/* FBG Whisker CFD page. Typography, hero, nav and section rhythm follow the
   Fluorescent Whisker project page (fluorescent-whisker.github.io). */
:root {
  --paper: #fff;
  --paper-2: #f7f7f7;
  --ink: #303030;
  --muted: #707070;
  --rule: #e5e5e5;
  --accent: #2d68b0;
  --scene: rgb(31, 54, 164); /* background of the STAR-CCM+ scalar scenes */
  --vort-pos: #ff4d3d;
  --vort-neg: #3d8bff;
  --max: 1040px;
  --read: 860px;
  --font: "Noto Sans", Arial, sans-serif;
  --serif: "Castoro", Georgia, serif;
}
* {
  box-sizing: border-box;
}
html {
  scroll-behavior: smooth;
  scroll-padding-top: 80px;
}
body {
  margin: 0;
  color: var(--ink);
  background: #fff;
  font: 17px/1.75 var(--font);
  -webkit-font-smoothing: antialiased;
}
a {
  color: inherit;
  text-decoration-color: #bbb;
  text-underline-offset: 4px;
}
a:hover {
  color: var(--accent);
}
a:focus-visible,
button:focus-visible,
summary:focus-visible {
  outline: 2px solid var(--accent);
  outline-offset: 5px;
}
img,
video {
  display: block;
  max-width: 100%;
  height: auto;
}
h1,
h2,
h3 {
  margin: 0;
  font-weight: 600;
  line-height: 1.25;
  letter-spacing: -0.035em;
}
h2 {
  font-size: 36px;
  margin-bottom: 14px;
}
h3 {
  font-size: 24px;
  margin: 36px 0 12px;
}
p {
  margin: 0 0 1em;
}
button {
  font: inherit;
}
sup {
  font-size: 0.65em;
}
figure {
  margin: 34px 0;
}
figcaption {
  font-size: 14px;
  line-height: 1.65;
  color: var(--muted);
  margin: 14px auto 0;
  text-align: center;
  max-width: 850px;
}

/* ---------- hero ---------- */
.hero {
  position: relative;
  isolation: isolate;
  overflow: hidden;
  background: #000;
  color: #fff;
  display: flex;
  flex-direction: column;
  align-items: center;
  padding-bottom: 36px;
}
.hero-inner {
  max-width: 1240px;
  text-align: center;
  padding: 56px 32px 0;
}
.eyebrow {
  margin: 0 0 10px;
  font-size: 13px;
  font-weight: 500;
  letter-spacing: 0.14em;
  text-transform: uppercase;
  color: #ffffff99;
}
.hero h1 {
  font-size: clamp(36px, 3.4vw, 50px);
  font-weight: 600;
  line-height: 1.15;
  letter-spacing: -0.035em;
  text-wrap: balance;
}
.hero h1 span {
  display: block;
}
.hero-media {
  position: relative;
  width: min(100%, 1040px);
  aspect-ratio: 2.3;
  overflow: hidden;
  margin-top: 18px;
}
.hero video,
.hero-poster {
  position: absolute;
  inset: 0;
  width: 100%;
  height: 100%;
  object-fit: cover;
  object-position: 60% 50%;
}
.hero-media:after {
  content: "";
  position: absolute;
  inset: 0;
  pointer-events: none;
  background:
    linear-gradient(90deg, #000, transparent 6%, transparent 94%, #000),
    linear-gradient(180deg, #000, transparent 14%, transparent 86%, #000);
}
.hero-foot {
  width: min(100%, 1040px);
  padding: 0 28px;
  display: flex;
  align-items: center;
  justify-content: space-between;
  gap: 20px;
  font-size: 12px;
  letter-spacing: 0.03em;
  color: #ffffffb3;
}
.hero-foot p {
  margin: 0;
}
/* The hero loop shows the fixed run, then the translating run; project.js
   marks the one on screen. */
.runs[data-on] > span {
  transition: color 0.3s;
}
.runs[data-on="fixed"] .run-translating,
.runs[data-on="translating"] .run-fixed {
  color: #ffffff59;
}
.runs[data-on="fixed"] .run-fixed,
.runs[data-on="translating"] .run-translating {
  color: #fff;
}
.key {
  display: inline-flex;
  flex-wrap: wrap;
  gap: 4px 14px;
  margin-left: 14px;
}
.key i {
  display: inline-block;
  width: 8px;
  height: 8px;
  border-radius: 50%;
  margin-right: 6px;
  vertical-align: 1px;
}
.key .pos {
  background: var(--vort-pos);
}
.key .neg {
  background: var(--vort-neg);
}
.hero-meta {
  max-width: 1100px;
  padding: 0 24px;
  text-align: center;
}
.authors {
  font-size: 17px;
  line-height: 1.9;
  margin: 22px auto 8px;
}
.affil {
  font-size: 15px;
  color: #ffffffd9;
  margin: 3px 0;
}
.motion-toggle {
  flex-shrink: 0;
  white-space: nowrap;
  color: inherit;
  background: transparent;
  border: 1px solid #ffffff55;
  border-radius: 20px;
  padding: 5px 12px;
  font-size: 12px;
  cursor: pointer;
}
.motion-toggle:hover {
  border-color: #fff;
  color: #fff;
}

