2 is conservative, as it misses waves that are apparent by eye (e.g., 
1830 UTC 4 August 2006). The threshold w_c^2=4e-4 m^2 s^-2 detects NLIWs at 
the moorings consistent with those waves observed from the ship that were 
used to compute the mean profile of heat flux in the waves (J_q^w). 
Using the less restrictive limit, waves weaker than the median observed from 
the ship would be included in the calculation of P^w, providing a less 
conservative estimate of the NLIW contribution to the total heat 
flux. The more restrictive criteria was not used because many waves that 
were energetically weaker were included in the average profile of J_q^w. The 
w_c^2 threshold selects for times of steep, nonlinear waves, which are 
associated with the majority of the dissipative loss, and correspondingly the 
largest turbulent diffusivities and heat fluxes. Since we are attempting to 
quantify a process driven by vertical mixing, this approach seems reasonable. 
In contrast, if we were attempting to estimate the energy content in the 
waves this type of method would not be useful, as the NLIWs and the internal 
tide are intricately linked to one another. Here, we may underestimate the 
NLIW contribution to the total heat flux, since we establish w_c^2=4e-4 m^2 
s^-2 from the median of the ship observations. However, the energy source of 
the NLIWs is itself the tide, and as such this work quantifies only a small 
portion of what is ultimately tidally-driven mixing.