![130420-Thumbnail Image.png](https://d1rbsgppyrdqq4.cloudfront.net/s3fs-public/styles/width_400/public/2021-04/130420-Thumbnail%20Image.png?versionId=URRD4WHrtGn80h9jWNIBb_xUx.RNJFyk&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIASBVQ3ZQ42ZLA5CUJ/20240616/us-west-2/s3/aws4_request&X-Amz-Date=20240616T013706Z&X-Amz-SignedHeaders=host&X-Amz-Expires=120&X-Amz-Signature=df6b814986d272aa6c935df0ed47568bf36f3a77b52f865043c7ad9b73b63b01&itok=RSw47axs)
Eigenvalues of the 3D critical point equation (∇u)ν = λν are normally computed numerically. In the letter, we present analytic solutions for 3D swirling strength in both compressible and incompressible flows. The solutions expose functional dependencies that cannot be seen in numerical solutions. To illustrate, we study the difference between using fluctuating and total velocity gradient tensors for vortex identification. Results show that mean shear influences vortex detection and that distortion can occur, depending on the strength of mean shear relative to the vorticity at the vortex center.
![130422-Thumbnail Image.png](https://d1rbsgppyrdqq4.cloudfront.net/s3fs-public/styles/width_400/public/2021-04/130422-Thumbnail%20Image.png?versionId=qog_dNSdxL9j4N_oM4EMHuowyC1yDxLT&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIASBVQ3ZQ42ZLA5CUJ/20240616/us-west-2/s3/aws4_request&X-Amz-Date=20240616T025211Z&X-Amz-SignedHeaders=host&X-Amz-Expires=120&X-Amz-Signature=94a1d474383695ce2b5f783c83033a458b969b717e732b9b064f7d78c9107dd1&itok=9lNHf9c0)
![130427-Thumbnail Image.png](https://d1rbsgppyrdqq4.cloudfront.net/s3fs-public/styles/width_400/public/2021-04/130427-Thumbnail%20Image.png?versionId=NOLKPedCEFrJNuW3R6NoFYpcGwrQ5yx7&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIASBVQ3ZQ42ZLA5CUJ/20240615/us-west-2/s3/aws4_request&X-Amz-Date=20240615T125839Z&X-Amz-SignedHeaders=host&X-Amz-Expires=120&X-Amz-Signature=cdcb06c80d32887c9598ffc787ecc5010e60e8e709e63935595917e78482cac7&itok=_mraHxQF)
![130428-Thumbnail Image.png](https://d1rbsgppyrdqq4.cloudfront.net/s3fs-public/styles/width_400/public/2021-04/130428-Thumbnail%20Image.png?versionId=d05A8iZoLPY4OIT60zZTLdT1MkqYf2MU&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIASBVQ3ZQ42ZLA5CUJ/20240616/us-west-2/s3/aws4_request&X-Amz-Date=20240616T025211Z&X-Amz-SignedHeaders=host&X-Amz-Expires=120&X-Amz-Signature=39a7cdd64e4a3938b9fe0625ac1a38c1ee8d421c6081f3e4d1e27646fd399c55&itok=SNjNeGwR)
![130433-Thumbnail Image.png](https://d1rbsgppyrdqq4.cloudfront.net/s3fs-public/styles/width_400/public/2021-04/130433-Thumbnail%20Image.png?versionId=5FWlNNKutwsGP2wwp2o9_1HyGN7huODW&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIASBVQ3ZQ42ZLA5CUJ/20240615/us-west-2/s3/aws4_request&X-Amz-Date=20240615T074139Z&X-Amz-SignedHeaders=host&X-Amz-Expires=120&X-Amz-Signature=95364beb3ccfc60893bcd883c452890ec4b38120d7e35ae312cc8b2bd2f10299&itok=VLnJC-x4)
![131287-Thumbnail Image.png](https://d1rbsgppyrdqq4.cloudfront.net/s3fs-public/styles/width_400/public/2021-07/131287-Thumbnail%20Image.png?versionId=T6jJwczZvIGRrtdooFJZ.tdRkJS3TIz0&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIASBVQ3ZQ42ZLA5CUJ/20240615/us-west-2/s3/aws4_request&X-Amz-Date=20240615T231202Z&X-Amz-SignedHeaders=host&X-Amz-Expires=120&X-Amz-Signature=772284f7a02a88b8ee80f82dc7798b41d2d16c406047c5bf9102786df42f5a75&itok=LTN3WMp9)