/* ---------- sticky section nav ---------- */
.nav {
  position: sticky;
  top: 0;
  z-index: 20;
  background: #fffffff2;
  backdrop-filter: blur(10px);
  border-bottom: 1px solid var(--rule);
}
.nav ul {
  list-style: none;
  max-width: var(--max);
  padding: 0 20px;
  margin: 0 auto;
  display: flex;
  justify-content: center;
  gap: 26px;
  overflow-x: auto;
  scrollbar-width: none;
}
.nav a {
  display: block;
  padding: 18px 0 16px;
  border-bottom: 2px solid transparent;
  text-decoration: none;
  white-space: nowrap;
  font-size: 13px;
  color: #656565;
}
.nav a.active {
  color: #222;
  border-bottom-color: #777;
}
.nav a:hover {
  color: #111;
}

/* ---------- sections ---------- */
.wrap {
  max-width: var(--max);
  margin: auto;
}
.read {
  max-width: var(--read);
  margin: auto;
}
.section {
  padding: 78px 28px 80px;
}
.section + .section > .read:first-child:before {
  content: "";
  display: block;
  height: 1px;
  background: var(--rule);
  margin: -78px 0 70px;
}
.section-heading {
  text-align: center;
  margin-bottom: 28px;
}
.question {
  font: italic 24px/1.45 var(--serif);
  letter-spacing: -0.015em;
  color: #666;
  text-align: center;
  margin: 0 auto 28px;
}
.section .lede {
  font-size: 17px;
  color: var(--ink);
}
.statement {
  padding: 84px 28px 34px;
  text-align: center;
}
.statement h2 {
  font-size: clamp(29px, 3vw, 40px);
  line-height: 1.3;
  margin: 0 auto 25px;
  max-width: 920px;
}
.statement h2 em {
  font-family: var(--serif);
  font-weight: 400;
}
.statement > p {
  max-width: 850px;
  font-size: 21px;
  line-height: 1.65;
  margin: 0 auto;
  color: #555;
}

/* ---------- demos and run tabs ---------- */
.section.demo-intro {
  padding-top: 48px;
}
.demo {
  margin: 0 0 28px;
}
.demo video {
  width: 100%;
  aspect-ratio: 16 / 9;
  background: #fff;
  border: 1px solid var(--rule);
}
.demo-tools {
  text-align: center;
  margin: 10px 0 0;
}
.demo-tools .motion-toggle {
  color: #666;
  border-color: #ddd;
}
.demo-tools .motion-toggle:hover {
  color: #222;
  border-color: #aaa;
}
.tabs {
  display: flex;
  flex-wrap: wrap;
  justify-content: center;
  gap: 8px;
  margin: 0 0 22px;
}
.tabs [role="tab"] {
  border: 1px solid #d5d5d5;
  border-radius: 20px;
  background: #fff;
  color: #555;
  padding: 7px 16px;
  font-size: 13px;
  cursor: pointer;
}
.tabs [role="tab"]:hover {
  border-color: #999;
  color: #222;
}
.tabs [role="tab"][aria-selected="true"] {
  background: #222;
  border-color: #222;
  color: #fff;
}

/* ---------- collapsible evidence ---------- */
.evidence {
  border-top: 1px solid var(--rule);
  border-bottom: 1px solid var(--rule);
  margin: 32px auto 0;
}
.evidence summary {
  cursor: pointer;
  font-size: 15px;
  padding: 16px 0;
  list-style: none;
  display: flex;
  justify-content: space-between;
  gap: 20px;
  font-weight: 500;
}
.evidence summary:after {
  content: "+";
  color: #777;
}
.evidence[open] summary:after {
  content: "−";
}
.evidence summary::-webkit-details-marker {
  display: none;
}
.evidence > summary span {
  margin-left: auto;
  font-weight: 400;
  color: var(--muted);
  font-size: 13px;
}
.evidence figure {
  margin-top: 16px;
}
.evidence .read p {
  font-size: 15px;
  color: #555;
}

/* ---------- figures ---------- */
.zoom {
  display: block;
  cursor: zoom-in;
}
figure img {
  width: 100%;
}
figure.narrow {
  max-width: 800px;
  margin-left: auto;
  margin-right: auto;
}
.scene {
  background: var(--scene);
}
.grid {
  display: grid;
  gap: 14px;
  align-items: center;
}
.grid.spaced {
  margin-top: 14px;
}
.grid.cols-2 {
  grid-template-columns: repeat(2, minmax(0, 1fr));
}
.grid.cols-3 {
  grid-template-columns: repeat(3, minmax(0, 1fr));
}
.grid.cols-4 {
  grid-template-columns: repeat(4, minmax(0, 1fr));
}
/* column widths follow each image's aspect ratio so the row shares one height */
.grid.model {
  grid-template-columns: 1.31fr 1.68fr 1.41fr;
}
.grid.flow {
  grid-template-columns: 1.35fr 0.98fr;
  align-items: start;
}
.grid.sweep {
  grid-template-columns: 2fr 3fr;
}
.sweep-plot {
  max-width: 720px;
  margin: 14px auto 0;
}
.panel p {
  margin: 6px 0 0;
  font-size: 13px;
  color: var(--muted);
  text-align: center;
}
.cases {
  display: grid;
  grid-template-columns: repeat(4, minmax(0, 1fr));
  gap: 18px 14px;
}
.case {
  margin: 0;
}
.case img {
  aspect-ratio: 0.86;
  object-fit: contain;
}
.case figcaption {
  margin-top: 8px;
  font-size: 13px;
  line-height: 1.5;
  color: #555;
}
.case figcaption b {
  margin-right: 4px;
  color: #222;
}

/* ---------- tables and lists ---------- */
.table-wrap {
  overflow-x: auto;
  margin-top: 8px;
}
table {
  width: 100%;
  border-collapse: collapse;
  font-size: 14px;
  margin: 16px 0 10px;
}
caption {
  caption-side: top;
  text-align: left;
  font-size: 13px;
  font-weight: 500;
  color: #555;
  padding-bottom: 6px;
}
th,
td {
  text-align: left;
  padding: 11px 10px;
  border-bottom: 1px solid var(--rule);
}
th {
  font-weight: 500;
  color: #666;
}
td.num,
th.num {
  text-align: right;
  font-variant-numeric: tabular-nums;
  white-space: nowrap;
}
/* design-study summary, laid out like the summary table in Siyue's slides:
   framed grid, shaded two-row header, blue for better and red for worse */
.table-title {
  text-align: center;
  font-size: 15px;
  font-weight: 600;
  color: var(--ink);
  margin: 0;
}
table.summary {
  border: 2px solid #333;
  font-size: 13.5px;
}
.summary th,
.summary td {
  text-align: center;
  padding: 9px 10px;
  border: 1px solid #d6d6d6;
  font-variant-numeric: tabular-nums;
  white-space: nowrap;
}
.summary thead th {
  background: #f2f2f2;
  color: #333;
  font-weight: 600;
}
.summary thead tr:last-child th,
.summary thead th[rowspan],
.summary tr.ref td {
  border-bottom: 2px solid #333;
}
.summary td:nth-child(2) {
  white-space: normal;
  min-width: 11em;
}
td.better,
td.worse {
  font-weight: 700;
}
.better {
  color: #1a35e8;
}
.worse {
  color: #e3241b;
}
.table-note {
  font-size: 13px;
  line-height: 1.7;
  color: var(--muted);
  margin-bottom: 1.6em;
}
.findings {
  padding-left: 1.1em;
  margin: 0 0 1.2em;
}
.findings li {
  margin-bottom: 0.7em;
}