![132294-Thumbnail Image.png](https://d1rbsgppyrdqq4.cloudfront.net/s3fs-public/styles/width_400/public/2021-07/132294-Thumbnail%20Image.png?versionId=R9WEQArUxfugsXj8W3raohvWrq90rEyN&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIASBVQ3ZQ42ZLA5CUJ/20240615/us-west-2/s3/aws4_request&X-Amz-Date=20240615T161821Z&X-Amz-SignedHeaders=host&X-Amz-Expires=120&X-Amz-Signature=a176afe680f8644379516540efb460afaf977f10eee7828b145db9eef5f6334d&itok=kcGmUUKT)
![131736-Thumbnail Image.png](https://d1rbsgppyrdqq4.cloudfront.net/s3fs-public/styles/width_400/public/2021-07/131736-Thumbnail%20Image.png?versionId=s_QyI5fJ.6rJncGdVovGAAkzXcOJkW.c&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIASBVQ3ZQ42ZLA5CUJ/20240615/us-west-2/s3/aws4_request&X-Amz-Date=20240615T163209Z&X-Amz-SignedHeaders=host&X-Amz-Expires=120&X-Amz-Signature=f706f172358f5f74fa8b2f6cf347434759b33505dd5ceb2352c580cd64a67590&itok=2rg56gud)
![131610-Thumbnail Image.png](https://d1rbsgppyrdqq4.cloudfront.net/s3fs-public/styles/width_400/public/2021-07/131610-Thumbnail%20Image.png?versionId=I7d3FFD9VuHqVV_o88k.Tltj1PbD70Wn&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIASBVQ3ZQ42ZLA5CUJ/20240615/us-west-2/s3/aws4_request&X-Amz-Date=20240615T163209Z&X-Amz-SignedHeaders=host&X-Amz-Expires=120&X-Amz-Signature=f24c6b93e0732ebacf51662a06b7f47eb84b20362cfb00db1b82931daf501a75&itok=vGEero8U)
The combined use of methamphetamine and opioids has been reported to be on the rise throughout the United States (U.S.). However, our knowledge of this phenomenon is largely based upon reported overdoses and overdose-related deaths, law enforcement seizures, and drug treatment records; data that are often slow, restricted, and only track a portion of the population participating in drug consumption activities. As an alternative, wastewater-based epidemiology (WBE) has the capability to track licit and illicit drug trends within an entire community, at a low cost and in near real-time, while providing anonymity to those contributing to the sewer shed. In this study, wastewater was collected from two Midwestern U.S. cities (2017-2019) and analyzed for the prevalence of methamphetamine and the opioids oxycodone, codeine, fentanyl, tramadol, hydrocodone, and hydromorphone. Monthly 24-hour time-weighted composite samples (n = 48) from each city were analyzed using isotope dilution liquid chromatography tandem mass spectrometry. Results showed that methamphetamine and total opioid consumption (milligram morphine equivalents) in City 1 were strongly correlated only in 2017 (Spearman rank order correlation coefficient, ρ = 0.78), the relationship driven by fentanyl, hydrocodone, and hydromorphone. For City 2, methamphetamine and total opioid consumption were strongly positively correlated during the entire study (ρ = 0.54), with the correlations driven by hydrocodone and hydromorphone. In both cities, hydrocodone and hydromorphone mass loads were highly correlated, suggesting a parent and metabolite relationship. WBE provides important insights into licit and illicit drug consumption patterns in near real-time as they evolve; important information for community stakeholders in municipalities across the U.S.
![132548-Thumbnail Image.png](https://d1rbsgppyrdqq4.cloudfront.net/s3fs-public/styles/width_400/public/2021-05/132548-Thumbnail%20Image.png?versionId=T8UHMMmN3s0NQTOZZxvy5ydgLWAQjIIW&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIASBVQ3ZQ42ZLA5CUJ/20240616/us-west-2/s3/aws4_request&X-Amz-Date=20240616T030232Z&X-Amz-SignedHeaders=host&X-Amz-Expires=120&X-Amz-Signature=96b700b438faf4909ec9eeacc562f916b27cd7a31f42d1ffe3f4177400a33826&itok=LYrilozt)
GitHub Repository: https://github.com/komal-agrawal/AD_GIS.git