/* ---------- Strouhal number: display formula and the Taylor et al. chart ---------- */
.formula {
  margin: 26px 0 24px;
  text-align: center;
}
.eq {
  display: inline-flex;
  align-items: center;
  gap: 0.3em;
  margin: 0;
  font: italic 32px/1 var(--serif);
  color: var(--ink);
}
.eq-sign {
  font-style: normal;
}
.eq sub {
  font-size: 0.5em;
}
.frac {
  display: inline-flex;
  flex-direction: column;
  align-items: center;
}
.frac > span {
  padding: 0.08em 0.2em;
}
.frac > span:first-child {
  border-bottom: 1.5px solid currentColor;
}
.symbols {
  display: flex;
  flex-wrap: wrap;
  justify-content: center;
  gap: 4px 26px;
  margin: 14px 0 0;
  font-size: 14px;
  color: var(--muted);
}
.symbols > div {
  display: flex;
  align-items: baseline;
  gap: 8px;
}
.symbols dt {
  font: italic 16px var(--serif);
  color: var(--ink);
}
.symbols dd {
  margin: 0;
}
.st-chart {
  max-width: 720px;
  margin: 28px auto 34px;
}
.st-plot {
  --name: 8.6em;
  --row: 28px;
  --gap: 0px;
  position: relative;
  display: grid;
  grid-template-columns: var(--name) minmax(0, 1fr);
  align-items: center;
  row-gap: var(--gap);
  font-size: 13.5px;
  line-height: 1.3;
}
.st-band {
  position: absolute;
  top: 0;
  height: calc(9 * var(--row) + 8 * var(--gap));
  left: calc(var(--name) + (100% - var(--name)) * 0.2);
  width: calc((100% - var(--name)) * 0.2);
  background: #2d68b014;
  border-left: 1px dashed #2d68b099;
  border-right: 1px dashed #2d68b099;
}
.st-legend {
  position: absolute;
  top: 0;
  right: 0;
  display: flex;
  flex-direction: column;
  gap: 2px;
  font-size: 12.5px;
  color: var(--muted);
}
.st-legend > span {
  display: flex;
  align-items: center;
  gap: 7px;
}
.st-name {
  padding-right: 12px;
  text-align: right;
  white-space: nowrap;
  color: var(--ink);
}
.st-track {
  position: relative;
  height: var(--row);
  border-left: 1px solid #bbb;
}
.st-bar {
  position: absolute;
  top: 50%;
  left: calc(var(--lo) * 100%);
  width: calc((var(--hi) - var(--lo)) * 100%);
  border-top: 1.5px solid var(--ink);
}
.st-bar::before,
.st-bar::after {
  content: "";
  position: absolute;
  top: -5.5px;
  height: 9px;
  border-left: 1.5px solid var(--ink);
}
.st-bar::before {
  left: 0;
}
.st-bar::after {
  right: 0;
}
.mk {
  position: absolute;
  top: 50%;
  left: calc(var(--x) * 100%);
  width: 11px;
  height: 11px;
  box-sizing: border-box;
  transform: translate(-50%, -50%);
}
.st-legend .mk {
  position: static;
  transform: none;
}
.mk.bony {
  background: var(--ink);
}
.mk.shark {
  background: #8c8c8c;
}
.mk.dolphin {
  background: #fff;
  border: 1.5px solid var(--ink);
}
.st-axis {
  position: relative;
  height: 24px;
  border-top: 1px solid #bbb;
  font-size: 12px;
  color: var(--muted);
}
.st-axis span {
  position: absolute;
  top: 5px;
  left: calc(var(--x) * 100%);
  transform: translateX(-50%);
}
.st-axis span::before {
  content: "";
  position: absolute;
  top: -5px;
  left: 50%;
  height: 4px;
  border-left: 1px solid #bbb;
}
.st-unit {
  text-align: center;
  font: italic 14px var(--serif);
  color: var(--muted);
}

/* ---------- notes (Q&A) ---------- */
.qa details {
  border-top: 1px solid var(--rule);
  padding: 7px 0;
}
.qa details:last-child {
  border-bottom: 1px solid var(--rule);
}
.qa summary {
  cursor: pointer;
  display: flex;
  justify-content: space-between;
  gap: 24px;
  font-size: 16px;
  font-weight: 500;
  list-style: none;
  padding: 14px 0;
}
.qa summary:after {
  content: "+";
  color: #999;
}
.qa details[open] summary:after {
  content: "−";
}
.qa details p {
  font-size: 15px;
  line-height: 1.8;
  color: #555;
  padding: 0 20px 10px 0;
}
.qa summary::-webkit-details-marker {
  display: none;
}

/* ---------- lightbox ---------- */
.lightbox {
  position: fixed;
  inset: 0;
  z-index: 50;
  background: #070c16eb;
  display: none;
  align-items: center;
  justify-content: center;
  padding: 35px;
  cursor: zoom-out;
}
.lightbox.open {
  display: flex;
}
.lightbox img {
  max-width: 100%;
  max-height: 100%;
  width: auto;
  background: #fff;
}
.lightbox button {
  position: absolute;
  top: 10px;
  right: 15px;
  border: 0;
  color: white;
  background: none;
  font: 32px/1 var(--font);
  padding: 10px;
  cursor: pointer;
}

footer {
  padding: 36px 24px 44px;
  border-top: 1px solid var(--rule);
  font-size: 12px;
  text-align: center;
  color: #888;
  line-height: 1.9;
}

@media (max-width: 800px) {
  .hero {
    padding-bottom: 30px;
  }
  .hero-inner {
    padding: 52px 26px 0;
  }
  .hero h1 {
    font-size: 34px;
  }
  .hero-media {
    aspect-ratio: 16 / 9;
  }
  .hero-foot {
    padding: 8px 24px 0;
    font-size: 11px;
    align-items: flex-start;
  }
  .key {
    display: flex;
    margin: 4px 0 0;
  }
  .authors {
    font-size: 15px;
  }
  .affil {
    font-size: 13px;
  }
  .nav ul {
    justify-content: flex-start;
    gap: 22px;
  }
  .section {
    padding: 60px 22px;
  }
  .section + .section > .read:first-child:before {
    margin: -60px 0 52px;
  }
  h2 {
    font-size: 30px;
  }
  .question {
    font-size: 22px;
  }
  .statement {
    padding: 58px 24px 16px;
  }
  .statement > p {
    font-size: 18px;
  }
  .evidence > summary span {
    display: none;
  }
  .grid.cols-4,
  .cases {
    grid-template-columns: repeat(2, minmax(0, 1fr));
  }
  .grid.sweep {
    grid-template-columns: 1fr;
  }
  .eq {
    font-size: 28px;
  }
  .st-plot {
    --name: 7.6em;
    font-size: 12.5px;
  }
}
@media (max-width: 440px) {
  body {
    font-size: 16px;
  }
  .hero-inner {
    padding: 48px 22px 0;
  }
  .hero h1 {
    font-size: 30px;
  }
  .grid.cols-2,
  .grid.cols-3 {
    grid-template-columns: 1fr;
  }
  .tabs [role="tab"] {
    padding: 6px 12px;
    font-size: 12px;
  }
  table {
    font-size: 13px;
  }
  th,
  td {
    padding: 9px 5px;
  }
  th.num {
    white-space: normal;
  }
  .lightbox {
    padding: 16px;
  }
}
@media (prefers-reduced-motion: reduce) {
  html {
    scroll-behavior: auto;
  }
}